methods of statistical analysis in research

Statistical Methods for Data Analysis: a Comprehensive Guide

In today’s data-driven world, understanding statistical methods for data analysis is like having a superpower.

Whether you’re a student, a professional, or just a curious mind, diving into the realm of data can unlock insights and decisions that propel success.

Statistical methods for data analysis are the tools and techniques used to collect, analyze, interpret, and present data in a meaningful way.

From businesses optimizing operations to researchers uncovering new discoveries, these methods are foundational to making informed decisions based on data.

In this blog post, we’ll embark on a journey through the fascinating world of statistical analysis, exploring its key concepts, methodologies, and applications.

Introduction to Statistical Methods

At its core, statistical methods are the backbone of data analysis, helping us make sense of numbers and patterns in the world around us.

Whether you’re looking at sales figures, medical research, or even your fitness tracker’s data, statistical methods are what turn raw data into useful insights.

But before we dive into complex formulas and tests, let’s start with the basics.

Data comes in two main types: qualitative and quantitative data .

Quantitative data is all about numbers and quantities (like your height or the number of steps you walked today), while qualitative data deals with categories and qualities (like your favorite color or the breed of your dog).

And when we talk about measuring these data points, we use different scales like nominal, ordinal , interval , and ratio.

These scales help us understand the nature of our data—whether we’re ranking it (ordinal), simply categorizing it (nominal), or measuring it with a true zero point (ratio).

In a nutshell, statistical methods start with understanding the type and scale of your data.

This foundational knowledge sets the stage for everything from summarizing your data to making complex predictions.

Descriptive Statistics: Simplifying Data

Imagine you’re at a party and you meet a bunch of new people.

When you go home, your roommate asks, “So, what were they like?” You could describe each person in detail, but instead, you give a summary: “Most were college students, around 20-25 years old, pretty fun crowd!”

That’s essentially what descriptive statistics does for data.

It summarizes and describes the main features of a collection of data in an easy-to-understand way. Let’s break this down further.

The Basics: Mean, Median, and Mode

• Mean is just a fancy term for the average. If you add up everyone’s age at the party and divide by the number of people, you’ve got your mean age.
• Median is the middle number in a sorted list. If you line up everyone from the youngest to the oldest and pick the person in the middle, their age is your median. This is super handy when someone’s age is way off the chart (like if your grandma crashed the party), as it doesn’t skew the data.
• Mode is the most common age at the party. If you notice a lot of people are 22, then 22 is your mode. It’s like the age that wins the popularity contest.

Spreading the News: Range, Variance, and Standard Deviation

• Range gives you an idea of how spread out the ages are. It’s the difference between the oldest and the youngest. A small range means everyone’s around the same age, while a big range means a wider variety.
• Variance is a bit more complex. It measures how much the ages differ from the average age. A higher variance means ages are more spread out.
• Standard Deviation is the square root of variance. It’s like variance but back on a scale that makes sense. It tells you, on average, how far each person’s age is from the mean age.

Picture Perfect: Graphical Representations

• Histograms are like bar charts showing how many people fall into different age groups. They give you a quick glance at how ages are distributed.
• Bar Charts are great for comparing different categories, like how many men vs. women were at the party.
• Box Plots (or box-and-whisker plots) show you the median, the range, and if there are any outliers (like grandma).
• Scatter Plots are used when you want to see if there’s a relationship between two things, like if bringing more snacks means people stay longer at the party.

Why Descriptive Statistics Matter?

Descriptive statistics are your first step in data analysis.

They help you understand your data at a glance and prepare you for deeper analysis.

Without them, you’re like someone trying to guess what a party was like without any context.

Whether you’re looking at survey responses, test scores, or party attendees, descriptive statistics give you the tools to summarize and describe your data in a way that’s easy to grasp.

This approach is crucial in educational settings, particularly for enhancing math learning outcomes. For those looking to deepen their understanding of math or seeking additional support, check out this link:  https://www.mathnasium.com/ math-tutors-near-me .

Remember, the goal of descriptive statistics is to simplify the complex.

Inferential Statistics: Beyond the Basics

Let’s keep the party analogy rolling, but this time, imagine you couldn’t attend the party yourself.

You’re curious if the party was as fun as everyone said it would be.

Instead of asking every single attendee, you decide to ask a few friends who went.

Based on their experiences, you try to infer what the entire party was like.

This is essentially what inferential statistics does with data.

It allows you to make predictions or draw conclusions about a larger group (the population) based on a smaller group (a sample). Let’s dive into how this works.

Probability

Inferential statistics is all about playing the odds.

When you make an inference, you’re saying, “Based on my sample, there’s a certain probability that my conclusion about the whole population is correct.”

It’s like betting on whether the party was fun, based on a few friends’ opinions.

The Central Limit Theorem (CLT)

The Central Limit Theorem is the superhero of statistics.

It tells us that if you take enough samples from a population, the sample means (averages) will form a normal distribution (a bell curve), no matter what the population distribution looks like.

This is crucial because it allows us to use sample data to make inferences about the population mean with a known level of uncertainty.

Confidence Intervals

Imagine you’re pretty sure the party was fun, but you want to know how fun.

A confidence interval gives you a range of values within which you believe the true mean fun level of the party lies.

It’s like saying, “I’m 95% confident the party’s fun rating was between 7 and 9 out of 10.”

Hypothesis Testing

This is where you get to be a bit of a detective. You start with a hypothesis (a guess) about the population.

For example, your null hypothesis might be “the party was average fun.” Then you use your sample data to test this hypothesis.

If the data strongly suggests otherwise, you might reject the null hypothesis and accept the alternative hypothesis, which could be “the party was super fun.”

The p-value tells you how likely it is that your data would have occurred by random chance if the null hypothesis were true.

A low p-value (typically less than 0.05) indicates that your findings are significant—that is, unlikely to have happened by chance.

It’s like saying, “The chance that all my friends are exaggerating about the party being fun is really low, so the party probably was fun.”

Why Inferential Statistics Matter?

Inferential statistics let us go beyond just describing our data.

They allow us to make educated guesses about a larger population based on a sample.

This is incredibly useful in almost every field—science, business, public health, and yes, even planning your next party.

By using probability, the Central Limit Theorem, confidence intervals, hypothesis testing, and p-values, we can make informed decisions without needing to ask every single person in the population.

It saves time, resources, and helps us understand the world more scientifically.

Remember, while inferential statistics gives us powerful tools for making predictions, those predictions come with a level of uncertainty.

Being a good data scientist means understanding and communicating that uncertainty clearly.

So next time you hear about a party you missed, use inferential statistics to figure out just how much FOMO (fear of missing out) you should really feel!

Common Statistical Tests: Choosing Your Data’s Best Friend

Alright, now that we’ve covered the basics of descriptive and inferential statistics, it’s time to talk about how we actually apply these concepts to make sense of data.

It’s like deciding on the best way to find out who was the life of the party.

You have several tools (tests) at your disposal, and choosing the right one depends on what you’re trying to find out and the type of data you have.

Let’s explore some of the most common statistical tests and when to use them.

T-Tests: Comparing Averages

Imagine you want to know if the average fun level was higher at this year’s party compared to last year’s.

A t-test helps you compare the means (averages) of two groups to see if they’re statistically different.

There are a couple of flavors:

• Independent t-test : Use this when comparing two different groups, like this year’s party vs. last year’s party.
• Paired t-test : Use this when comparing the same group at two different times or under two different conditions, like if you measured everyone’s fun level before and after the party.

ANOVA : When Three’s Not a Crowd.

But what if you had three or more parties to compare? That’s where ANOVA (Analysis of Variance) comes in handy.

It lets you compare the means across multiple groups at once to see if at least one of them is significantly different.

It’s like comparing the fun levels across several years’ parties to see if one year stood out.

Chi-Square Test: Categorically Speaking

Now, let’s say you’re interested in whether the type of music (pop, rock, electronic) affects party attendance.

Since you’re dealing with categories (types of music) and counts (number of attendees), you’ll use the Chi-Square test.

It’s great for seeing if there’s a relationship between two categorical variables.

Correlation and Regression: Finding Relationships

What if you suspect that the amount of snacks available at the party affects how long guests stay? To explore this, you’d use:

• Correlation analysis to see if there’s a relationship between two continuous variables (like snacks and party duration). It tells you how closely related two things are.
• Regression analysis goes a step further by not only showing if there’s a relationship but also how one variable predicts the other. It’s like saying, “For every extra bag of chips, guests stay an average of 10 minutes longer.”

Non-parametric Tests: When Assumptions Don’t Hold

All the tests mentioned above assume your data follows a normal distribution and meets other criteria.

But what if your data doesn’t play by these rules?

Enter non-parametric tests, like the Mann-Whitney U test (for comparing two groups when you can’t use a t-test) or the Kruskal-Wallis test (like ANOVA but for non-normal distributions).

Picking the Right Test

Choosing the right statistical test is crucial and depends on:

• The type of data you have (categorical vs. continuous).
• Whether you’re comparing groups or looking for relationships.
• The distribution of your data (normal vs. non-normal).

Why These Tests Matter?

Just like you’d pick the right tool for a job, selecting the appropriate statistical test helps you make valid and reliable conclusions about your data.

Whether you’re trying to prove a point, make a decision, or just understand the world a bit better, these tests are your gateway to insights.

By mastering these tests, you become a detective in the world of data, ready to uncover the truth behind the numbers!

Regression Analysis: Predicting the Future

Ever wondered if you could predict how much fun you’re going to have at a party based on the number of friends going, or how the amount of snacks available might affect the overall party vibe?

That’s where regression analysis comes into play, acting like a crystal ball for your data.

What is Regression Analysis?

Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest.

Think of it as detective work, where you’re trying to figure out if, how, and to what extent certain factors (like snacks and music volume) predict an outcome (like the fun level at a party).

The Two Main Characters: Independent and Dependent Variables

• Independent Variable(s): These are the predictors or factors that you suspect might influence the outcome. For example, the quantity of snacks.
• Dependent Variable: This is the outcome you’re interested in predicting. In our case, it could be the fun level of the party.

Linear Regression: The Straight Line Relationship

The most basic form of regression analysis is linear regression .

It predicts the outcome based on a linear relationship between the independent and dependent variables.

If you plot this on a graph, you’d ideally see a straight line where, as the amount of snacks increases, so does the fun level (hopefully!).

• Simple Linear Regression involves just one independent variable. It’s like saying, “Let’s see if just the number of snacks can predict the fun level.”
• Multiple Linear Regression takes it up a notch by including more than one independent variable. Now, you’re looking at whether the quantity of snacks, type of music, and number of guests together can predict the fun level.

Logistic Regression: When Outcomes are Either/Or

Not all predictions are about numbers.

Sometimes, you just want to know if something will happen or not—will the party be a hit or a flop?

Logistic regression is used for these binary outcomes.

Instead of predicting a precise fun level, it predicts the probability of the party being a hit based on the same predictors (snacks, music, guests).

Making Sense of the Results

• Coefficients: In regression analysis, each predictor has a coefficient, telling you how much the dependent variable is expected to change when that predictor changes by one unit, all else being equal.
• R-squared : This value tells you how much of the variation in your dependent variable can be explained by the independent variables. A higher R-squared means a better fit between your model and the data.

Why Regression Analysis Rocks?

Regression analysis is like having a superpower. It helps you understand which factors matter most, which can be ignored, and how different factors come together to influence the outcome.

This insight is invaluable whether you’re planning a party, running a business, or conducting scientific research.

Bringing It All Together

Imagine you’ve gathered data on several parties, including the number of guests, type of music, and amount of snacks, along with a fun level rating for each.

By running a regression analysis, you can start to predict future parties’ success, tailoring your planning to maximize fun.

It’s a practical tool for making informed decisions based on past data, helping you throw legendary parties, optimize business strategies, or understand complex relationships in your research.

In essence, regression analysis helps turn your data into actionable insights, guiding you towards smarter decisions and better predictions.

So next time you’re knee-deep in data, remember: regression analysis might just be the key to unlocking its secrets.

Non-parametric Methods: Playing By Different Rules

So far, we’ve talked a lot about statistical methods that rely on certain assumptions about your data, like it being normally distributed (forming that classic bell curve) or having a specific scale of measurement.

But what happens when your data doesn’t fit these molds?

Maybe the scores from your last party’s karaoke contest are all over the place, or you’re trying to compare the popularity of various party games but only have rankings, not scores.

This is where non-parametric methods come to the rescue.

Breaking Free from Assumptions

Non-parametric methods are the rebels of the statistical world.

They don’t assume your data follows a normal distribution or that it meets strict requirements regarding measurement scales.

These methods are perfect for dealing with ordinal data (like rankings), nominal data (like categories), or when your data is skewed or has outliers that would throw off other tests.

When to Use Non-parametric Methods?

• Your data is not normally distributed, and transformations don’t help.
• You have ordinal data (like survey responses that range from “Strongly Disagree” to “Strongly Agree”).
• You’re dealing with ranks or categories rather than precise measurements.
• Your sample size is small, making it hard to meet the assumptions required for parametric tests.

Some Popular Non-parametric Tests

• Mann-Whitney U Test: Think of it as the non-parametric counterpart to the independent samples t-test. Use this when you want to compare the differences between two independent groups on a ranking or ordinal scale.
• Kruskal-Wallis Test: This is your go-to when you have three or more groups to compare, and it’s similar to an ANOVA but for ranked/ordinal data or when your data doesn’t meet ANOVA’s assumptions.
• Spearman’s Rank Correlation: When you want to see if there’s a relationship between two sets of rankings, Spearman’s got your back. It’s like Pearson’s correlation for continuous data but designed for ranks.
• Wilcoxon Signed-Rank Test: Use this for comparing two related samples when you can’t use the paired t-test, typically because the differences between pairs are not normally distributed.

The Beauty of Flexibility

The real charm of non-parametric methods is their flexibility.

They let you work with data that’s not textbook perfect, which is often the case in the real world.

Whether you’re analyzing customer satisfaction surveys, comparing the effectiveness of different marketing strategies, or just trying to figure out if people prefer pizza or tacos at parties, non-parametric tests provide a robust way to get meaningful insights.

Keeping It Real

It’s important to remember that while non-parametric methods are incredibly useful, they also come with their own limitations.

They might be more conservative, meaning you might need a larger effect to detect a significant result compared to parametric tests.

Plus, because they often work with ranks rather than actual values, some information about your data might get lost in translation.

Non-parametric methods are your statistical toolbox’s Swiss Army knife, ready to tackle data that doesn’t fit into the neat categories required by more traditional tests.

They remind us that in the world of data analysis, there’s more than one way to uncover insights and make informed decisions.

So, the next time you’re faced with skewed distributions or rankings instead of scores, remember that non-parametric methods have got you covered, offering a way to navigate the complexities of real-world data.

Data Cleaning and Preparation: The Unsung Heroes of Data Analysis

Before any party can start, there’s always a bit of housecleaning to do—sweeping the floors, arranging the furniture, and maybe even hiding those laundry piles you’ve been ignoring all week.

Similarly, in the world of data analysis, before we can dive into the fun stuff like statistical tests and predictive modeling, we need to roll up our sleeves and get our data nice and tidy.

This process of data cleaning and preparation might not be the most glamorous part of data science, but it’s absolutely critical.

Let’s break down what this involves and why it’s so important.

Why Clean and Prepare Data?

Imagine trying to analyze party RSVPs when half the responses are “yes,” a quarter are “Y,” and the rest are a creative mix of “yup,” “sure,” and “why not?”

Without standardization, it’s hard to get a clear picture of how many guests to expect.

The same goes for any data set. Cleaning ensures that your data is consistent, accurate, and ready for analysis.

Preparation involves transforming this clean data into a format that’s useful for your specific analysis needs.

The Steps to Sparkling Clean Data

• Dealing with Missing Values: Sometimes, data is incomplete. Maybe a survey respondent skipped a question, or a sensor failed to record a reading. You’ll need to decide whether to fill in these gaps (imputation), ignore them, or drop the observations altogether.
• Identifying and Handling Outliers: Outliers are data points that are significantly different from the rest. They might be errors, or they might be valuable insights. The challenge is determining which is which and deciding how to handle them—remove, adjust, or analyze separately.
• Correcting Inconsistencies: This is like making sure all your RSVPs are in the same format. It could involve standardizing text entries, correcting typos, or converting all measurements to the same units.
• Formatting Data: Your analysis might require data in a specific format. This could mean transforming data types (e.g., converting dates into a uniform format) or restructuring data tables to make them easier to work with.
• Reducing Dimensionality: Sometimes, your data set might have more information than you actually need. Reducing dimensionality (through methods like Principal Component Analysis) can help simplify your data without losing valuable information.
• Creating New Variables: You might need to derive new variables from your existing ones to better capture the relationships in your data. For example, turning raw survey responses into a numerical satisfaction score.

The Tools of the Trade

There are many tools available to help with data cleaning and preparation, ranging from spreadsheet software like Excel to programming languages like Python and R.

These tools offer functions and libraries specifically designed to make data cleaning as painless as possible.

Why It Matters

Skipping the data cleaning and preparation stage is like trying to cook without prepping your ingredients first.

Sure, you might end up with something edible, but it’s not going to be as good as it could have been.

Clean and well-prepared data leads to more accurate, reliable, and meaningful analysis results.

It’s the foundation upon which all good data analysis is built.

Data cleaning and preparation might not be the flashiest part of data science, but it’s where all successful data analysis projects begin.

By taking the time to thoroughly clean and prepare your data, you’re setting yourself up for clearer insights, better decisions, and, ultimately, more impactful outcomes.

Software Tools for Statistical Analysis: Your Digital Assistants

Diving into the world of data without the right tools can feel like trying to cook a gourmet meal without a kitchen.

Just as you need pots, pans, and a stove to create a culinary masterpiece, you need the right software tools to analyze data and uncover the insights hidden within.

These digital assistants range from user-friendly applications for beginners to powerful suites for the pros.

Let’s take a closer look at some of the most popular software tools for statistical analysis.

R and RStudio: The Dynamic Duo

• R is like the Swiss Army knife of statistical analysis. It’s a programming language designed specifically for data analysis, graphics, and statistical modeling. Think of R as the kitchen where you’ll be cooking up your data analysis.
• RStudio is an integrated development environment (IDE) for R. It’s like having the best kitchen setup with organized countertops (your coding space) and all your tools and ingredients within reach (packages and datasets).

Why They Rock:

R is incredibly powerful and can handle almost any data analysis task you throw at it, from the basics to the most advanced statistical models.

Plus, there’s a vast community of users, which means a wealth of tutorials, forums, and free packages to add on.

Python with pandas and scipy: The Versatile Virtuoso

• Python is not just for programming; with the right libraries, it becomes an excellent tool for data analysis. It’s like a kitchen that’s not only great for baking but also equipped for gourmet cooking.
• pandas is a library that provides easy-to-use data structures and data analysis tools for Python. Imagine it as your sous-chef, helping you to slice and dice data with ease.
• scipy is another library used for scientific and technical computing. It’s like having a set of precision knives for the more intricate tasks.

Why They Rock: Python is known for its readability and simplicity, making it accessible for beginners. When combined with pandas and scipy, it becomes a powerhouse for data manipulation, analysis, and visualization.

SPSS: The Point-and-Click Professional

SPSS (Statistical Package for the Social Sciences) is a software package used for interactive, or batched, statistical analysis. Long produced by SPSS Inc., it was acquired by IBM in 2009.

Why It Rocks: SPSS is particularly user-friendly with its point-and-click interface, making it a favorite among non-programmers and researchers in the social sciences. It’s like having a kitchen gadget that does the job with the push of a button—no manual setup required.

SAS: The Corporate Chef

SAS (Statistical Analysis System) is a software suite developed for advanced analytics, multivariate analysis, business intelligence, data management, and predictive analytics.

Why It Rocks: SAS is a powerhouse in the corporate world, known for its stability, deep analytical capabilities, and support for large data sets. It’s like the industrial kitchen used by professional chefs to serve hundreds of guests.

Excel: The Accessible Apprentice

Excel might not be a specialized statistical software, but it’s widely accessible and capable of handling basic statistical analyses. Think of Excel as the microwave in your kitchen—it might not be fancy, but it gets the job done for quick and simple tasks.

Why It Rocks: Almost everyone has access to Excel and knows the basics, making it a great starting point for those new to data analysis. Plus, with add-ons like the Analysis ToolPak, Excel’s capabilities can be extended further into statistical territory.

Choosing Your Tool

Selecting the right software tool for statistical analysis is like choosing the right kitchen for your cooking style—it depends on your needs, expertise, and the complexity of your recipes (data).

Whether you’re a coding chef ready to tackle R or Python, or someone who prefers the straightforwardness of SPSS or Excel, there’s a tool out there that’s perfect for your data analysis kitchen.

Ethical Considerations

Embarking on a data analysis journey is like setting sail on the vast ocean of information.

Just as a captain needs a compass to navigate the seas safely and responsibly, a data analyst requires a strong sense of ethics to guide their exploration of data.

Ethical considerations in data analysis are the moral compass that ensures we respect privacy, consent, and integrity while uncovering the truths hidden within data. Let’s delve into why ethics are so crucial and what principles you should keep in mind.

Respect for Privacy

Imagine you’ve found a diary filled with personal secrets.

Reading it without permission would be a breach of privacy.

Similarly, when you’re handling data, especially personal or sensitive information, it’s essential to ensure that privacy is protected.

This means not only securing data against unauthorized access but also anonymizing data to prevent individuals from being identified.

Informed Consent

Before you can set sail, you need the ship owner’s permission.

In the world of data, this translates to informed consent. Participants should be fully aware of what their data will be used for and voluntarily agree to participate.

This is particularly important in research or when collecting data directly from individuals. It’s like asking for permission before you start the journey.

Data Integrity

Maintaining data integrity is like keeping the ship’s log accurate and unaltered during your voyage.

It involves ensuring the data is not corrupted or modified inappropriately and that any data analysis is conducted accurately and reliably.

Tampering with data or cherry-picking results to fit a narrative is not just unethical—it’s like falsifying the ship’s log, leading to mistrust and potentially dangerous outcomes.

Avoiding Bias

The sea is vast, and your compass must be calibrated correctly to avoid going off course. Similarly, avoiding bias in data analysis ensures your findings are valid and unbiased.

This means being aware of and actively addressing any personal, cultural, or statistical biases that might skew your analysis.

It’s about striving for objectivity and ensuring your journey is guided by truth, not preconceived notions.

Transparency and Accountability

A trustworthy captain is open about their navigational choices and ready to take responsibility for them.

In data analysis, this translates to transparency about your methods and accountability for your conclusions.

Sharing your methodologies, data sources, and any limitations of your analysis helps build trust and allows others to verify or challenge your findings.

Ethical Use of Findings

Finally, just as a captain must consider the impact of their journey on the wider world, you must consider how your data analysis will be used.

This means thinking about the potential consequences of your findings and striving to ensure they are used to benefit, not harm, society.

It’s about being mindful of the broader implications of your work and using data for good.

Navigating with a Moral Compass

In the realm of data analysis, ethical considerations form the moral compass that guides us through complex moral waters.

They ensure that our work respects individuals’ rights, contributes positively to society, and upholds the highest standards of integrity and professionalism.

Just as a captain navigates the seas with respect for the ocean and its dangers, a data analyst must navigate the world of data with a deep commitment to ethical principles.

This commitment ensures that the insights gained from data analysis serve to enlighten and improve, rather than exploit or harm.

Conclusion and Key Takeaways

And there you have it—a whirlwind tour through the fascinating landscape of statistical methods for data analysis.

From the grounding principles of descriptive and inferential statistics to the nuanced details of regression analysis and beyond, we’ve explored the tools and ethical considerations that guide us in turning raw data into meaningful insights.

The Takeaway

Think of data analysis as embarking on a grand adventure, one where numbers and facts are your map and compass.

Just as every explorer needs to understand the terrain, every aspiring data analyst must grasp these foundational concepts.

Whether it’s summarizing data sets with descriptive statistics, making predictions with inferential statistics, choosing the right statistical test, or navigating the ethical considerations that ensure our analyses benefit society, each aspect is a crucial step on your journey.

The Importance of Preparation

Remember, the key to a successful voyage is preparation.

Cleaning and preparing your data sets the stage for a smooth journey, while choosing the right software tools ensures you have the best equipment at your disposal.

And just as every responsible navigator respects the sea, every data analyst must navigate the ethical dimensions of their work with care and integrity.

Charting Your Course

As you embark on your own data analysis adventures, remember that the path you chart is unique to you.

Your questions will guide your journey, your curiosity will fuel your exploration, and the insights you gain will be your treasure.

The world of data is vast and full of mysteries waiting to be uncovered. With the tools and principles we’ve discussed, you’re well-equipped to start uncovering those mysteries, one data set at a time.

The Journey Ahead

The journey of statistical methods for data analysis is ongoing, and the landscape is ever-evolving.

As new methods emerge and our understanding deepens, there will always be new horizons to explore and new insights to discover.

But the fundamentals we’ve covered will remain your steadfast guide, helping you navigate the challenges and opportunities that lie ahead.

So set your sights on the questions that spark your curiosity, arm yourself with the tools of the trade, and embark on your data analysis journey with confidence.

About The Author

Silvia Valcheva

Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI (Artificial Intelligence), IoT (Internet of Things), process automation, etc.

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What Is Statistical Analysis?

Statistical analysis helps you pull meaningful insights from data. The process involves working with data and deducing numbers to tell quantitative stories.

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment. 

In its simplest form, statistical analysis answers questions about:

• Quantification — how big/small/tall/wide is it?
• Variability — growth, increase, decline
• The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

• Descriptive Statistics:  Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 
• Inferential Statistics:  Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential. 

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures. 

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range). 

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests. 

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .  

Statistical Analysis Steps  

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem. 

2. Plan

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it. 

The third stage involves data collection, understanding the data and checking its quality. 

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations.  You also develop and scrutinize your hypothesis in this stage of analysis. 

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

• Statistical quality control and analysis in product development 
• Clinical trials
• Customer satisfaction surveys and customer experience research 
• Marketing operations management
• Process improvement and optimization
• Training needs 

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative. 

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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Table of Contents

Types of statistical analysis, importance of statistical analysis, benefits of statistical analysis, statistical analysis process, statistical analysis methods, statistical analysis software, statistical analysis examples, career in statistical analysis, choose the right program, become proficient in statistics today, what is statistical analysis types, methods and examples.

Statistical analysis is the process of collecting and analyzing data in order to discern patterns and trends. It is a method for removing bias from evaluating data by employing numerical analysis. This technique is useful for collecting the interpretations of research, developing statistical models, and planning surveys and studies.

Statistical analysis is a scientific tool in AI and ML that helps collect and analyze large amounts of data to identify common patterns and trends to convert them into meaningful information. In simple words, statistical analysis is a data analysis tool that helps draw meaningful conclusions from raw and unstructured data. 

The conclusions are drawn using statistical analysis facilitating decision-making and helping businesses make future predictions on the basis of past trends. It can be defined as a science of collecting and analyzing data to identify trends and patterns and presenting them. Statistical analysis involves working with numbers and is used by businesses and other institutions to make use of data to derive meaningful information. 

Given below are the 6 types of statistical analysis:

Descriptive Analysis

Descriptive statistical analysis involves collecting, interpreting, analyzing, and summarizing data to present them in the form of charts, graphs, and tables. Rather than drawing conclusions, it simply makes the complex data easy to read and understand.

Inferential Analysis

The inferential statistical analysis focuses on drawing meaningful conclusions on the basis of the data analyzed. It studies the relationship between different variables or makes predictions for the whole population.

Predictive Analysis

Predictive statistical analysis is a type of statistical analysis that analyzes data to derive past trends and predict future events on the basis of them. It uses machine learning algorithms, data mining , data modelling , and artificial intelligence to conduct the statistical analysis of data.

Prescriptive Analysis

The prescriptive analysis conducts the analysis of data and prescribes the best course of action based on the results. It is a type of statistical analysis that helps you make an informed decision. 

Exploratory Data Analysis

Exploratory analysis is similar to inferential analysis, but the difference is that it involves exploring the unknown data associations. It analyzes the potential relationships within the data. 

Causal Analysis

The causal statistical analysis focuses on determining the cause and effect relationship between different variables within the raw data. In simple words, it determines why something happens and its effect on other variables. This methodology can be used by businesses to determine the reason for failure. 

Statistical analysis eliminates unnecessary information and catalogs important data in an uncomplicated manner, making the monumental work of organizing inputs appear so serene. Once the data has been collected, statistical analysis may be utilized for a variety of purposes. Some of them are listed below:

• The statistical analysis aids in summarizing enormous amounts of data into clearly digestible chunks.
• The statistical analysis aids in the effective design of laboratory, field, and survey investigations.
• Statistical analysis may help with solid and efficient planning in any subject of study.
• Statistical analysis aid in establishing broad generalizations and forecasting how much of something will occur under particular conditions.
• Statistical methods, which are effective tools for interpreting numerical data, are applied in practically every field of study. Statistical approaches have been created and are increasingly applied in physical and biological sciences, such as genetics.
• Statistical approaches are used in the job of a businessman, a manufacturer, and a researcher. Statistics departments can be found in banks, insurance businesses, and government agencies.
• A modern administrator, whether in the public or commercial sector, relies on statistical data to make correct decisions.
• Politicians can utilize statistics to support and validate their claims while also explaining the issues they address.

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Statistical analysis can be called a boon to mankind and has many benefits for both individuals and organizations. Given below are some of the reasons why you should consider investing in statistical analysis:

• It can help you determine the monthly, quarterly, yearly figures of sales profits, and costs making it easier to make your decisions.
• It can help you make informed and correct decisions.
• It can help you identify the problem or cause of the failure and make corrections. For example, it can identify the reason for an increase in total costs and help you cut the wasteful expenses.
• It can help you conduct market analysis and make an effective marketing and sales strategy.
• It helps improve the efficiency of different processes.

Given below are the 5 steps to conduct a statistical analysis that you should follow:

• Step 1: Identify and describe the nature of the data that you are supposed to analyze.
• Step 2: The next step is to establish a relation between the data analyzed and the sample population to which the data belongs. 
• Step 3: The third step is to create a model that clearly presents and summarizes the relationship between the population and the data.
• Step 4: Prove if the model is valid or not.
• Step 5: Use predictive analysis to predict future trends and events likely to happen. 

Although there are various methods used to perform data analysis, given below are the 5 most used and popular methods of statistical analysis:

Mean or average mean is one of the most popular methods of statistical analysis. Mean determines the overall trend of the data and is very simple to calculate. Mean is calculated by summing the numbers in the data set together and then dividing it by the number of data points. Despite the ease of calculation and its benefits, it is not advisable to resort to mean as the only statistical indicator as it can result in inaccurate decision making. 

Standard Deviation

Standard deviation is another very widely used statistical tool or method. It analyzes the deviation of different data points from the mean of the entire data set. It determines how data of the data set is spread around the mean. You can use it to decide whether the research outcomes can be generalized or not. 

Regression is a statistical tool that helps determine the cause and effect relationship between the variables. It determines the relationship between a dependent and an independent variable. It is generally used to predict future trends and events.

Hypothesis Testing

Hypothesis testing can be used to test the validity or trueness of a conclusion or argument against a data set. The hypothesis is an assumption made at the beginning of the research and can hold or be false based on the analysis results. 

Sample Size Determination

Sample size determination or data sampling is a technique used to derive a sample from the entire population, which is representative of the population. This method is used when the size of the population is very large. You can choose from among the various data sampling techniques such as snowball sampling, convenience sampling, and random sampling. 

Everyone can't perform very complex statistical calculations with accuracy making statistical analysis a time-consuming and costly process. Statistical software has become a very important tool for companies to perform their data analysis. The software uses Artificial Intelligence and Machine Learning to perform complex calculations, identify trends and patterns, and create charts, graphs, and tables accurately within minutes. 

Look at the standard deviation sample calculation given below to understand more about statistical analysis.

The weights of 5 pizza bases in cms are as follows:

Calculation of Mean = (9+2+5+4+12)/5 = 32/5 = 6.4

Calculation of mean of squared mean deviation = (6.76+19.36+1.96+5.76+31.36)/5 = 13.04

Sample Variance = 13.04

Standard deviation = √13.04 = 3.611

A Statistical Analyst's career path is determined by the industry in which they work. Anyone interested in becoming a Data Analyst may usually enter the profession and qualify for entry-level Data Analyst positions right out of high school or a certificate program — potentially with a Bachelor's degree in statistics, computer science, or mathematics. Some people go into data analysis from a similar sector such as business, economics, or even the social sciences, usually by updating their skills mid-career with a statistical analytics course.

Statistical Analyst is also a great way to get started in the normally more complex area of data science. A Data Scientist is generally a more senior role than a Data Analyst since it is more strategic in nature and necessitates a more highly developed set of technical abilities, such as knowledge of multiple statistical tools, programming languages, and predictive analytics models.

Aspiring Data Scientists and Statistical Analysts generally begin their careers by learning a programming language such as R or SQL. Following that, they must learn how to create databases, do basic analysis, and make visuals using applications such as Tableau. However, not every Statistical Analyst will need to know how to do all of these things, but if you want to advance in your profession, you should be able to do them all.

Based on your industry and the sort of work you do, you may opt to study Python or R, become an expert at data cleaning, or focus on developing complicated statistical models.

You could also learn a little bit of everything, which might help you take on a leadership role and advance to the position of Senior Data Analyst. A Senior Statistical Analyst with vast and deep knowledge might take on a leadership role leading a team of other Statistical Analysts. Statistical Analysts with extra skill training may be able to advance to Data Scientists or other more senior data analytics positions.

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Hope this article assisted you in understanding the importance of statistical analysis in every sphere of life. Artificial Intelligence (AI) can help you perform statistical analysis and data analysis very effectively and efficiently. 

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Quantitative Data Analysis 101

The lingo, methods and techniques, explained simply.

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Quantitative data analysis is one of those things that often strikes fear in students. It’s totally understandable – quantitative analysis is a complex topic, full of daunting lingo , like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a little more attention in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t that hard , even for those of us who avoid numbers and math . In this post, we’ll break quantitative analysis down into simple , bite-sized chunks so you can approach your research with confidence.

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Don’t be a sucker – give your descriptive statistics the love and attention they deserve!

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the composition of your sample is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post .

What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are just a handful of inferential techniques – there are many, many more. Importantly, each statistical method has its own assumptions and limitations .

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why descriptive statistics are so important – they’re the first step to knowing which inferential techniques you can and can’t use.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Why does this matter?

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why descriptive statistics are so important – they tell you all about the shape of your data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

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76 Comments

Hi, I have read your article. Such a brilliant post you have created.

Thank you for the feedback. Good luck with your quantitative analysis.

Thank you so much.

Thank you so much. I learnt much well. I love your summaries of the concepts. I had love you to explain how to input data using SPSS

Amazing and simple way of breaking down quantitative methods.

This is beautiful….especially for non-statisticians. I have skimmed through but I wish to read again. and please include me in other articles of the same nature when you do post. I am interested. I am sure, I could easily learn from you and get off the fear that I have had in the past. Thank you sincerely.

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Thank you for the blog. It is quite informative. Dr Peter Nemaenzhe PhD

It is wonderful. l’ve understood some of the concepts in a more compréhensive manner

Your article is so good! However, I am still a bit lost. I am doing a secondary research on Gun control in the US and increase in crime rates and I am not sure which analysis method I should use?

Based on the given learning points, this is inferential analysis, thus, use ‘t-tests, ANOVA, correlation and regression analysis’

Well explained notes. Am an MPH student and currently working on my thesis proposal, this has really helped me understand some of the things I didn’t know.

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This is great GRADACOACH I am not a statistician but I require more of this in my thesis

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Avery good presentation followed by the write up. yes you simplified statistics to make sense even to a layman like me. Thank so much keep it up. The presenter did ell too. i would like more of this for Qualitative and exhaust more of the test example like the Anova.

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VERY INTERESTING AND SUPPORTIVE TO NEW RESEARCHERS LIKE ME. AT LEAST SOME BASICS ABOUT QUANTITATIVE.

An outstanding, well explained and helpful article. This will help me so much with my data analysis for my research project. Thank you!

wow this has just simplified everything i was scared of how i am gonna analyse my data but thanks to you i will be able to do so

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Do you provide any assistance for other steps of research methodology like making research problem testing hypothesis report and thesis writing?

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Very insightfull. Thanks

I am doing a quality improvement project to determine if the implementation of a protocol will change prescribing habits. Would this be a t-test?

The is a very helpful blog, however, I’m still not sure how to analyze my data collected. I’m doing a research on “Free Education at the University of Guyana”

tnx. fruitful blog!

So I am writing exams and would like to know how do establish which method of data analysis to use from the below research questions: I am a bit lost as to how I determine the data analysis method from the research questions.

Do female employees report higher job satisfaction than male employees with similar job descriptions across the South African telecommunications sector? – I though that maybe Chi Square could be used here. – Is there a gender difference in talented employees’ actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – Is there a gender difference in the cost of actual turnover decisions across the South African telecommunications sector? T-tests or Correlation in this one. – What practical recommendations can be made to the management of South African telecommunications companies on leveraging gender to mitigate employee turnover decisions?

Your assistance will be appreciated if I could get a response as early as possible tomorrow

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Many thanks for your useful lecture, I would be really appreciated if you could possibly share with me the PPT of presentation related to Data type?

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Very interesting mostly for social scientists

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You’re welcome 🙂

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JAMA Guide to Statistics and Methods

Explore this JAMA essay series that explains the basics of statistical techniques used in clinical research, to help clinicians interpret and critically appraise the medical literature.

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Article type.

This JAMA Guide to Statistics and Methods article discusses accounting for competing risks in clinical research.

This JAMA Guide to Statistics and Methods article explains effect score analyses, an approach for evaluating the heterogeneity of treatment effects, and examines its use in a study of oxygen-saturation targets in critically ill patients.

This JAMA Guide to Statistics and Methods explains the use of historical controls—persons who had received a specific control treatment in a previous study—when randomizing participants to that control treatment in a subsequent trial may not be practical or ethical.

This JAMA Guide to Statistics and Methods discusses the early stopping of clinical trials for futility due to lack of evidence supporting the desired benefit, evidence of harm, or practical issues that make successful completion unlikely.

This JAMA Guide to Statistics and Methods explains sequential, multiple assignment, randomized trial (SMART) study designs, in which some or all participants are randomized at 2 or more decision points depending on the participant’s response to prior treatment.

This JAMA Guide to Statistics and Methods article examines conditional power, calculated while a trial is ongoing and based on both the currently observed data and an assumed treatment effect for future patients.

This Guide to Statistics and Methods describes the use of target trial emulation to design an observational study so it preserves the advantages of a randomized clinical trial, points out the limitations of the method, and provides an example of its use.

This Guide to Statistics and Methods provides an overview of the use of adjustment for baseline characteristics in the analysis of randomized clinical trials and emphasizes several important considerations.

This Guide to Statistics and Methods provides an overview of regression models for ordinal outcomes, including an explanation of why they are used and their limitations.

This Guide to Statistics and Methods provides an overview of patient-reported outcome measures for clinical research, emphasizes several important considerations when using them, and points out their limitations.

This JAMA Guide to Statistics and Methods discusses instrumental variable analysis, a method designed to reduce or eliminate unobserved confounding in observational studies, with the goal of achieving unbiased estimation of treatment effects.

This JAMA Guide to Statistics and Methods describes collider bias, illustrates examples in directed acyclic graphs, and explains how it can threaten the internal validity of a study and the accurate estimation of causal relationships in randomized clinical trials and observational studies.

This JAMA Guide to Statistics and Methods discusses the CONSERVE guidelines, which address how to report extenuating circumstances that lead to a modification in trial design, conduct, or analysis.

This JAMA Guide to Statistics and Methods discusses the basics of causal directed acyclic graphs, which are useful tools for communicating researchers’ understanding of the potential interplay among variables and are commonly used for mediation analysis.

This JAMA Guide to Statistics and Methods discusses cardinality matching, a method for finding the largest possible number of matched pairs in an observational data set, with the goal of balanced and representative samples of study participants between groups.

This Guide to Statistics and Methods discusses the various approaches to estimating variability in treatment effects, including heterogeneity of treatment effect, which was used to assess the association between surgery to close patent foramen ovale and risk of recurrent stroke in patients who presented with a stroke in a related JAMA article.

This Guide to Statistics and Methods describes how confidence intervals can be used to help in the interpretation of nonsignificant findings across all study designs.

This JAMA Guide to Statistics and Methods describes why interim analyses are performed during group sequential trials, provides examples of the limitations of interim analyses, and provides guidance on interpreting the results of interim analyses performed during group sequential trials.

This JAMA Guide to Statistics and Methods describes how ACC/AHA guidelines are formatted to rate class (denoting strength of a recommendation) and level (indicating the level of evidence on which a recommendation is based) and summarizes the strengths and benefits of this rating system in comparison with other commonly used ones.

This JAMA Guide to Statistics and Methods takes a look at estimands, estimators, and estimates in the context of randomized clinical trials and suggests several qualities that make for good estimands, including their scope, ability to summarize treatment effects, external validity, and ability to provide good estimates.

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Effective Use of Statistics in Research – Methods and Tools for Data Analysis

Remember that impending feeling you get when you are asked to analyze your data! Now that you have all the required raw data, you need to statistically prove your hypothesis. Representing your numerical data as part of statistics in research will also help in breaking the stereotype of being a biology student who can’t do math.

Statistical methods are essential for scientific research. In fact, statistical methods dominate the scientific research as they include planning, designing, collecting data, analyzing, drawing meaningful interpretation and reporting of research findings. Furthermore, the results acquired from research project are meaningless raw data unless analyzed with statistical tools. Therefore, determining statistics in research is of utmost necessity to justify research findings. In this article, we will discuss how using statistical methods for biology could help draw meaningful conclusion to analyze biological studies.

Table of Contents

Role of Statistics in Biological Research

Statistics is a branch of science that deals with collection, organization and analysis of data from the sample to the whole population. Moreover, it aids in designing a study more meticulously and also give a logical reasoning in concluding the hypothesis. Furthermore, biology study focuses on study of living organisms and their complex living pathways, which are very dynamic and cannot be explained with logical reasoning. However, statistics is more complex a field of study that defines and explains study patterns based on the sample sizes used. To be precise, statistics provides a trend in the conducted study.

Biological researchers often disregard the use of statistics in their research planning, and mainly use statistical tools at the end of their experiment. Therefore, giving rise to a complicated set of results which are not easily analyzed from statistical tools in research. Statistics in research can help a researcher approach the study in a stepwise manner, wherein the statistical analysis in research follows –

1. Establishing a Sample Size

Usually, a biological experiment starts with choosing samples and selecting the right number of repetitive experiments. Statistics in research deals with basics in statistics that provides statistical randomness and law of using large samples. Statistics teaches how choosing a sample size from a random large pool of sample helps extrapolate statistical findings and reduce experimental bias and errors.

2. Testing of Hypothesis

When conducting a statistical study with large sample pool, biological researchers must make sure that a conclusion is statistically significant. To achieve this, a researcher must create a hypothesis before examining the distribution of data. Furthermore, statistics in research helps interpret the data clustered near the mean of distributed data or spread across the distribution. These trends help analyze the sample and signify the hypothesis.

3. Data Interpretation Through Analysis

When dealing with large data, statistics in research assist in data analysis. This helps researchers to draw an effective conclusion from their experiment and observations. Concluding the study manually or from visual observation may give erroneous results; therefore, thorough statistical analysis will take into consideration all the other statistical measures and variance in the sample to provide a detailed interpretation of the data. Therefore, researchers produce a detailed and important data to support the conclusion.

Types of Statistical Research Methods That Aid in Data Analysis

Statistical analysis is the process of analyzing samples of data into patterns or trends that help researchers anticipate situations and make appropriate research conclusions. Based on the type of data, statistical analyses are of the following type:

1. Descriptive Analysis

The descriptive statistical analysis allows organizing and summarizing the large data into graphs and tables . Descriptive analysis involves various processes such as tabulation, measure of central tendency, measure of dispersion or variance, skewness measurements etc.

2. Inferential Analysis

The inferential statistical analysis allows to extrapolate the data acquired from a small sample size to the complete population. This analysis helps draw conclusions and make decisions about the whole population on the basis of sample data. It is a highly recommended statistical method for research projects that work with smaller sample size and meaning to extrapolate conclusion for large population.

3. Predictive Analysis

Predictive analysis is used to make a prediction of future events. This analysis is approached by marketing companies, insurance organizations, online service providers, data-driven marketing, and financial corporations.

4. Prescriptive Analysis

Prescriptive analysis examines data to find out what can be done next. It is widely used in business analysis for finding out the best possible outcome for a situation. It is nearly related to descriptive and predictive analysis. However, prescriptive analysis deals with giving appropriate suggestions among the available preferences.

5. Exploratory Data Analysis

EDA is generally the first step of the data analysis process that is conducted before performing any other statistical analysis technique. It completely focuses on analyzing patterns in the data to recognize potential relationships. EDA is used to discover unknown associations within data, inspect missing data from collected data and obtain maximum insights.

6. Causal Analysis

Causal analysis assists in understanding and determining the reasons behind “why” things happen in a certain way, as they appear. This analysis helps identify root cause of failures or simply find the basic reason why something could happen. For example, causal analysis is used to understand what will happen to the provided variable if another variable changes.

7. Mechanistic Analysis

This is a least common type of statistical analysis. The mechanistic analysis is used in the process of big data analytics and biological science. It uses the concept of understanding individual changes in variables that cause changes in other variables correspondingly while excluding external influences.

Important Statistical Tools In Research

Researchers in the biological field find statistical analysis in research as the scariest aspect of completing research. However, statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible.

1. Statistical Package for Social Science (SPSS)

It is a widely used software package for human behavior research. SPSS can compile descriptive statistics, as well as graphical depictions of result. Moreover, it includes the option to create scripts that automate analysis or carry out more advanced statistical processing.

2. R Foundation for Statistical Computing

This software package is used among human behavior research and other fields. R is a powerful tool and has a steep learning curve. However, it requires a certain level of coding. Furthermore, it comes with an active community that is engaged in building and enhancing the software and the associated plugins.

3. MATLAB (The Mathworks)

It is an analytical platform and a programming language. Researchers and engineers use this software and create their own code and help answer their research question. While MatLab can be a difficult tool to use for novices, it offers flexibility in terms of what the researcher needs.

4. Microsoft Excel

Not the best solution for statistical analysis in research, but MS Excel offers wide variety of tools for data visualization and simple statistics. It is easy to generate summary and customizable graphs and figures. MS Excel is the most accessible option for those wanting to start with statistics.

5. Statistical Analysis Software (SAS)

It is a statistical platform used in business, healthcare, and human behavior research alike. It can carry out advanced analyzes and produce publication-worthy figures, tables and charts .

6. GraphPad Prism

It is a premium software that is primarily used among biology researchers. But, it offers a range of variety to be used in various other fields. Similar to SPSS, GraphPad gives scripting option to automate analyses to carry out complex statistical calculations.

This software offers basic as well as advanced statistical tools for data analysis. However, similar to GraphPad and SPSS, minitab needs command over coding and can offer automated analyses.

Use of Statistical Tools In Research and Data Analysis

Statistical tools manage the large data. Many biological studies use large data to analyze the trends and patterns in studies. Therefore, using statistical tools becomes essential, as they manage the large data sets, making data processing more convenient.

Following these steps will help biological researchers to showcase the statistics in research in detail, and develop accurate hypothesis and use correct tools for it.

There are a range of statistical tools in research which can help researchers manage their research data and improve the outcome of their research by better interpretation of data. You could use statistics in research by understanding the research question, knowledge of statistics and your personal experience in coding.

Have you faced challenges while using statistics in research? How did you manage it? Did you use any of the statistical tools to help you with your research data? Do write to us or comment below!

Frequently Asked Questions

Statistics in research can help a researcher approach the study in a stepwise manner: 1. Establishing a sample size 2. Testing of hypothesis 3. Data interpretation through analysis

Statistical methods are essential for scientific research. In fact, statistical methods dominate the scientific research as they include planning, designing, collecting data, analyzing, drawing meaningful interpretation and reporting of research findings. Furthermore, the results acquired from research project are meaningless raw data unless analyzed with statistical tools. Therefore, determining statistics in research is of utmost necessity to justify research findings.

Statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible. They can manage large data sets, making data processing more convenient. A great number of tools are available to carry out statistical analysis of data like SPSS, SAS (Statistical Analysis Software), and Minitab.

nice article to read

Holistic but delineating. A very good read.

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5 Statistical Analysis Methods for Research and Analysis

It all boils down to using the power of statistical analysis methods, which is how academics collaborate and collect data to identify trends and patterns.

Over the last ten years, everyday business has undergone a significant transformation. It’s not very uncommon for things to still appear to be the same, whether it’s the technology used in workspaces or the software used to communicate.

There is now an overwhelming amount of information available that was once rare. But it could be overwhelming if you don’t have the slightest concept of going through your company’s data to find meaningful and accurate meaning.

5 different statistical analysis methods will be covered in this blog, along with a detailed discussion of each method.

What is a statistical analysis method?

The practice of gathering and analyzing data to identify patterns and trends is known as statistical analysis . It is a method for eliminating bias from data evaluation by using numerical analysis. Data analytics and data analysis are closely related processes that involve extracting insights from data to make informed decisions.

And these statistical analysis methods are beneficial for gathering research interpretations, creating statistical models, and organizing surveys and studies.

Data analysis employs two basic statistical methods:

• Descriptive statistics, which use indexes like mean and median to summarize data,
• Inferential statistics , extrapolate results from data by utilizing statistical tests like the student t-test.

LEARN ABOUT: Descriptive Analysis

The following three factors determine whether a statistical approach is most appropriate:

• The study’s goal and primary purpose,
• The kind and dispersion of the data utilized, and
• The type of observations (Paired/Unpaired).

“Parametric” refers to all types of statistical procedures used to compare means. In contrast, “nonparametric” refers to statistical methods that compare measures other than means, such as medians, mean ranks, and proportions.

For each unique circumstance, statistical analytic methods in biostatistics can be used to analyze and interpret the data. Knowing the assumptions and conditions of the statistical methods is necessary for choosing the best statistical method for data analysis.

Whether you’re a data scientist or not, there’s no doubt that big data is taking the globe by storm. As a result, you must be aware of where to begin. There are 5 options for this statistical analysis method:

Big data is taking over the globe, no matter how you slice it. Mean, more often known as the average, is the initial technique used to conduct the statistical analysis. To find the mean, add a list of numbers, divide that total by the list’s components, and then add another list of numbers.

When this technique is applied, it is possible to quickly view the data while also determining the overall trend of the data collection . The straightforward and quick calculation is also advantageous to the method’s users.

The center of the data under consideration is determined using the statistical mean. The outcome is known as the presented data’s mean. Real-world interactions involving research, education, and athletics frequently use derogatory language. Consider how frequently a baseball player’s batting average—their mean—is brought up in conversation if you consider yourself a data scientist. As a result, you must be aware of where to begin.

Standard deviation

A statistical technique called standard deviation measures how widely distributed the data is from the mean.

When working with data, a high standard deviation indicates that the data is widely dispersed from the mean. A low deviation indicates that most data is in line with the mean and can also be referred to as the set’s expected value.

Standard deviation is frequently used when analyzing the dispersion of data points—whether or not they are clustered.

Imagine you are a marketer who just finished a client survey. Suppose you want to determine whether a bigger group of customers will likely provide the same responses. In that case, you should assess the responses’ dependability after receiving the survey findings. If the standard deviation is low, a greater range of customers may be projected with the answers.

Regression in statistics studies the connection between an independent variable and a dependent variable (the information you’re trying to assess) (the data used to predict the dependent variable).

It can also be explained in terms of how one variable influences another, or how changes in one inconsistent result in changes in another, or vice versa, simple cause and effect. It suggests that the result depends on one or more factors.

Regression analysis graphs and charts employ lines to indicate trends over a predetermined period as well as the strength or weakness of the correlations between the variables.

Hypothesis testing

The two sets of random variables inside the data set must be tested using hypothesis testing, sometimes referred to as “T Testing,” in statistical analysis.

This approach focuses on determining whether a given claim or conclusion holds for the data collection. It enables a comparison of the data with numerous assumptions and hypotheses. It can also help in predicting how choices will impact the company.

A hypothesis test in statistics determines a quantity under a particular assumption. The test’s outcome indicates whether the assumption is correct or whether it has been broken. The null hypothesis, sometimes known as hypothesis 0, is this presumption. The first hypothesis, often known as hypothesis 1, is any other theory that would conflict with hypothesis 0.

When you perform hypothesis testing, the test’s results are statistically significant if they demonstrate that the event could not have occurred by chance or at random.

Sample size determination

When evaluating data for statistical analysis, gathering reliable data can occasionally be challenging since the dataset is too huge. When this is the case, the majority choose the method known as sample size determination , which involves examining a sample or smaller data size.

You must choose the appropriate sample size for accuracy to complete this task effectively. You won’t get reliable results after your analysis if the sample size is too small.

You will use several data sampling techniques to achieve this result. To accomplish this, you may send a survey to your customers and then use the straightforward random sampling method to select the customer data for random analysis.

Conversely, excessive sample size can result in time and money lost. You can look at factors like cost, time, or the ease of data collection to decide the sample size.

Are you confused? Don’t worry! you can use our sample size calculator .

LEARN ABOUT: Theoretical Research

The ability to think analytically is vital for corporate success. Since data is one of the most important resources available today, using it effectively can result in better outcomes and decision-making.

Regardless of the statistical analysis methods you select, be sure to pay close attention to each potential drawback and its particular formula. No method is right or wrong, and there is no gold standard. It will depend on the information you’ve gathered and the conclusions you hope to draw.

By using QuestionPro, you can make crucial judgments more efficiently while better comprehending your clients and other study subjects. Use the features of the enterprise-grade research suite right away!

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Your Modern Business Guide To Data Analysis Methods And Techniques

Table of Contents

1) What Is Data Analysis?

2) Why Is Data Analysis Important?

3) What Is The Data Analysis Process?

4) Types Of Data Analysis Methods

5) Top Data Analysis Techniques To Apply

6) Quality Criteria For Data Analysis

7) Data Analysis Limitations & Barriers

8) Data Analysis Skills

9) Data Analysis In The Big Data Environment

In our data-rich age, understanding how to analyze and extract true meaning from our business’s digital insights is one of the primary drivers of success.

Despite the colossal volume of data we create every day, a mere 0.5% is actually analyzed and used for data discovery , improvement, and intelligence. While that may not seem like much, considering the amount of digital information we have at our fingertips, half a percent still accounts for a vast amount of data.

With so much data and so little time, knowing how to collect, curate, organize, and make sense of all of this potentially business-boosting information can be a minefield – but online data analysis is the solution.

In science, data analysis uses a more complex approach with advanced techniques to explore and experiment with data. On the other hand, in a business context, data is used to make data-driven decisions that will enable the company to improve its overall performance. In this post, we will cover the analysis of data from an organizational point of view while still going through the scientific and statistical foundations that are fundamental to understanding the basics of data analysis. 

To put all of that into perspective, we will answer a host of important analytical questions, explore analytical methods and techniques, while demonstrating how to perform analysis in the real world with a 17-step blueprint for success.

What Is Data Analysis?

Data analysis is the process of collecting, modeling, and analyzing data using various statistical and logical methods and techniques. Businesses rely on analytics processes and tools to extract insights that support strategic and operational decision-making.

All these various methods are largely based on two core areas: quantitative and qualitative research.

To explain the key differences between qualitative and quantitative research, here’s a video for your viewing pleasure:

Gaining a better understanding of different techniques and methods in quantitative research as well as qualitative insights will give your analyzing efforts a more clearly defined direction, so it’s worth taking the time to allow this particular knowledge to sink in. Additionally, you will be able to create a comprehensive analytical report that will skyrocket your analysis.

Apart from qualitative and quantitative categories, there are also other types of data that you should be aware of before dividing into complex data analysis processes. These categories include: 

• Big data: Refers to massive data sets that need to be analyzed using advanced software to reveal patterns and trends. It is considered to be one of the best analytical assets as it provides larger volumes of data at a faster rate. 
• Metadata: Putting it simply, metadata is data that provides insights about other data. It summarizes key information about specific data that makes it easier to find and reuse for later purposes. 
• Real time data: As its name suggests, real time data is presented as soon as it is acquired. From an organizational perspective, this is the most valuable data as it can help you make important decisions based on the latest developments. Our guide on real time analytics will tell you more about the topic. 
• Machine data: This is more complex data that is generated solely by a machine such as phones, computers, or even websites and embedded systems, without previous human interaction.

Why Is Data Analysis Important?

Before we go into detail about the categories of analysis along with its methods and techniques, you must understand the potential that analyzing data can bring to your organization.

• Informed decision-making : From a management perspective, you can benefit from analyzing your data as it helps you make decisions based on facts and not simple intuition. For instance, you can understand where to invest your capital, detect growth opportunities, predict your income, or tackle uncommon situations before they become problems. Through this, you can extract relevant insights from all areas in your organization, and with the help of dashboard software , present the data in a professional and interactive way to different stakeholders.
• Reduce costs : Another great benefit is to reduce costs. With the help of advanced technologies such as predictive analytics, businesses can spot improvement opportunities, trends, and patterns in their data and plan their strategies accordingly. In time, this will help you save money and resources on implementing the wrong strategies. And not just that, by predicting different scenarios such as sales and demand you can also anticipate production and supply. 
• Target customers better : Customers are arguably the most crucial element in any business. By using analytics to get a 360° vision of all aspects related to your customers, you can understand which channels they use to communicate with you, their demographics, interests, habits, purchasing behaviors, and more. In the long run, it will drive success to your marketing strategies, allow you to identify new potential customers, and avoid wasting resources on targeting the wrong people or sending the wrong message. You can also track customer satisfaction by analyzing your client’s reviews or your customer service department’s performance.

What Is The Data Analysis Process?

When we talk about analyzing data there is an order to follow in order to extract the needed conclusions. The analysis process consists of 5 key stages. We will cover each of them more in detail later in the post, but to start providing the needed context to understand what is coming next, here is a rundown of the 5 essential steps of data analysis. 

• Identify: Before you get your hands dirty with data, you first need to identify why you need it in the first place. The identification is the stage in which you establish the questions you will need to answer. For example, what is the customer's perception of our brand? Or what type of packaging is more engaging to our potential customers? Once the questions are outlined you are ready for the next step. 
• Collect: As its name suggests, this is the stage where you start collecting the needed data. Here, you define which sources of data you will use and how you will use them. The collection of data can come in different forms such as internal or external sources, surveys, interviews, questionnaires, and focus groups, among others.  An important note here is that the way you collect the data will be different in a quantitative and qualitative scenario. 
• Clean: Once you have the necessary data it is time to clean it and leave it ready for analysis. Not all the data you collect will be useful, when collecting big amounts of data in different formats it is very likely that you will find yourself with duplicate or badly formatted data. To avoid this, before you start working with your data you need to make sure to erase any white spaces, duplicate records, or formatting errors. This way you avoid hurting your analysis with bad-quality data. 
• Analyze : With the help of various techniques such as statistical analysis, regressions, neural networks, text analysis, and more, you can start analyzing and manipulating your data to extract relevant conclusions. At this stage, you find trends, correlations, variations, and patterns that can help you answer the questions you first thought of in the identify stage. Various technologies in the market assist researchers and average users with the management of their data. Some of them include business intelligence and visualization software, predictive analytics, and data mining, among others. 
• Interpret: Last but not least you have one of the most important steps: it is time to interpret your results. This stage is where the researcher comes up with courses of action based on the findings. For example, here you would understand if your clients prefer packaging that is red or green, plastic or paper, etc. Additionally, at this stage, you can also find some limitations and work on them. 

Now that you have a basic understanding of the key data analysis steps, let’s look at the top 17 essential methods.

17 Essential Types Of Data Analysis Methods

Before diving into the 17 essential types of methods, it is important that we go over really fast through the main analysis categories. Starting with the category of descriptive up to prescriptive analysis, the complexity and effort of data evaluation increases, but also the added value for the company.

a) Descriptive analysis - What happened.

The descriptive analysis method is the starting point for any analytic reflection, and it aims to answer the question of what happened? It does this by ordering, manipulating, and interpreting raw data from various sources to turn it into valuable insights for your organization.

Performing descriptive analysis is essential, as it enables us to present our insights in a meaningful way. Although it is relevant to mention that this analysis on its own will not allow you to predict future outcomes or tell you the answer to questions like why something happened, it will leave your data organized and ready to conduct further investigations.

b) Exploratory analysis - How to explore data relationships.

As its name suggests, the main aim of the exploratory analysis is to explore. Prior to it, there is still no notion of the relationship between the data and the variables. Once the data is investigated, exploratory analysis helps you to find connections and generate hypotheses and solutions for specific problems. A typical area of ​​application for it is data mining.

c) Diagnostic analysis - Why it happened.

Diagnostic data analytics empowers analysts and executives by helping them gain a firm contextual understanding of why something happened. If you know why something happened as well as how it happened, you will be able to pinpoint the exact ways of tackling the issue or challenge.

Designed to provide direct and actionable answers to specific questions, this is one of the world’s most important methods in research, among its other key organizational functions such as retail analytics , e.g.

c) Predictive analysis - What will happen.

The predictive method allows you to look into the future to answer the question: what will happen? In order to do this, it uses the results of the previously mentioned descriptive, exploratory, and diagnostic analysis, in addition to machine learning (ML) and artificial intelligence (AI). Through this, you can uncover future trends, potential problems or inefficiencies, connections, and casualties in your data.

With predictive analysis, you can unfold and develop initiatives that will not only enhance your various operational processes but also help you gain an all-important edge over the competition. If you understand why a trend, pattern, or event happened through data, you will be able to develop an informed projection of how things may unfold in particular areas of the business.

e) Prescriptive analysis - How will it happen.

Another of the most effective types of analysis methods in research. Prescriptive data techniques cross over from predictive analysis in the way that it revolves around using patterns or trends to develop responsive, practical business strategies.

By drilling down into prescriptive analysis, you will play an active role in the data consumption process by taking well-arranged sets of visual data and using it as a powerful fix to emerging issues in a number of key areas, including marketing, sales, customer experience, HR, fulfillment, finance, logistics analytics , and others.

As mentioned at the beginning of the post, data analysis methods can be divided into two big categories: quantitative and qualitative. Each of these categories holds a powerful analytical value that changes depending on the scenario and type of data you are working with. Below, we will discuss 17 methods that are divided into qualitative and quantitative approaches. 

Without further ado, here are the 17 essential types of data analysis methods with some use cases in the business world: 

A. Quantitative Methods 

To put it simply, quantitative analysis refers to all methods that use numerical data or data that can be turned into numbers (e.g. category variables like gender, age, etc.) to extract valuable insights. It is used to extract valuable conclusions about relationships, differences, and test hypotheses. Below we discuss some of the key quantitative methods. 

1. Cluster analysis

The action of grouping a set of data elements in a way that said elements are more similar (in a particular sense) to each other than to those in other groups – hence the term ‘cluster.’ Since there is no target variable when clustering, the method is often used to find hidden patterns in the data. The approach is also used to provide additional context to a trend or dataset.

Let's look at it from an organizational perspective. In a perfect world, marketers would be able to analyze each customer separately and give them the best-personalized service, but let's face it, with a large customer base, it is timely impossible to do that. That's where clustering comes in. By grouping customers into clusters based on demographics, purchasing behaviors, monetary value, or any other factor that might be relevant for your company, you will be able to immediately optimize your efforts and give your customers the best experience based on their needs.

2. Cohort analysis

This type of data analysis approach uses historical data to examine and compare a determined segment of users' behavior, which can then be grouped with others with similar characteristics. By using this methodology, it's possible to gain a wealth of insight into consumer needs or a firm understanding of a broader target group.

Cohort analysis can be really useful for performing analysis in marketing as it will allow you to understand the impact of your campaigns on specific groups of customers. To exemplify, imagine you send an email campaign encouraging customers to sign up for your site. For this, you create two versions of the campaign with different designs, CTAs, and ad content. Later on, you can use cohort analysis to track the performance of the campaign for a longer period of time and understand which type of content is driving your customers to sign up, repurchase, or engage in other ways.  

A useful tool to start performing cohort analysis method is Google Analytics. You can learn more about the benefits and limitations of using cohorts in GA in this useful guide . In the bottom image, you see an example of how you visualize a cohort in this tool. The segments (devices traffic) are divided into date cohorts (usage of devices) and then analyzed week by week to extract insights into performance.

3. Regression analysis

Regression uses historical data to understand how a dependent variable's value is affected when one (linear regression) or more independent variables (multiple regression) change or stay the same. By understanding each variable's relationship and how it developed in the past, you can anticipate possible outcomes and make better decisions in the future.

Let's bring it down with an example. Imagine you did a regression analysis of your sales in 2019 and discovered that variables like product quality, store design, customer service, marketing campaigns, and sales channels affected the overall result. Now you want to use regression to analyze which of these variables changed or if any new ones appeared during 2020. For example, you couldn’t sell as much in your physical store due to COVID lockdowns. Therefore, your sales could’ve either dropped in general or increased in your online channels. Through this, you can understand which independent variables affected the overall performance of your dependent variable, annual sales.

If you want to go deeper into this type of analysis, check out this article and learn more about how you can benefit from regression.

4. Neural networks

The neural network forms the basis for the intelligent algorithms of machine learning. It is a form of analytics that attempts, with minimal intervention, to understand how the human brain would generate insights and predict values. Neural networks learn from each and every data transaction, meaning that they evolve and advance over time.

A typical area of application for neural networks is predictive analytics. There are BI reporting tools that have this feature implemented within them, such as the Predictive Analytics Tool from datapine. This tool enables users to quickly and easily generate all kinds of predictions. All you have to do is select the data to be processed based on your KPIs, and the software automatically calculates forecasts based on historical and current data. Thanks to its user-friendly interface, anyone in your organization can manage it; there’s no need to be an advanced scientist. 

Here is an example of how you can use the predictive analysis tool from datapine:

**click to enlarge**

5. Factor analysis

The factor analysis also called “dimension reduction” is a type of data analysis used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. The aim here is to uncover independent latent variables, an ideal method for streamlining specific segments.

A good way to understand this data analysis method is a customer evaluation of a product. The initial assessment is based on different variables like color, shape, wearability, current trends, materials, comfort, the place where they bought the product, and frequency of usage. Like this, the list can be endless, depending on what you want to track. In this case, factor analysis comes into the picture by summarizing all of these variables into homogenous groups, for example, by grouping the variables color, materials, quality, and trends into a brother latent variable of design.

If you want to start analyzing data using factor analysis we recommend you take a look at this practical guide from UCLA.

6. Data mining

A method of data analysis that is the umbrella term for engineering metrics and insights for additional value, direction, and context. By using exploratory statistical evaluation, data mining aims to identify dependencies, relations, patterns, and trends to generate advanced knowledge.  When considering how to analyze data, adopting a data mining mindset is essential to success - as such, it’s an area that is worth exploring in greater detail.

An excellent use case of data mining is datapine intelligent data alerts . With the help of artificial intelligence and machine learning, they provide automated signals based on particular commands or occurrences within a dataset. For example, if you’re monitoring supply chain KPIs , you could set an intelligent alarm to trigger when invalid or low-quality data appears. By doing so, you will be able to drill down deep into the issue and fix it swiftly and effectively.

In the following picture, you can see how the intelligent alarms from datapine work. By setting up ranges on daily orders, sessions, and revenues, the alarms will notify you if the goal was not completed or if it exceeded expectations.

7. Time series analysis

As its name suggests, time series analysis is used to analyze a set of data points collected over a specified period of time. Although analysts use this method to monitor the data points in a specific interval of time rather than just monitoring them intermittently, the time series analysis is not uniquely used for the purpose of collecting data over time. Instead, it allows researchers to understand if variables changed during the duration of the study, how the different variables are dependent, and how did it reach the end result. 

In a business context, this method is used to understand the causes of different trends and patterns to extract valuable insights. Another way of using this method is with the help of time series forecasting. Powered by predictive technologies, businesses can analyze various data sets over a period of time and forecast different future events. 

A great use case to put time series analysis into perspective is seasonality effects on sales. By using time series forecasting to analyze sales data of a specific product over time, you can understand if sales rise over a specific period of time (e.g. swimwear during summertime, or candy during Halloween). These insights allow you to predict demand and prepare production accordingly.  

8. Decision Trees 

The decision tree analysis aims to act as a support tool to make smart and strategic decisions. By visually displaying potential outcomes, consequences, and costs in a tree-like model, researchers and company users can easily evaluate all factors involved and choose the best course of action. Decision trees are helpful to analyze quantitative data and they allow for an improved decision-making process by helping you spot improvement opportunities, reduce costs, and enhance operational efficiency and production.

But how does a decision tree actually works? This method works like a flowchart that starts with the main decision that you need to make and branches out based on the different outcomes and consequences of each decision. Each outcome will outline its own consequences, costs, and gains and, at the end of the analysis, you can compare each of them and make the smartest decision. 

Businesses can use them to understand which project is more cost-effective and will bring more earnings in the long run. For example, imagine you need to decide if you want to update your software app or build a new app entirely.  Here you would compare the total costs, the time needed to be invested, potential revenue, and any other factor that might affect your decision.  In the end, you would be able to see which of these two options is more realistic and attainable for your company or research.

9. Conjoint analysis 

Last but not least, we have the conjoint analysis. This approach is usually used in surveys to understand how individuals value different attributes of a product or service and it is one of the most effective methods to extract consumer preferences. When it comes to purchasing, some clients might be more price-focused, others more features-focused, and others might have a sustainable focus. Whatever your customer's preferences are, you can find them with conjoint analysis. Through this, companies can define pricing strategies, packaging options, subscription packages, and more. 

A great example of conjoint analysis is in marketing and sales. For instance, a cupcake brand might use conjoint analysis and find that its clients prefer gluten-free options and cupcakes with healthier toppings over super sugary ones. Thus, the cupcake brand can turn these insights into advertisements and promotions to increase sales of this particular type of product. And not just that, conjoint analysis can also help businesses segment their customers based on their interests. This allows them to send different messaging that will bring value to each of the segments. 

10. Correspondence Analysis

Also known as reciprocal averaging, correspondence analysis is a method used to analyze the relationship between categorical variables presented within a contingency table. A contingency table is a table that displays two (simple correspondence analysis) or more (multiple correspondence analysis) categorical variables across rows and columns that show the distribution of the data, which is usually answers to a survey or questionnaire on a specific topic. 

This method starts by calculating an “expected value” which is done by multiplying row and column averages and dividing it by the overall original value of the specific table cell. The “expected value” is then subtracted from the original value resulting in a “residual number” which is what allows you to extract conclusions about relationships and distribution. The results of this analysis are later displayed using a map that represents the relationship between the different values. The closest two values are in the map, the bigger the relationship. Let’s put it into perspective with an example. 

Imagine you are carrying out a market research analysis about outdoor clothing brands and how they are perceived by the public. For this analysis, you ask a group of people to match each brand with a certain attribute which can be durability, innovation, quality materials, etc. When calculating the residual numbers, you can see that brand A has a positive residual for innovation but a negative one for durability. This means that brand A is not positioned as a durable brand in the market, something that competitors could take advantage of. 

11. Multidimensional Scaling (MDS)

MDS is a method used to observe the similarities or disparities between objects which can be colors, brands, people, geographical coordinates, and more. The objects are plotted using an “MDS map” that positions similar objects together and disparate ones far apart. The (dis) similarities between objects are represented using one or more dimensions that can be observed using a numerical scale. For example, if you want to know how people feel about the COVID-19 vaccine, you can use 1 for “don’t believe in the vaccine at all”  and 10 for “firmly believe in the vaccine” and a scale of 2 to 9 for in between responses.  When analyzing an MDS map the only thing that matters is the distance between the objects, the orientation of the dimensions is arbitrary and has no meaning at all. 

Multidimensional scaling is a valuable technique for market research, especially when it comes to evaluating product or brand positioning. For instance, if a cupcake brand wants to know how they are positioned compared to competitors, it can define 2-3 dimensions such as taste, ingredients, shopping experience, or more, and do a multidimensional scaling analysis to find improvement opportunities as well as areas in which competitors are currently leading. 

Another business example is in procurement when deciding on different suppliers. Decision makers can generate an MDS map to see how the different prices, delivery times, technical services, and more of the different suppliers differ and pick the one that suits their needs the best. 

A final example proposed by a research paper on "An Improved Study of Multilevel Semantic Network Visualization for Analyzing Sentiment Word of Movie Review Data". Researchers picked a two-dimensional MDS map to display the distances and relationships between different sentiments in movie reviews. They used 36 sentiment words and distributed them based on their emotional distance as we can see in the image below where the words "outraged" and "sweet" are on opposite sides of the map, marking the distance between the two emotions very clearly.

Aside from being a valuable technique to analyze dissimilarities, MDS also serves as a dimension-reduction technique for large dimensional data. 

B. Qualitative Methods

Qualitative data analysis methods are defined as the observation of non-numerical data that is gathered and produced using methods of observation such as interviews, focus groups, questionnaires, and more. As opposed to quantitative methods, qualitative data is more subjective and highly valuable in analyzing customer retention and product development.

12. Text analysis

Text analysis, also known in the industry as text mining, works by taking large sets of textual data and arranging them in a way that makes it easier to manage. By working through this cleansing process in stringent detail, you will be able to extract the data that is truly relevant to your organization and use it to develop actionable insights that will propel you forward.

Modern software accelerate the application of text analytics. Thanks to the combination of machine learning and intelligent algorithms, you can perform advanced analytical processes such as sentiment analysis. This technique allows you to understand the intentions and emotions of a text, for example, if it's positive, negative, or neutral, and then give it a score depending on certain factors and categories that are relevant to your brand. Sentiment analysis is often used to monitor brand and product reputation and to understand how successful your customer experience is. To learn more about the topic check out this insightful article .

By analyzing data from various word-based sources, including product reviews, articles, social media communications, and survey responses, you will gain invaluable insights into your audience, as well as their needs, preferences, and pain points. This will allow you to create campaigns, services, and communications that meet your prospects’ needs on a personal level, growing your audience while boosting customer retention. There are various other “sub-methods” that are an extension of text analysis. Each of them serves a more specific purpose and we will look at them in detail next. 

13. Content Analysis

This is a straightforward and very popular method that examines the presence and frequency of certain words, concepts, and subjects in different content formats such as text, image, audio, or video. For example, the number of times the name of a celebrity is mentioned on social media or online tabloids. It does this by coding text data that is later categorized and tabulated in a way that can provide valuable insights, making it the perfect mix of quantitative and qualitative analysis.

There are two types of content analysis. The first one is the conceptual analysis which focuses on explicit data, for instance, the number of times a concept or word is mentioned in a piece of content. The second one is relational analysis, which focuses on the relationship between different concepts or words and how they are connected within a specific context. 

Content analysis is often used by marketers to measure brand reputation and customer behavior. For example, by analyzing customer reviews. It can also be used to analyze customer interviews and find directions for new product development. It is also important to note, that in order to extract the maximum potential out of this analysis method, it is necessary to have a clearly defined research question. 

14. Thematic Analysis

Very similar to content analysis, thematic analysis also helps in identifying and interpreting patterns in qualitative data with the main difference being that the first one can also be applied to quantitative analysis. The thematic method analyzes large pieces of text data such as focus group transcripts or interviews and groups them into themes or categories that come up frequently within the text. It is a great method when trying to figure out peoples view’s and opinions about a certain topic. For example, if you are a brand that cares about sustainability, you can do a survey of your customers to analyze their views and opinions about sustainability and how they apply it to their lives. You can also analyze customer service calls transcripts to find common issues and improve your service. 

Thematic analysis is a very subjective technique that relies on the researcher’s judgment. Therefore,  to avoid biases, it has 6 steps that include familiarization, coding, generating themes, reviewing themes, defining and naming themes, and writing up. It is also important to note that, because it is a flexible approach, the data can be interpreted in multiple ways and it can be hard to select what data is more important to emphasize. 

15. Narrative Analysis 

A bit more complex in nature than the two previous ones, narrative analysis is used to explore the meaning behind the stories that people tell and most importantly, how they tell them. By looking into the words that people use to describe a situation you can extract valuable conclusions about their perspective on a specific topic. Common sources for narrative data include autobiographies, family stories, opinion pieces, and testimonials, among others. 

From a business perspective, narrative analysis can be useful to analyze customer behaviors and feelings towards a specific product, service, feature, or others. It provides unique and deep insights that can be extremely valuable. However, it has some drawbacks.  

The biggest weakness of this method is that the sample sizes are usually very small due to the complexity and time-consuming nature of the collection of narrative data. Plus, the way a subject tells a story will be significantly influenced by his or her specific experiences, making it very hard to replicate in a subsequent study. 

16. Discourse Analysis

Discourse analysis is used to understand the meaning behind any type of written, verbal, or symbolic discourse based on its political, social, or cultural context. It mixes the analysis of languages and situations together. This means that the way the content is constructed and the meaning behind it is significantly influenced by the culture and society it takes place in. For example, if you are analyzing political speeches you need to consider different context elements such as the politician's background, the current political context of the country, the audience to which the speech is directed, and so on. 

From a business point of view, discourse analysis is a great market research tool. It allows marketers to understand how the norms and ideas of the specific market work and how their customers relate to those ideas. It can be very useful to build a brand mission or develop a unique tone of voice. 

17. Grounded Theory Analysis

Traditionally, researchers decide on a method and hypothesis and start to collect the data to prove that hypothesis. The grounded theory is the only method that doesn’t require an initial research question or hypothesis as its value lies in the generation of new theories. With the grounded theory method, you can go into the analysis process with an open mind and explore the data to generate new theories through tests and revisions. In fact, it is not necessary to collect the data and then start to analyze it. Researchers usually start to find valuable insights as they are gathering the data. 

All of these elements make grounded theory a very valuable method as theories are fully backed by data instead of initial assumptions. It is a great technique to analyze poorly researched topics or find the causes behind specific company outcomes. For example, product managers and marketers might use the grounded theory to find the causes of high levels of customer churn and look into customer surveys and reviews to develop new theories about the causes. 

How To Analyze Data? Top 17 Data Analysis Techniques To Apply

Now that we’ve answered the questions “what is data analysis’”, why is it important, and covered the different data analysis types, it’s time to dig deeper into how to perform your analysis by working through these 17 essential techniques.

1. Collaborate your needs

Before you begin analyzing or drilling down into any techniques, it’s crucial to sit down collaboratively with all key stakeholders within your organization, decide on your primary campaign or strategic goals, and gain a fundamental understanding of the types of insights that will best benefit your progress or provide you with the level of vision you need to evolve your organization.

2. Establish your questions

Once you’ve outlined your core objectives, you should consider which questions will need answering to help you achieve your mission. This is one of the most important techniques as it will shape the very foundations of your success.

To help you ask the right things and ensure your data works for you, you have to ask the right data analysis questions .

3. Data democratization

After giving your data analytics methodology some real direction, and knowing which questions need answering to extract optimum value from the information available to your organization, you should continue with democratization.

Data democratization is an action that aims to connect data from various sources efficiently and quickly so that anyone in your organization can access it at any given moment. You can extract data in text, images, videos, numbers, or any other format. And then perform cross-database analysis to achieve more advanced insights to share with the rest of the company interactively.  

Once you have decided on your most valuable sources, you need to take all of this into a structured format to start collecting your insights. For this purpose, datapine offers an easy all-in-one data connectors feature to integrate all your internal and external sources and manage them at your will. Additionally, datapine’s end-to-end solution automatically updates your data, allowing you to save time and focus on performing the right analysis to grow your company.

4. Think of governance 

When collecting data in a business or research context you always need to think about security and privacy. With data breaches becoming a topic of concern for businesses, the need to protect your client's or subject’s sensitive information becomes critical. 

To ensure that all this is taken care of, you need to think of a data governance strategy. According to Gartner , this concept refers to “ the specification of decision rights and an accountability framework to ensure the appropriate behavior in the valuation, creation, consumption, and control of data and analytics .” In simpler words, data governance is a collection of processes, roles, and policies, that ensure the efficient use of data while still achieving the main company goals. It ensures that clear roles are in place for who can access the information and how they can access it. In time, this not only ensures that sensitive information is protected but also allows for an efficient analysis as a whole. 

5. Clean your data

After harvesting from so many sources you will be left with a vast amount of information that can be overwhelming to deal with. At the same time, you can be faced with incorrect data that can be misleading to your analysis. The smartest thing you can do to avoid dealing with this in the future is to clean the data. This is fundamental before visualizing it, as it will ensure that the insights you extract from it are correct.

There are many things that you need to look for in the cleaning process. The most important one is to eliminate any duplicate observations; this usually appears when using multiple internal and external sources of information. You can also add any missing codes, fix empty fields, and eliminate incorrectly formatted data.

Another usual form of cleaning is done with text data. As we mentioned earlier, most companies today analyze customer reviews, social media comments, questionnaires, and several other text inputs. In order for algorithms to detect patterns, text data needs to be revised to avoid invalid characters or any syntax or spelling errors. 

Most importantly, the aim of cleaning is to prevent you from arriving at false conclusions that can damage your company in the long run. By using clean data, you will also help BI solutions to interact better with your information and create better reports for your organization.

6. Set your KPIs

Once you’ve set your sources, cleaned your data, and established clear-cut questions you want your insights to answer, you need to set a host of key performance indicators (KPIs) that will help you track, measure, and shape your progress in a number of key areas.

KPIs are critical to both qualitative and quantitative analysis research. This is one of the primary methods of data analysis you certainly shouldn’t overlook.

To help you set the best possible KPIs for your initiatives and activities, here is an example of a relevant logistics KPI : transportation-related costs. If you want to see more go explore our collection of key performance indicator examples .

7. Omit useless data

Having bestowed your data analysis tools and techniques with true purpose and defined your mission, you should explore the raw data you’ve collected from all sources and use your KPIs as a reference for chopping out any information you deem to be useless.

Trimming the informational fat is one of the most crucial methods of analysis as it will allow you to focus your analytical efforts and squeeze every drop of value from the remaining ‘lean’ information.

Any stats, facts, figures, or metrics that don’t align with your business goals or fit with your KPI management strategies should be eliminated from the equation.

8. Build a data management roadmap

While, at this point, this particular step is optional (you will have already gained a wealth of insight and formed a fairly sound strategy by now), creating a data governance roadmap will help your data analysis methods and techniques become successful on a more sustainable basis. These roadmaps, if developed properly, are also built so they can be tweaked and scaled over time.

Invest ample time in developing a roadmap that will help you store, manage, and handle your data internally, and you will make your analysis techniques all the more fluid and functional – one of the most powerful types of data analysis methods available today.

9. Integrate technology

There are many ways to analyze data, but one of the most vital aspects of analytical success in a business context is integrating the right decision support software and technology.

Robust analysis platforms will not only allow you to pull critical data from your most valuable sources while working with dynamic KPIs that will offer you actionable insights; it will also present them in a digestible, visual, interactive format from one central, live dashboard . A data methodology you can count on.

By integrating the right technology within your data analysis methodology, you’ll avoid fragmenting your insights, saving you time and effort while allowing you to enjoy the maximum value from your business’s most valuable insights.

For a look at the power of software for the purpose of analysis and to enhance your methods of analyzing, glance over our selection of dashboard examples .

10. Answer your questions

By considering each of the above efforts, working with the right technology, and fostering a cohesive internal culture where everyone buys into the different ways to analyze data as well as the power of digital intelligence, you will swiftly start to answer your most burning business questions. Arguably, the best way to make your data concepts accessible across the organization is through data visualization.

11. Visualize your data

Online data visualization is a powerful tool as it lets you tell a story with your metrics, allowing users across the organization to extract meaningful insights that aid business evolution – and it covers all the different ways to analyze data.

The purpose of analyzing is to make your entire organization more informed and intelligent, and with the right platform or dashboard, this is simpler than you think, as demonstrated by our marketing dashboard .

This visual, dynamic, and interactive online dashboard is a data analysis example designed to give Chief Marketing Officers (CMO) an overview of relevant metrics to help them understand if they achieved their monthly goals.

In detail, this example generated with a modern dashboard creator displays interactive charts for monthly revenues, costs, net income, and net income per customer; all of them are compared with the previous month so that you can understand how the data fluctuated. In addition, it shows a detailed summary of the number of users, customers, SQLs, and MQLs per month to visualize the whole picture and extract relevant insights or trends for your marketing reports .

The CMO dashboard is perfect for c-level management as it can help them monitor the strategic outcome of their marketing efforts and make data-driven decisions that can benefit the company exponentially.

12. Be careful with the interpretation

We already dedicated an entire post to data interpretation as it is a fundamental part of the process of data analysis. It gives meaning to the analytical information and aims to drive a concise conclusion from the analysis results. Since most of the time companies are dealing with data from many different sources, the interpretation stage needs to be done carefully and properly in order to avoid misinterpretations. 

To help you through the process, here we list three common practices that you need to avoid at all costs when looking at your data:

• Correlation vs. causation: The human brain is formatted to find patterns. This behavior leads to one of the most common mistakes when performing interpretation: confusing correlation with causation. Although these two aspects can exist simultaneously, it is not correct to assume that because two things happened together, one provoked the other. A piece of advice to avoid falling into this mistake is never to trust just intuition, trust the data. If there is no objective evidence of causation, then always stick to correlation. 
• Confirmation bias: This phenomenon describes the tendency to select and interpret only the data necessary to prove one hypothesis, often ignoring the elements that might disprove it. Even if it's not done on purpose, confirmation bias can represent a real problem, as excluding relevant information can lead to false conclusions and, therefore, bad business decisions. To avoid it, always try to disprove your hypothesis instead of proving it, share your analysis with other team members, and avoid drawing any conclusions before the entire analytical project is finalized.
• Statistical significance: To put it in short words, statistical significance helps analysts understand if a result is actually accurate or if it happened because of a sampling error or pure chance. The level of statistical significance needed might depend on the sample size and the industry being analyzed. In any case, ignoring the significance of a result when it might influence decision-making can be a huge mistake.

13. Build a narrative

Now, we’re going to look at how you can bring all of these elements together in a way that will benefit your business - starting with a little something called data storytelling.

The human brain responds incredibly well to strong stories or narratives. Once you’ve cleansed, shaped, and visualized your most invaluable data using various BI dashboard tools , you should strive to tell a story - one with a clear-cut beginning, middle, and end.

By doing so, you will make your analytical efforts more accessible, digestible, and universal, empowering more people within your organization to use your discoveries to their actionable advantage.

14. Consider autonomous technology

Autonomous technologies, such as artificial intelligence (AI) and machine learning (ML), play a significant role in the advancement of understanding how to analyze data more effectively.

Gartner predicts that by the end of this year, 80% of emerging technologies will be developed with AI foundations. This is a testament to the ever-growing power and value of autonomous technologies.

At the moment, these technologies are revolutionizing the analysis industry. Some examples that we mentioned earlier are neural networks, intelligent alarms, and sentiment analysis.

15. Share the load

If you work with the right tools and dashboards, you will be able to present your metrics in a digestible, value-driven format, allowing almost everyone in the organization to connect with and use relevant data to their advantage.

Modern dashboards consolidate data from various sources, providing access to a wealth of insights in one centralized location, no matter if you need to monitor recruitment metrics or generate reports that need to be sent across numerous departments. Moreover, these cutting-edge tools offer access to dashboards from a multitude of devices, meaning that everyone within the business can connect with practical insights remotely - and share the load.

Once everyone is able to work with a data-driven mindset, you will catalyze the success of your business in ways you never thought possible. And when it comes to knowing how to analyze data, this kind of collaborative approach is essential.

16. Data analysis tools

In order to perform high-quality analysis of data, it is fundamental to use tools and software that will ensure the best results. Here we leave you a small summary of four fundamental categories of data analysis tools for your organization.

• Business Intelligence: BI tools allow you to process significant amounts of data from several sources in any format. Through this, you can not only analyze and monitor your data to extract relevant insights but also create interactive reports and dashboards to visualize your KPIs and use them for your company's good. datapine is an amazing online BI software that is focused on delivering powerful online analysis features that are accessible to beginner and advanced users. Like this, it offers a full-service solution that includes cutting-edge analysis of data, KPIs visualization, live dashboards, reporting, and artificial intelligence technologies to predict trends and minimize risk.
• Statistical analysis: These tools are usually designed for scientists, statisticians, market researchers, and mathematicians, as they allow them to perform complex statistical analyses with methods like regression analysis, predictive analysis, and statistical modeling. A good tool to perform this type of analysis is R-Studio as it offers a powerful data modeling and hypothesis testing feature that can cover both academic and general data analysis. This tool is one of the favorite ones in the industry, due to its capability for data cleaning, data reduction, and performing advanced analysis with several statistical methods. Another relevant tool to mention is SPSS from IBM. The software offers advanced statistical analysis for users of all skill levels. Thanks to a vast library of machine learning algorithms, text analysis, and a hypothesis testing approach it can help your company find relevant insights to drive better decisions. SPSS also works as a cloud service that enables you to run it anywhere.
• SQL Consoles: SQL is a programming language often used to handle structured data in relational databases. Tools like these are popular among data scientists as they are extremely effective in unlocking these databases' value. Undoubtedly, one of the most used SQL software in the market is MySQL Workbench . This tool offers several features such as a visual tool for database modeling and monitoring, complete SQL optimization, administration tools, and visual performance dashboards to keep track of KPIs.
• Data Visualization: These tools are used to represent your data through charts, graphs, and maps that allow you to find patterns and trends in the data. datapine's already mentioned BI platform also offers a wealth of powerful online data visualization tools with several benefits. Some of them include: delivering compelling data-driven presentations to share with your entire company, the ability to see your data online with any device wherever you are, an interactive dashboard design feature that enables you to showcase your results in an interactive and understandable way, and to perform online self-service reports that can be used simultaneously with several other people to enhance team productivity.

17. Refine your process constantly 

Last is a step that might seem obvious to some people, but it can be easily ignored if you think you are done. Once you have extracted the needed results, you should always take a retrospective look at your project and think about what you can improve. As you saw throughout this long list of techniques, data analysis is a complex process that requires constant refinement. For this reason, you should always go one step further and keep improving. 

Quality Criteria For Data Analysis

So far we’ve covered a list of methods and techniques that should help you perform efficient data analysis. But how do you measure the quality and validity of your results? This is done with the help of some science quality criteria. Here we will go into a more theoretical area that is critical to understanding the fundamentals of statistical analysis in science. However, you should also be aware of these steps in a business context, as they will allow you to assess the quality of your results in the correct way. Let’s dig in. 

• Internal validity: The results of a survey are internally valid if they measure what they are supposed to measure and thus provide credible results. In other words , internal validity measures the trustworthiness of the results and how they can be affected by factors such as the research design, operational definitions, how the variables are measured, and more. For instance, imagine you are doing an interview to ask people if they brush their teeth two times a day. While most of them will answer yes, you can still notice that their answers correspond to what is socially acceptable, which is to brush your teeth at least twice a day. In this case, you can’t be 100% sure if respondents actually brush their teeth twice a day or if they just say that they do, therefore, the internal validity of this interview is very low. 
• External validity: Essentially, external validity refers to the extent to which the results of your research can be applied to a broader context. It basically aims to prove that the findings of a study can be applied in the real world. If the research can be applied to other settings, individuals, and times, then the external validity is high. 
• Reliability : If your research is reliable, it means that it can be reproduced. If your measurement were repeated under the same conditions, it would produce similar results. This means that your measuring instrument consistently produces reliable results. For example, imagine a doctor building a symptoms questionnaire to detect a specific disease in a patient. Then, various other doctors use this questionnaire but end up diagnosing the same patient with a different condition. This means the questionnaire is not reliable in detecting the initial disease. Another important note here is that in order for your research to be reliable, it also needs to be objective. If the results of a study are the same, independent of who assesses them or interprets them, the study can be considered reliable. Let’s see the objectivity criteria in more detail now. 
• Objectivity: In data science, objectivity means that the researcher needs to stay fully objective when it comes to its analysis. The results of a study need to be affected by objective criteria and not by the beliefs, personality, or values of the researcher. Objectivity needs to be ensured when you are gathering the data, for example, when interviewing individuals, the questions need to be asked in a way that doesn't influence the results. Paired with this, objectivity also needs to be thought of when interpreting the data. If different researchers reach the same conclusions, then the study is objective. For this last point, you can set predefined criteria to interpret the results to ensure all researchers follow the same steps. 

The discussed quality criteria cover mostly potential influences in a quantitative context. Analysis in qualitative research has by default additional subjective influences that must be controlled in a different way. Therefore, there are other quality criteria for this kind of research such as credibility, transferability, dependability, and confirmability. You can see each of them more in detail on this resource . 

Data Analysis Limitations & Barriers

Analyzing data is not an easy task. As you’ve seen throughout this post, there are many steps and techniques that you need to apply in order to extract useful information from your research. While a well-performed analysis can bring various benefits to your organization it doesn't come without limitations. In this section, we will discuss some of the main barriers you might encounter when conducting an analysis. Let’s see them more in detail. 

• Lack of clear goals: No matter how good your data or analysis might be if you don’t have clear goals or a hypothesis the process might be worthless. While we mentioned some methods that don’t require a predefined hypothesis, it is always better to enter the analytical process with some clear guidelines of what you are expecting to get out of it, especially in a business context in which data is utilized to support important strategic decisions. 
• Objectivity: Arguably one of the biggest barriers when it comes to data analysis in research is to stay objective. When trying to prove a hypothesis, researchers might find themselves, intentionally or unintentionally, directing the results toward an outcome that they want. To avoid this, always question your assumptions and avoid confusing facts with opinions. You can also show your findings to a research partner or external person to confirm that your results are objective. 
• Data representation: A fundamental part of the analytical procedure is the way you represent your data. You can use various graphs and charts to represent your findings, but not all of them will work for all purposes. Choosing the wrong visual can not only damage your analysis but can mislead your audience, therefore, it is important to understand when to use each type of data depending on your analytical goals. Our complete guide on the types of graphs and charts lists 20 different visuals with examples of when to use them. 
• Flawed correlation : Misleading statistics can significantly damage your research. We’ve already pointed out a few interpretation issues previously in the post, but it is an important barrier that we can't avoid addressing here as well. Flawed correlations occur when two variables appear related to each other but they are not. Confusing correlations with causation can lead to a wrong interpretation of results which can lead to building wrong strategies and loss of resources, therefore, it is very important to identify the different interpretation mistakes and avoid them. 
• Sample size: A very common barrier to a reliable and efficient analysis process is the sample size. In order for the results to be trustworthy, the sample size should be representative of what you are analyzing. For example, imagine you have a company of 1000 employees and you ask the question “do you like working here?” to 50 employees of which 49 say yes, which means 95%. Now, imagine you ask the same question to the 1000 employees and 950 say yes, which also means 95%. Saying that 95% of employees like working in the company when the sample size was only 50 is not a representative or trustworthy conclusion. The significance of the results is way more accurate when surveying a bigger sample size.   
• Privacy concerns: In some cases, data collection can be subjected to privacy regulations. Businesses gather all kinds of information from their customers from purchasing behaviors to addresses and phone numbers. If this falls into the wrong hands due to a breach, it can affect the security and confidentiality of your clients. To avoid this issue, you need to collect only the data that is needed for your research and, if you are using sensitive facts, make it anonymous so customers are protected. The misuse of customer data can severely damage a business's reputation, so it is important to keep an eye on privacy. 
• Lack of communication between teams : When it comes to performing data analysis on a business level, it is very likely that each department and team will have different goals and strategies. However, they are all working for the same common goal of helping the business run smoothly and keep growing. When teams are not connected and communicating with each other, it can directly affect the way general strategies are built. To avoid these issues, tools such as data dashboards enable teams to stay connected through data in a visually appealing way. 
• Innumeracy : Businesses are working with data more and more every day. While there are many BI tools available to perform effective analysis, data literacy is still a constant barrier. Not all employees know how to apply analysis techniques or extract insights from them. To prevent this from happening, you can implement different training opportunities that will prepare every relevant user to deal with data. 

Key Data Analysis Skills

As you've learned throughout this lengthy guide, analyzing data is a complex task that requires a lot of knowledge and skills. That said, thanks to the rise of self-service tools the process is way more accessible and agile than it once was. Regardless, there are still some key skills that are valuable to have when working with data, we list the most important ones below.

• Critical and statistical thinking: To successfully analyze data you need to be creative and think out of the box. Yes, that might sound like a weird statement considering that data is often tight to facts. However, a great level of critical thinking is required to uncover connections, come up with a valuable hypothesis, and extract conclusions that go a step further from the surface. This, of course, needs to be complemented by statistical thinking and an understanding of numbers. 
• Data cleaning: Anyone who has ever worked with data before will tell you that the cleaning and preparation process accounts for 80% of a data analyst's work, therefore, the skill is fundamental. But not just that, not cleaning the data adequately can also significantly damage the analysis which can lead to poor decision-making in a business scenario. While there are multiple tools that automate the cleaning process and eliminate the possibility of human error, it is still a valuable skill to dominate. 
• Data visualization: Visuals make the information easier to understand and analyze, not only for professional users but especially for non-technical ones. Having the necessary skills to not only choose the right chart type but know when to apply it correctly is key. This also means being able to design visually compelling charts that make the data exploration process more efficient. 
• SQL: The Structured Query Language or SQL is a programming language used to communicate with databases. It is fundamental knowledge as it enables you to update, manipulate, and organize data from relational databases which are the most common databases used by companies. It is fairly easy to learn and one of the most valuable skills when it comes to data analysis. 
• Communication skills: This is a skill that is especially valuable in a business environment. Being able to clearly communicate analytical outcomes to colleagues is incredibly important, especially when the information you are trying to convey is complex for non-technical people. This applies to in-person communication as well as written format, for example, when generating a dashboard or report. While this might be considered a “soft” skill compared to the other ones we mentioned, it should not be ignored as you most likely will need to share analytical findings with others no matter the context. 

Data Analysis In The Big Data Environment

Big data is invaluable to today’s businesses, and by using different methods for data analysis, it’s possible to view your data in a way that can help you turn insight into positive action.

To inspire your efforts and put the importance of big data into context, here are some insights that you should know:

• By 2026 the industry of big data is expected to be worth approximately $273.4 billion.
• 94% of enterprises say that analyzing data is important for their growth and digital transformation. 
• Companies that exploit the full potential of their data can increase their operating margins by 60% .
• We already told you the benefits of Artificial Intelligence through this article. This industry's financial impact is expected to grow up to $40 billion by 2025.

Data analysis concepts may come in many forms, but fundamentally, any solid methodology will help to make your business more streamlined, cohesive, insightful, and successful than ever before.

Key Takeaways From Data Analysis 

As we reach the end of our data analysis journey, we leave a small summary of the main methods and techniques to perform excellent analysis and grow your business.

17 Essential Types of Data Analysis Methods:

• Cluster analysis
• Cohort analysis
• Regression analysis
• Factor analysis
• Neural Networks
• Data Mining
• Text analysis
• Time series analysis
• Decision trees
• Conjoint analysis 
• Correspondence Analysis
• Multidimensional Scaling 
• Content analysis 
• Thematic analysis
• Narrative analysis 
• Grounded theory analysis
• Discourse analysis 

Top 17 Data Analysis Techniques:

• Collaborate your needs
• Establish your questions
• Data democratization
• Think of data governance 
• Clean your data
• Set your KPIs
• Omit useless data
• Build a data management roadmap
• Integrate technology
• Answer your questions
• Visualize your data
• Interpretation of data
• Consider autonomous technology
• Build a narrative
• Share the load
• Data Analysis tools
• Refine your process constantly 

We’ve pondered the data analysis definition and drilled down into the practical applications of data-centric analytics, and one thing is clear: by taking measures to arrange your data and making your metrics work for you, it’s possible to transform raw information into action - the kind of that will push your business to the next level.

Yes, good data analytics techniques result in enhanced business intelligence (BI). To help you understand this notion in more detail, read our exploration of business intelligence reporting .

And, if you’re ready to perform your own analysis, drill down into your facts and figures while interacting with your data on astonishing visuals, you can try our software for a free, 14-day trial .

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Table of contents

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

• Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
• Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
• Null hypothesis: Parental income and GPA have no relationship with each other in college students.
• Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

• In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
• In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
• In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

• In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
• In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
• In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
• Experimental
• Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

• Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
• Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

• Probability sampling: every member of the population has a chance of being selected for the study through random selection.
• Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

• your sample is representative of the population you’re generalising your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

• Will you have resources to advertise your study widely, including outside of your university setting?
• Will you have the means to recruit a diverse sample that represents a broad population?
• Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

• Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
• Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
• Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
• Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

• Organising data from each variable in frequency distribution tables .
• Displaying data from a key variable in a bar chart to view the distribution of responses.
• Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

• Mode : the most popular response or value in the data set.
• Median : the value in the exact middle of the data set when ordered from low to high.
• Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

• Range : the highest value minus the lowest value of the data set.
• Interquartile range : the range of the middle half of the data set.
• Standard deviation : the average distance between each value in your data set and the mean.
• Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

• Estimation: calculating population parameters based on sample statistics.
• Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

• A point estimate : a value that represents your best guess of the exact parameter.
• An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

• A test statistic tells you how much your data differs from the null hypothesis of the test.
• A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

• Comparison tests assess group differences in outcomes.
• Regression tests assess cause-and-effect relationships between variables.
• Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

• A simple linear regression includes one predictor variable and one outcome variable.
• A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

• A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
• A z test is for exactly 1 or 2 groups when the sample is large.
• An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

• If you have only one sample that you want to compare to a population mean, use a one-sample test .
• If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
• If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
• If you expect a difference between groups in a specific direction, use a one-tailed test .
• If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

• a t value (test statistic) of 3.00
• a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

• a t value of 3.08
• a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
• If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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• Central Limit Theorem | Formula, Definition & Examples
• Central Tendency | Understanding the Mean, Median & Mode
• Correlation Coefficient | Types, Formulas & Examples
• Descriptive Statistics | Definitions, Types, Examples
• How to Calculate Standard Deviation (Guide) | Calculator & Examples
• How to Calculate Variance | Calculator, Analysis & Examples
• How to Find Degrees of Freedom | Definition & Formula
• How to Find Interquartile Range (IQR) | Calculator & Examples
• How to Find Outliers | Meaning, Formula & Examples
• How to Find the Geometric Mean | Calculator & Formula
• How to Find the Mean | Definition, Examples & Calculator
• How to Find the Median | Definition, Examples & Calculator
• How to Find the Range of a Data Set | Calculator & Formula
• Inferential Statistics | An Easy Introduction & Examples
• Levels of measurement: Nominal, ordinal, interval, ratio
• Missing Data | Types, Explanation, & Imputation
• Normal Distribution | Examples, Formulas, & Uses
• Null and Alternative Hypotheses | Definitions & Examples
• Poisson Distributions | Definition, Formula & Examples
• Skewness | Definition, Examples & Formula
• T-Distribution | What It Is and How To Use It (With Examples)
• The Standard Normal Distribution | Calculator, Examples & Uses
• Type I & Type II Errors | Differences, Examples, Visualizations
• Understanding Confidence Intervals | Easy Examples & Formulas
• Variability | Calculating Range, IQR, Variance, Standard Deviation
• What is Effect Size and Why Does It Matter? (Examples)
• What Is Interval Data? | Examples & Definition
• What Is Nominal Data? | Examples & Definition
• What Is Ordinal Data? | Examples & Definition
• What Is Ratio Data? | Examples & Definition
• What Is the Mode in Statistics? | Definition, Examples & Calculator

Statistical Analysis | Overview, Methods & Examples

Dr. Aamir Fidai has taught Algebra 2, Precalculus, and Calculus to high school students for over 10 years. Dr. Fidai has a Ph.D. in Curriculum and Instruction from Texas A&M University where he also taught Mathematics Education courses to pre-service elementary school teachers.

David holds a Master of Arts in Education

Table of Contents

What is statistical analysis, basic statistical analysis, statistical analysis methods, statistical analysis examples, lesson summary, what are the 5 basic methods of statistical analysis.

The five basic methods of statistical analysis are descriptive, inferential, exploratory, causal, and predictive analysis. Of these methods, descriptive and inferential analysis are most commonly used.

What are the three types of statistical analysis?

There are many different types of statistical analysis. The three major statistical analysis methods are descriptive, inferential, and exploratory analysis. These three are the most commonly used statistical methods.

What is statistical analysis and why is it important?

Statistical analysis is used to make decisions in real-life situations using data. Statistical analysis allows us to identify patterns, look for cause and effect relationships, and predict future behavior based on past or experimental data.

What is statistical analysis? Statistical analysis is the process of analyzing data collected through observation and/or experiments to arrive at decisions. Researchers in all academic fields and industry undertake statistical analysis to answer questions, develop cause and effect relationships, identify patterns, and develop further research ideas. Statistical analysis is routinely used in agriculture, arts and literature, biology, business and economics, education, entertainment, environment, finance, food/drink, games, health, law, media, psychology, politics, and many other fields.

The process of statistical analysis is defined as studying data to answer questions about the relationship between real-life events. The study of data collected through observation can help:

• establish cause and effect relationships
• predict future behavior
• suggest solutions
• identify patterns
• look for changes in behavior

Examples: Statistical analysis of data enables us to make important decisions in real-life situations. Statistical analysis is used in all aspects of life and business to evaluate the patterns in data to explore possible relationships, to determine cause and effects, to identify patterns, and to predict possible outcomes. Some examples of data analysis include:

• Drug manufacturers analyzing vaccine data for efficacy
• Teacher analyzing student scores data for lesson effectiveness
• Researcher analyzing poverty and crime data for causal inferences
• Learning center analyzing income and education data for exploring future business opportunities

Types of Statistical Analysis:

There are three major types of statistical analysis: descriptive, inferential, and exploratory.

• Descriptive analysis of data provides us with information about the central tendencies of the data as well as the measures of dispersion of the data. Central tendencies of data include mean, median, and mode. Mean is the average value, median is the middle value of the ordered data, and mode is the data value that appears the most. Measures of dispersion of data include, range, interquartile range, mean deviation and standard deviation.
• Inferential analysis of data is conducted when we are trying to find cause and effect relationships within and between data sets. Inferential statistics are induction based statistics and allow us to make inferences about the population by examining the sample.
• Exploratory analysis of data is concerned with exploring data using multiple representation of data (i.e., graphs, stem and leaf diagrams, histograms. Exploratory data analysis is usually done before descriptive and inferential data analysis to develop useful hypothesis for testing.

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• 0:04 Definition of…
• 0:37 The Mean
• 1:38 Standard Deviation
• 2:28 Regression
• 3:20 Sample Size and…
• 5:02 Lesson Summary

The process of conducting basic statistical analysis generally has six steps. Establishing a hypothesis, considering the variables and conducting an experiment, collecting data, conducting descriptive statistics to summarize the resulting data, using inferential statistics to test the hypothesis, and interpreting the results.

• Writing Hypothesis: A hypothesis is a proposition that is tested using an experiment or data. For example, a teacher may hypothesize that engaging students in more technology learning activities can result in better test scores.
• Considering variables and conducting an experiment : There are usually two or more variables involved in statistical analysis, the predictor or independent (cause) and the outcome or dependent (effect). For example, time spent in class doing technology activities is the predictor variable while the test score is the outcome variable.
• Collecting data: Once the experiment is conducted, the data is collected for all variables, directly and indirectly, involved in the experiment. For example, time spent on the technology activity and the test score are two variables directly involved in the experiment, but there may be other variables acting on the student scores such as time of the day, age of the students, etc.
• Conducting descriptive statistical analysis: Once the data is collected, conducting the descriptive analysis can provide summary information about the central and dispersion tendencies of the data such as mean, median, mode, range, interquartile range, distribution, variance, and standard deviation.
• Conducting inferential analysis to test the hypothesis: The data collected from the experiment can also be used to test the hypothesis and conduct inferential analysis. For example, the teacher interested in the effects of technology learning can compare the test score data for students engaged in technology learning with the test score data for students who did not engage in technology learning to infer the effects of the use of technology learning in the classroom.
• Interpreting results: Using the descriptive statistics and the results from hypothesis testing using inferential statistical analysis, researchers can interpret the results of the experiment to establish the effectiveness of the use of technology learning in the classroom. If the results show that test scores for students who used technology learning went up compared to those who did not use technology learning, then the hypothesis would be rejected, otherwise, the researcher would fail to reject the hypothesis.

What is statistical method? Statistical analysis methods that have been developed over the centuries and more recent computer-based statistical techniques allow us to analyze the data and make important decisions. There are five major statistical methods to consider when conducting statistical analysis: mean, standard deviation, regression, sample size, and hypothesis testing.

The mean or average value of a data set provides us with information about the central tendency of a data set. Mean is different from median as the mean is the average value of the data set while the median is the value in the data set that happens to be in the middle of all ordered data values. Similarly, the mean is also different from the mode because the mode is the value in the data set that appears the most times.

To calculate the mean value of a data set add all the individual values in the data set and then divide them by the total number of values in the data set.

$$\frac{\sum (x_i)}{n} $$

For example, test scores for ten students in class A were 70, 70, 80, 80, 90, 90, 60, 70, 80, 90. The sum of their scores is 780. Dividing 780 by 10 gives us the mean value of 78.

Sometimes, the data set would contain extreme values that are too high or too low when compared to the other values in the data set. These extreme values are called Outliers . The outlier values can be valid data points or they can be a result of erroneous data collection. Outliers can affect the calculation of mean, median, and range. When faced with an outlier, you must decide if you are going to include the outlier values in the calculation or not. This decision is not a simple one and should be made after a proper investigation of the entire data set and the circumstances under which the data was collected.

Mean, median, and mode are measures of central tendency and are often used when conducting descriptive statistical analysis. However, mean, median, and mode are three distinct statistical concept. While mean informs us about the average value of the data set, median only tells us the data value that is in the middle of the ordered data set. Mode is the data value that appears the most number of times in the data set. In terms of information, mean provides us with the most information while median and mode provide us with little to no information about the data set.

Standard Deviation

Standard deviation is one of the most trusted statistical analysis techniques. The standard deviation of a data set informs us about how widely the data is spread out. The spread of the data refers to the distance of each data point to the mean value of the data set. This distance is also called the error. The standard deviation of a data set X can be calculated using the following formula:

$$\sqrt{\frac{(\sum(x_i-\bar{x})^2)}{n}} $$

For example, to calculate the standard deviation for the test scores we considered earlier, we would first find each (x_i-x\ \bar\ ) and square it and sum it. This sum is called the sum of squares of SS. In our case, the sum of square is 960 and the standard deviation is 9.8. This means that about 70% of the scores were between 70 and 80.

Regression analysis allows us to explore and determine the linear relationship between the predictor (X) and outcome (Y) variables. We get a regression equation in the form of y=mx+b as a result of regression analysis. Using this equation, we can predict other data points not available in the data set. The power of predictability of the regression equation depends heavily on the coefficient of correlation which tells us about the linear relationship between the predictor and outcome variable. This coefficient also tells us about the strength of the relationship between the two sets of variables. The following formula in Figure 1 can be used to calculate a regression equation.

Regression to the mean is a phenomenon that occurs as we include more and more observations into the data set and as the data set gets larger. Regression analysis of an ever-increasing or very large data set will result in a set of predicted Y values that are closer and closer to the mean. In other words, regression to the mean simply means that regardless of how small or large the predictor (X) values are, the predicted outcome values (Y) will always be within 2 to 3 standard deviations of the mean. This happens because the coefficient of correlation (r) cannot be more than 1.

For example, below is a data set containing height and shoe size in centimeters (cm).

By exploring the data using a chart and a scatter plot we can see that as the height of a person increases, their shoe size increases as well. Performing regression analysis allows us to fit a linear model to this data. The solid line on the scatter plot represents the linear regression model along with the regression equation.

Sample Size

Sample size has a very important role to play in statistical analysis. It is crucial to conduct an experiment with an appropriate sample size to arrive at reasonable and trustworthy inferences. Most of the time in real-life situations, we do not know the size of the population and therefore we cannot determine the population mean, so using an appropriate sample to conduct the experiment becomes very important for statistical analysis. The larger the sample size, the better the power of inference of the statistical analysis. A small sample size can increase the likelihood of Type II error in statistical analysis which means that the researcher fails to reject the null hypothesis. Sample size can be calculated using a statistical process called Power Anaysis . To conduct power analysis, a researcher follows the following three steps:

• Identify the r (correlation coefficient) effect size or Cohen's d effect size that you wish to achieve
• Identify the power level of the test (experiment)
• Determine the sample size from a statistical table such as the one in Figure 2.

Hypothesis Testing

Before an experiment is conducted, a researcher states a hypothesis about the findings. For example, the teacher testing the effectiveness of technology use in the classroom may hypothesize that the students who use technology will have a higher score on the test than those who did not use technology in the classroom. This hypothesis is called the Null hypothesis {eq}H_o = {/eq}. To test this hypothesis the researcher would follow the following process.

• State the Null hypothesis and select a significance level (p-value or alpha level) for the test. Researchers usually use an alpha level of .05 for rigorous testing in social sciences and an alpha level of .01 or .001 for medical testing.
• Choose a statistical test to calculate a test statistic. This choice will be based on the type of experiment, participants, and other factors such as the method of comparison, etc. For example, t-test , Z-test, etc.
• Evaluate the results of the test and interpret the findings

Often during statistical analysis an alternative hypothesis ({eq}H_a = {/eq}) is also considered along with a null hypothesis. An alternative hypothesis is exactly what it sounds like, it is an alternative to what is being proposed. For example, when comparing the test scores of students from two different class sections (section A and B), a teacher might propose two sets of hypotheses.

{eq}H_o = {/eq} There will be no difference between the mean scores between section A and section B.

{eq}H_a = {/eq} The mean score from Section A will be higher than the average score from Section B.

Statistical analysis methods are used to analyze data for decision-making. Statistical analysis is used in almost every field both commercial and non-commercial. Following are some examples of the use of statistical analysis in different areas:

• Medicine: Comparing two sets of patients, one who received the vaccine and the other who received the placebo.
• Education: Comparing two groups of students, one who engaged in technology learning and the other who did not use technology for learning.
• Logistics and Transportation: Comparing two sets of trucks, one that used fuel type A and the other that used fuel type B.
• Criminology: Determining cause and effect relationship between the level of education in a geographic location and the frequency of non-violent crime.
• Social Justice: Identifying historical patterns in the availability of certified teachers in certain geographic locations

Understanding statistical analysis technique and their proper usage is a very important aspect of statistical analysis. Some of the major concerns when conducting a proper statistical analysis are

• Adequate sample size
• Determining correct effect size and power level
• Proper choice of statistical test
• Correct calculation of the test statistic
• Appropriate evaluation and interpretation of the result

Keeping the above requirements will ensure the statistical analysis was not biased and the results are reliable.

Statistical analysis is the process researchers used to test their hypothesis about the results of an experiment. Statistical analysis of data means studying data to answer questions about the relationship between real-life events. Statistical analysis is used to establish cause and effect relationships, predict future behavior, suggest solutions, identify patterns, and look for changes in behavior. A hypothesis is a proposition set forth by the researcher about the results of the statistical analysis of the data collected from the experiment. This hypothesis is called the Null hypothesis. The opposite of this hypothesis is called the alternate hypothesis. When conducting an experiment like tossing a coin, the experimenter may suggest a Null hypothesis about the outcome of the experiment. The opposite of that hypothesis would be an alternative hypothesis.

A regression equation can provide us with information about the direction of the relationship between the predictor and outcome variable. The coefficient of correlation tells us how strong that relationship is. For example, r = -1 means strong negative relationship, r = 1 means a strong positive relationship, and r = 0 means no relationship at all. Standard deviation is a measure of how spread out the data is when compared to the mean value of the data set. For example, the spread of test scores is usually described in terms of standard deviation. While conducting regression analysis it is important to have an appropriately large sample size to avoid biased results because often in a real-world situation, population size and population mean are unknown. A large enough mean provides researchers with a better estimate of the mean or average value of the data set.

Video Transcript

Definition of statistical analysis.

Anybody can collect data, but how do you analyze it so that it means something, so that it can help you make conclusions or decisions based on it? Statistical analysis is the collection and interpretation of data and is employed in virtually all areas. It's been used by scientists since the invention of the scientific method and today is typically used in politics, marketing, and education, among many others.

There are five primary methods of statistical analysis that get most of the work done. Let's get into these in more detail.

In statistics, the mean is the most commonly used measure of center, also known as the central tendency. There are several types of mean; if the type is not given, it's understood to be an arithmetic mean. The mean is frequently referred to outside of statistical arenas as the 'average'.

To find the arithmetic mean , add the items in the set of data together and then divide by the number of items. You can see how this plays out in the example below:

Find the mean: (14, 20, 26, 31, 31)

14 + 20 + 26 + 31 + 31 = 122

122 / 5 = 24.4

But let's look at another example. Have you ever gotten an exam back from your teacher, saw your score, and wondered how you did compared to the rest of the class? The mean can help you make that comparison. If you received an 81% on the exam and the class mean was 72%, you can feel a little self-satisfaction knowing you did better than most.

One advantage of using the mean is that it's simple to calculate. A disadvantage is that it's sensitive to extreme values, called outliers , in the data. Other ways of measuring center are median, mode, and mid-range.

Before you get too smug about your 81% on the last exam, you should realize that it's the second lowest grade in the class. There are only eight students. Two of them didn't take the exam and received a zero. Five of them got a 100%. Almost all of the grades for this exam were extremes, zero or hundreds. This scenario illustrates the need for standard deviation.

The standard deviation is the mean of how far away each item of your data is from the mean of that data. It's the most commonly used measure of variation. The empirical rule for standard deviation states that if data has a distribution that's basically bell shaped, then 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% will fall within 3 standard deviations.

This emotional roller coaster that you may have been on concerning your last exam grade has probably got you wondering: is there a connection between preparation time and exam score? You create a graph showing each of your exam grades along with the time spent in preparation for that exam. You notice that the points of the exam seem to suggest a straight line.

When data is paired and then graphed onto a xy grid, you can use regression to create an equation of a line that will come close to as many of those data points as possible. The line is then assigned a correlation coefficient, which is a measure of how well this line meets the data.

Correlation coefficients that are close to zero are weak and do not show correlation. Correlation coefficients of 1, -1, or close to them are strong. These regression lines can be used to predict future behavior of the data and value of data not included in the set.

Sample Size and Hypothesis Testing

Let's now say that your curiosity now turns itself to more national concerns. Since the exam is taken by students across the country, you want to know if your grade is above the national average. You don't have access to the population mean, so you have to determine how large your sample should be so that the sample mean is a decent indicator of the population mean.

In many cases, the population size is too large to collect data from every member of the population. If this is the case, then the data collector will have to rely on a sample of the population to perform the inferential statistics.

Sample size determination is finding out the size of the sample that's needed to achieve a sample mean that's reasonably close to the population mean. The sample size that's chosen will create a confidence interval around the mean of the sample. The sample size also determines how confident (90%, 95%, etc.) you can be that the population mean is indeed inside of the confidence interval of the sample mean.

Unless you're living in a cave by yourself, you cannot make it through a day without hearing someone make a claim about something. Hypothesis testing is the process of determining if claims have any merit to them.

For example, Jason, another student in your class (one of those who got 100%) claims that his strong score was due to AlertNReady, which helps him stay focused during studying. Hypothesis testing allows you to say if use of AlertNReady results in higher exam scores than those not using it.

Jason's assumption is the null hypothesis (the assumed case). You think the real reason, or alternate hypothesis, is that he spent more time preparing for the test. These hypotheses would have to be tested and either rejected or failed to be rejected (or supported, in other words).

Let's briefly review what we've learned in this statistics lesson. Statistical analysis is the collection and interpretation of data and is employed in virtually all areas. The primary techniques of statistical analysis are:

• Mean , aka average : add the items in the set of data together and then divide by the number of items.
• Standard deviation : the mean of how far away each item of your data is from the mean of that data.
• Regression lines: an equation of a line that will come close to as many of those data points as possible. Correlation coefficients that are close to zero are weak and do not show correlation; 1 or -1 are strong.
• Sample size determination : finding out the size of the sample needed to achieve a sample mean that is reasonably close to the population mean.
• Hypothesis testing : the process of determining if claims have any merit to them. A null hypothesis is the commonly held belief of the cause, while the alternate is the one the researcher posits as the real reason.

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Methodology

Research Methods | Definitions, Types, Examples

Research methods are specific procedures for collecting and analyzing data. Developing your research methods is an integral part of your research design . When planning your methods, there are two key decisions you will make.

First, decide how you will collect data . Your methods depend on what type of data you need to answer your research question :

• Qualitative vs. quantitative : Will your data take the form of words or numbers?
• Primary vs. secondary : Will you collect original data yourself, or will you use data that has already been collected by someone else?
• Descriptive vs. experimental : Will you take measurements of something as it is, or will you perform an experiment?

Second, decide how you will analyze the data .

• For quantitative data, you can use statistical analysis methods to test relationships between variables.
• For qualitative data, you can use methods such as thematic analysis to interpret patterns and meanings in the data.

Table of contents

Methods for collecting data, examples of data collection methods, methods for analyzing data, examples of data analysis methods, other interesting articles, frequently asked questions about research methods.

Data is the information that you collect for the purposes of answering your research question . The type of data you need depends on the aims of your research.

Qualitative vs. quantitative data

Your choice of qualitative or quantitative data collection depends on the type of knowledge you want to develop.

For questions about ideas, experiences and meanings, or to study something that can’t be described numerically, collect qualitative data .

If you want to develop a more mechanistic understanding of a topic, or your research involves hypothesis testing , collect quantitative data .

You can also take a mixed methods approach , where you use both qualitative and quantitative research methods.

Primary vs. secondary research

Primary research is any original data that you collect yourself for the purposes of answering your research question (e.g. through surveys , observations and experiments ). Secondary research is data that has already been collected by other researchers (e.g. in a government census or previous scientific studies).

If you are exploring a novel research question, you’ll probably need to collect primary data . But if you want to synthesize existing knowledge, analyze historical trends, or identify patterns on a large scale, secondary data might be a better choice.

Descriptive vs. experimental data

In descriptive research , you collect data about your study subject without intervening. The validity of your research will depend on your sampling method .

In experimental research , you systematically intervene in a process and measure the outcome. The validity of your research will depend on your experimental design .

To conduct an experiment, you need to be able to vary your independent variable , precisely measure your dependent variable, and control for confounding variables . If it’s practically and ethically possible, this method is the best choice for answering questions about cause and effect.

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Your data analysis methods will depend on the type of data you collect and how you prepare it for analysis.

Data can often be analyzed both quantitatively and qualitatively. For example, survey responses could be analyzed qualitatively by studying the meanings of responses or quantitatively by studying the frequencies of responses.

Qualitative analysis methods

Qualitative analysis is used to understand words, ideas, and experiences. You can use it to interpret data that was collected:

• From open-ended surveys and interviews , literature reviews , case studies , ethnographies , and other sources that use text rather than numbers.
• Using non-probability sampling methods .

Qualitative analysis tends to be quite flexible and relies on the researcher’s judgement, so you have to reflect carefully on your choices and assumptions and be careful to avoid research bias .

Quantitative analysis methods

Quantitative analysis uses numbers and statistics to understand frequencies, averages and correlations (in descriptive studies) or cause-and-effect relationships (in experiments).

You can use quantitative analysis to interpret data that was collected either:

• During an experiment .
• Using probability sampling methods .

Because the data is collected and analyzed in a statistically valid way, the results of quantitative analysis can be easily standardized and shared among researchers.

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square test of independence
• Statistical power
• Descriptive statistics
• Degrees of freedom
• Pearson correlation
• Null hypothesis
• Double-blind study
• Case-control study
• Research ethics
• Data collection
• Hypothesis testing
• Structured interviews

Research bias

• Hawthorne effect
• Unconscious bias
• Recall bias
• Halo effect
• Self-serving bias
• Information bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

The research methods you use depend on the type of data you need to answer your research question .

• If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
• If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
• If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Data Analysis in Research: Types & Methods

Data analysis is a crucial step in the research process, transforming raw data into meaningful insights that drive informed decisions and advance knowledge. This article explores the various types and methods of data analysis in research, providing a comprehensive guide for researchers across disciplines.

Data Analysis in Research

Overview of Data analysis in research

Data analysis in research is the systematic use of statistical and analytical tools to describe, summarize, and draw conclusions from datasets. This process involves organizing, analyzing, modeling, and transforming data to identify trends, establish connections, and inform decision-making. The main goals include describing data through visualization and statistics, making inferences about a broader population, predicting future events using historical data, and providing data-driven recommendations. The stages of data analysis involve collecting relevant data, preprocessing to clean and format it, conducting exploratory data analysis to identify patterns, building and testing models, interpreting results, and effectively reporting findings.

• Main Goals : Describe data, make inferences, predict future events, and provide data-driven recommendations.
• Stages of Data Analysis : Data collection, preprocessing, exploratory data analysis, model building and testing, interpretation, and reporting.

Types of Data Analysis

1. descriptive analysis.

Descriptive analysis focuses on summarizing and describing the features of a dataset. It provides a snapshot of the data, highlighting central tendencies, dispersion, and overall patterns.

• Central Tendency Measures : Mean, median, and mode are used to identify the central point of the dataset.
• Dispersion Measures : Range, variance, and standard deviation help in understanding the spread of the data.
• Frequency Distribution : This shows how often each value in a dataset occurs.

2. Inferential Analysis

Inferential analysis allows researchers to make predictions or inferences about a population based on a sample of data. It is used to test hypotheses and determine the relationships between variables.

• Hypothesis Testing : Techniques like t-tests, chi-square tests, and ANOVA are used to test assumptions about a population.
• Regression Analysis : This method examines the relationship between dependent and independent variables.
• Confidence Intervals : These provide a range of values within which the true population parameter is expected to lie.

3. Exploratory Data Analysis (EDA)

EDA is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. It helps in discovering patterns, spotting anomalies, and checking assumptions with the help of graphical representations.

• Visual Techniques : Histograms, box plots, scatter plots, and bar charts are commonly used in EDA.
• Summary Statistics : Basic statistical measures are used to describe the dataset.

4. Predictive Analysis

Predictive analysis uses statistical techniques and machine learning algorithms to predict future outcomes based on historical data.

• Machine Learning Models : Algorithms like linear regression, decision trees, and neural networks are employed to make predictions.
• Time Series Analysis : This method analyzes data points collected or recorded at specific time intervals to forecast future trends.

5. Causal Analysis

Causal analysis aims to identify cause-and-effect relationships between variables. It helps in understanding the impact of one variable on another.

• Experiments : Controlled experiments are designed to test the causality.
• Quasi-Experimental Designs : These are used when controlled experiments are not feasible.

6. Mechanistic Analysis

Mechanistic analysis seeks to understand the underlying mechanisms or processes that drive observed phenomena. It is common in fields like biology and engineering.

Methods of Data Analysis

1. quantitative methods.

Quantitative methods involve numerical data and statistical analysis to uncover patterns, relationships, and trends.

• Statistical Analysis : Includes various statistical tests and measures.
• Mathematical Modeling : Uses mathematical equations to represent relationships among variables.
• Simulation : Computer-based models simulate real-world processes to predict outcomes.

2. Qualitative Methods

Qualitative methods focus on non-numerical data, such as text, images, and audio, to understand concepts, opinions, or experiences.

• Content Analysis : Systematic coding and categorizing of textual information.
• Thematic Analysis : Identifying themes and patterns within qualitative data.
• Narrative Analysis : Examining the stories or accounts shared by participants.

3. Mixed Methods

Mixed methods combine both quantitative and qualitative approaches to provide a more comprehensive analysis.

• Sequential Explanatory Design : Quantitative data is collected and analyzed first, followed by qualitative data to explain the quantitative results.
• Concurrent Triangulation Design : Both qualitative and quantitative data are collected simultaneously but analyzed separately to compare results.

4. Data Mining

Data mining involves exploring large datasets to discover patterns and relationships.

• Clustering : Grouping data points with similar characteristics.
• Association Rule Learning : Identifying interesting relations between variables in large databases.
• Classification : Assigning items to predefined categories based on their attributes.

5. Big Data Analytics

Big data analytics involves analyzing vast amounts of data to uncover hidden patterns, correlations, and other insights.

• Hadoop and Spark : Frameworks for processing and analyzing large datasets.
• NoSQL Databases : Designed to handle unstructured data.
• Machine Learning Algorithms : Used to analyze and predict complex patterns in big data.

Applications and Case Studies

Numerous fields and industries use data analysis methods, which provide insightful information and facilitate data-driven decision-making. The following case studies demonstrate the effectiveness of data analysis in research:

Medical Care:

• Predicting Patient Readmissions: By using data analysis to create predictive models, healthcare facilities may better identify patients who are at high risk of readmission and implement focused interventions to enhance patient care.
• Disease Outbreak Analysis: Researchers can monitor and forecast disease outbreaks by examining both historical and current data. This information aids public health authorities in putting preventative and control measures in place.
• Fraud Detection: To safeguard clients and lessen financial losses, financial institutions use data analysis tools to identify fraudulent transactions and activities.
• investing Strategies: By using data analysis, quantitative investing models that detect trends in stock prices may be created, assisting investors in optimizing their portfolios and making well-informed choices.
• Customer Segmentation: Businesses may divide up their client base into discrete groups using data analysis, which makes it possible to launch focused marketing efforts and provide individualized services.
• Social Media Analytics: By tracking brand sentiment, identifying influencers, and understanding consumer preferences, marketers may develop more successful marketing strategies by analyzing social media data.
• Predicting Student Performance: By using data analysis tools, educators may identify at-risk children and forecast their performance. This allows them to give individualized learning plans and timely interventions.
• Education Policy Analysis: Data may be used by researchers to assess the efficacy of policies, initiatives, and programs in education, offering insights for evidence-based decision-making.

Social Science Fields:

• Opinion mining in politics: By examining public opinion data from news stories and social media platforms, academics and policymakers may get insight into prevailing political opinions and better understand how the public feels about certain topics or candidates.
• Crime Analysis: Researchers may spot trends, anticipate high-risk locations, and help law enforcement use resources wisely in order to deter and lessen crime by studying crime data.

Data analysis is a crucial step in the research process because it enables companies and researchers to glean insightful information from data. By using diverse analytical methodologies and approaches, scholars may reveal latent patterns, arrive at well-informed conclusions, and tackle intricate research inquiries. Numerous statistical, machine learning, and visualization approaches are among the many data analysis tools available, offering a comprehensive toolbox for addressing a broad variety of research problems.

Data Analysis in Research FAQs:

What are the main phases in the process of analyzing data.

In general, the steps involved in data analysis include gathering data, preparing it, doing exploratory data analysis, constructing and testing models, interpreting the results, and reporting the results. Every stage is essential to guaranteeing the analysis’s efficacy and correctness.

What are the differences between the examination of qualitative and quantitative data?

In order to comprehend and analyze non-numerical data, such text, pictures, or observations, qualitative data analysis often employs content analysis, grounded theory, or ethnography. Comparatively, quantitative data analysis works with numerical data and makes use of statistical methods to identify, deduce, and forecast trends in the data.

What are a few popular statistical methods for analyzing data?

In data analysis, predictive modeling, inferential statistics, and descriptive statistics are often used. While inferential statistics establish assumptions and draw inferences about a wider population, descriptive statistics highlight the fundamental characteristics of the data. To predict unknown values or future events, predictive modeling is used.

In what ways might data analysis methods be used in the healthcare industry?

In the healthcare industry, data analysis may be used to optimize treatment regimens, monitor disease outbreaks, forecast patient readmissions, and enhance patient care. It is also essential for medication development, clinical research, and the creation of healthcare policies.

What difficulties may one encounter while analyzing data?

Answer: Typical problems with data quality include missing values, outliers, and biased samples, all of which may affect how accurate the analysis is. Furthermore, it might be computationally demanding to analyze big and complicated datasets, necessitating certain tools and knowledge. It’s also critical to handle ethical issues, such as data security and privacy.

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16 min read Get more from your survey results with tried and trusted statistical tests and analysis methods. The kind of data analysis you choose depends on your survey data, so it makes sense to understand as many statistical analysis options as possible. Here’s a one-stop guide.

Why use survey statistical analysis methods?

Using statistical analysis for survey data is a best practice for businesses and market researchers. But why?

Statistical tests can help you improve your knowledge of the market, create better experiences for your customers, give employees more of what they need to do their jobs, and sell more of your products and services to the people that want them. As data becomes more available and easier to manage using digital tools, businesses are increasingly using it to make decisions, rather than relying on gut instinct or opinion.

When it comes to survey data , collection is only half the picture. What you do with your results can make the difference between uninspiring top-line findings and deep, revelatory insights. Using data processing tools and techniques like statistical tests can help you discover:

• whether the trends you see in your data are meaningful or just happened by chance
• what your results mean in the context of other information you have
• whether one factor affecting your business is more important than others
• what your next research question should be
• how to generate insights that lead to meaningful changes

There are several types of statistical analysis for surveys . The one you choose will depend on what you want to know, what type of data you have, the method of data collection, how much time and resources you have available, and the level of sophistication of your data analysis software.

Learn how Qualtrics iQ can help you with advanced statistical analysis

Before you start

Whichever statistical techniques or methods you decide to use, there are a few things to consider before you begin.

Nail your sampling approach

One of the most important aspects of survey research is getting your sampling technique right and choosing the right sample size . Sampling allows you to study a large population without having to survey every member of it. A sample, if it’s chosen correctly, represents the larger population, so you can study your sample data and then use the results to confidently predict what would be found in the population at large.

There will always be some discrepancy between the sample data and the population, a phenomenon known as sampling error , but with a well-designed study, this error is usually so small that the results are still valuable.

There are several sampling methods, including probabilit y and non-probability sampling . Like statistical analysis, the method you choose will depend on what you want to know, the type of data you’re collecting and practical constraints around what is possible.

Define your null hypothesis and alternative hypothesis

A null hypothesis is a prediction you make at the start of your research process to help define what you want to find out. It’s called a null hypothesis because you predict that your expected outcome won’t happen – that it will be null and void. Put simply: you work to reject, nullify or disprove the null hypothesis.

Along with your null hypothesis, you’ll define the alternative hypothesis, which states that what you expect to happen will happen.

For example, your null hypothesis might be that you’ll find no relationship between two variables, and your alternative hypothesis might be that you’ll find a correlation between them. If you disprove the null hypothesis, either your alternative hypothesis is true or something else is happening. Either way, it points you towards your next research question.

Use a benchmark

Benchmarking is a way of standardizing – leveling the playing field – so that you get a clearer picture of what your results are telling you. It involves taking outside factors into account so that you can adjust the parameters of your research and have a more precise understanding of what’s happening.

Benchmarking techniques use weighting to adjust for variables that may affect overall results. What does that mean? Well for example, imagine you’re interested in the growth of crops over a season. Your benchmarking will take into account variables that have an effect on crop growth, such as rainfall, hours of sunlight, any pests or diseases, type and frequency of fertilizer, so that you can adjust for anything unusual that might have happened, such as an unexpected plant disease outbreak on a single farm within your sample that would skew your results.

With benchmarks in place, you have a reference for what is “standard” in your area of interest, so that you can better identify and investigate variance from the norm.

The goal, as in so much of survey data analysis, is to make sure that your sample is representative of the whole population, and that any comparisons with other data are like-for-like.

Inferential or descriptive?

Statistical methods can be divided into inferential statistics and descriptive statistics.

• Descriptive statistics shed light on how the data is distributed across the population of interest, giving you details like variance within a group and mean values for measurements.
• Inferential statistics help you to make judgments and predict what might happen in the future, or to extrapolate from the sample you are studying to the whole population. Inferential statistics are the types of analyses used to test a null hypothesis. We’ll mostly discuss inferential statistics in this guide.

Types of statistical analysis

Regression analysis.

Regression is a statistical technique used for working out the relationship between two (or more) variables.

To understand regressions, we need a quick terminology check:

• Independent variables are “standalone” phenomena (in the context of the study) that influence dependent variables
• Dependent variables are things that change as a result of their relationship to independent variables

Let’s use an example: if we’re looking at crop growth during the month of August in Iowa, that’s our dependent variable. It’s affected by independent variables including sunshine, rainfall, pollution levels and the prevalence of certain bugs and pests.

A change in a dependent variable depends on, and is associated with, a change in one (or more) of the independent variables.

• Linear regression uses a single independent variable to predict an outcome of the dependent variable.
• Multiple regression uses at least two independent variables to predict the effect on the dependent variable. A multiple regression can be linear or non-linear.

The results from a linear regression analysis are shown as a graph with variables on the axes and a ‘regression curve’ that shows the relationships between them. Data is rarely directly proportional, so there’s usually some degree of curve rather than a straight line.

With this kind of statistical test, the null hypothesis is that there is no relationship between the dependent variable and the independent variable. The resulting graph would probably (though not always) look quite random rather than following a clear line.

Regression is a useful test statistic as you’re able to identify not only whether a relationship is statistically significant, but the precise impact of a change in your independent variable.

The T-test (aka Student’s T-test) is a tool for comparing two data groups which have different mean values. The T-test allows the user to interpret whether differences are statistically significant or merely coincidental.

For example, do women and men have different mean heights? We can tell from running a t-test that there is a meaningful difference between the average height of a man and the average height of a woman – i.e. the difference is statistically significant.

For this test statistic, the null hypothesis would be that there’s no statistically significant difference.

The results of a T-test are expressed in terms of probability (p-value). If the p-value is below a certain threshold, usually 0.05, then you can be very confident that your two groups really are different and it wasn’t just a chance variation between your sample data.

Analysis of variance (ANOVA) test

Like the T-test, ANOVA (analysis of variance) is a way of testing the differences between groups to see if they’re statistically significant. However, ANOVA allows you to compare three or more groups rather than just two.

Also like the T-test, you’ll start off with the null hypothesis that there is no meaningful difference between your groups.

ANOVA is used with a regression study to find out what effect independent variables have on the dependent variable. It can compare multiple groups simultaneously to see if there is a relationship between them.

An example of ANOVA in action would be studying whether different types of advertisements get different consumer responses. The null hypothesis is that none of them have more effect on the audience than the others and they’re all basically as effective as one another. The audience reaction is the dependent variable here, and the different ads are the independent variables.

Cluster analysis

Cluster analysis is a way of processing datasets by identifying how closely related the individual data points are. Using cluster analysis, you can identify whether there are defined groups (clusters) within a large pool of data, or if the data is continuously and evenly spread out.

Cluster analysis comes in a few different forms, depending on the type of data you have and what you’re looking to find out. It can be used in an exploratory way, such as discovering clusters in survey data around demographic trends or preferences, or to confirm and clarify an existing alternative or null hypothesis.

Cluster analysis is one of the more popular statistical techniques in market research , since it can be used to uncover market segments and customer groups.

Factor analysis

Factor analysis is a way to reduce the complexity of your research findings by trading a large number of initial variables for a smaller number of deeper, underlying ones. In performing factor analysis, you uncover “hidden” factors that explain variance (difference from the average) in your findings.

Because it delves deep into the causality behind your data, factor analysis is also a form of research in its own right, as it gives you access to drivers of results that can’t be directly measured.

Conjoint analysis

Market researchers love to understand and predict why people make the complex choices they do. Conjoint analysis comes closest to doing this: it asks people to make trade-offs when making decisions, just as they do in the real world, then analyses the results to give the most popular outcome.

For example, an investor wants to open a new restaurant in a town. They think one of the following options might be the most profitable:

The investor commissions market research. The options are turned into a survey for the residents:

• Which type of restaurant do you prefer? (Gourmet burger/Spanish tapas/Thai)
• What would you be prepared to spend per head? (£20, $40, £60)
• How far would you be willing to travel? (5km, 2km, 10km)
• Would your partner…? (Love it, be OK with it)

There are lots of possible combinations of answers – 54 in this case: (3 restaurant types) x (3 price levels) x (3 distances) x (2 partner preferences). Once the survey data is in, conjoint analysis software processes it to figure out how important each option is in driving customer decisions, which levels for each option are preferred, and by how much.

So, from conjoint analysis , the restaurant investor may discover that there’s a statistically significant preference for an expensive Spanish tapas bar on the outskirts of town – something they may not have considered before.

Crosstab analysis

Crosstab (cross-tabulation) is used in quantitative market research to analyze categorical data – that is, variables that are different and mutually exclusive, such as: ‘men’ and ‘women’, or ‘under 30’ and ‘over 30’.

Also known by names like contingency table and data tabulation, crosstab analysis allows you to compare the relationship between two variables by presenting them in easy-to-understand tables.

A statistical method called chi-squared can be used to test whether the variables in a crosstab analysis are independent or not by looking at whether the differences between them are statistically significant.

Text analysis and sentiment analysis

Analyzing human language is a relatively new form of data processing, and one that offers huge benefits in experience management. As part of the Stats iQ package, TextiQ from Qualtrics uses machine learning and natural language processing to parse and categorize data from text feedback, assigning positive, negative or neutral sentiment to customer messages and reviews.

With this data from text analysis in place, you can then employ statistical tools to analyze trends, make predictions and identify drivers of positive change.

The easy way to run statistical analysis

As you can see, using statistical methods is a powerful and versatile way to get more value from your research data, whether you’re running a simple linear regression to show a relationship between two variables, or performing natural language processing to evaluate the thoughts and feelings of a huge population.

Knowing whether what you notice in your results is statistically significant or not gives you the green light to confidently make decisions and present findings based on your results, since statistical methods provide a degree of certainty that most people recognize as valid. So having results that are statistically significant is a hugely important detail for businesses as well as academics and researchers.

Fortunately, using statistical methods, even the highly sophisticated kind, doesn’t have to involve years of study. With the right tools at your disposal, you can jump into exploratory data analysis almost straight away.

Our Stats iQ™ product can perform the most complicated statistical tests at the touch of a button using our online survey software , or data brought in from other sources. Turn your data into insights and actions with CoreXM and Stats iQ . Powerful statistical analysis. No stats degree required.

Learn how Qualtrics iQ can help you understand the experience like never before

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• Open access
• Published: 01 February 2024

An empirical comparison of statistical methods for multiple cut-off diagnostic test accuracy meta-analysis of the Edinburgh postnatal depression scale (EPDS) depression screening tool using published results vs individual participant data

• Zelalem F. Negeri 1 ,
• Brooke Levis 2 , 3 ,
• John P. A. Ioannidis 4 ,
• Brett D. Thombs 2 , 3 , 5 , 6 , 7 , 8 ,
• Andrea Benedetti 3 , 6 , 9 , 10 &

the DEPRESsion Screening Data (DEPRESSD) EPDS Group

BMC Medical Research Methodology volume  24 , Article number:  28 ( 2024 ) Cite this article

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Selective reporting of results from only well-performing cut-offs leads to biased estimates of accuracy in primary studies of questionnaire-based screening tools and in meta-analyses that synthesize results. Individual participant data meta-analysis (IPDMA) of sensitivity and specificity at each cut-off via bivariate random-effects models (BREMs) can overcome this problem. However, IPDMA is laborious and depends on the ability to successfully obtain primary datasets, and BREMs ignore the correlation between cut-offs within primary studies.

We compared the performance of three recent multiple cut-off models developed by Steinhauser et al., Jones et al., and Hoyer and Kuss, that account for missing cut-offs when meta-analyzing diagnostic accuracy studies with multiple cut-offs, to BREMs fitted at each cut-off. We used data from 22 studies of the accuracy of the Edinburgh Postnatal Depression Scale (EPDS; 4475 participants, 758 major depression cases). We fitted each of the three multiple cut-off models and BREMs to a dataset with results from only published cut-offs from each study (published data) and an IPD dataset with results for all cut-offs (full IPD data). We estimated pooled sensitivity and specificity with 95% confidence intervals (CIs) for each cut-off and the area under the curve.

Compared to the BREMs fitted to the full IPD data, the Steinhauser et al., Jones et al., and Hoyer and Kuss models fitted to the published data produced similar receiver operating characteristic curves; though, the Hoyer and Kuss model had lower area under the curve, mainly due to estimating slightly lower sensitivity at lower cut-offs. When fitting the three multiple cut-off models to the full IPD data, a similar pattern of results was observed. Importantly, all models had similar 95% CIs for sensitivity and specificity, and the CI width increased with cut-off levels for sensitivity and decreased with an increasing cut-off for specificity, even the BREMs which treat each cut-off separately.

Conclusions

Multiple cut-off models appear to be the favorable methods when only published data are available. While collecting IPD is expensive and time consuming, IPD can facilitate subgroup analyses that cannot be conducted with published data only.

Peer Review reports

The accuracy of a screening test when compared with a reference standard is measured by its sensitivity and specificity [ 1 ]. For continuous or ordinal tests, sensitivity and specificity are inversely related as a function of the positivity threshold, or cut-off; for tests where higher scores are associated with increased likelihood the underlying target condition is present, as the cut-off is increased, sensitivity decreases, and specificity increases.

For questionnaire-based screening tests, which have ordinal scores and multiple possible cut-offs, authors of primary studies often only report sensitivity and specificity for a standard cut-off or for an “optimal” cut-off that maximizes combined sensitivity and specificity according to a statistical criterion (e.g., Youden’s J) [ 2 ]. Sometimes results from other cut-offs close to the standard or optimal cut-off are also reported. This selective cut-off reporting has been shown to positively bias estimates of accuracy of screening tests in primary studies and in meta-analyses that synthesize results from primary studies [ 2 , 3 ].

Researchers have used several approaches to meta-analyze results from test accuracy studies with missing results for some cut-offs. Some have meta-analyzed studies at one or several cut-offs selected in advance [ 4 ] by including reported accuracy estimates at those cut-offs from individual studies [ 5 , 6 ]; this approach may lead to overestimated accuracy, however, if primary studies selected the cut-offs to report based on maximized test accuracy [ 2 ]. Others have combined primary studies using accuracy estimates from a single cut-off from each primary study, presumably the best-performing cut-off, combining results from different cut-offs across studies [ 7 ]; this method would also lead to even greater bias and to a clinically meaningless summary receiver operating characteristic (SROC) curve and combined accuracy estimates [ 8 ]. More recently, individual participant data meta-analyses (IPDMA) [ 9 , 10 , 11 , 12 ], have evaluated sensitivity and specificity at each cut-off, separately, using the bivariate random-effects model (BREM) of Chu and Cole [ 13 ], as discussed in Riley et al. [ 14 , 15 ], which overcomes the selective cut-off bias problem but ignores correlations between cut-offs within the same primary study.

Statistical methods [ 16 , 17 , 18 , 19 ] that take the correlation between cut-offs into consideration and do not require the same number of cut-offs or identical cut-off values to be reported in each primary study have recently been proposed to simultaneously model data from multiple cut-offs in diagnostic test accuracy studies. Steinhauser et al. [ 16 ] proposed a class of linear mixed-effects models to model negative or positive test results as a linear function of cut-offs. Hoyer et al. [ 17 ] proposed approaches based on survival methods that are random-effects models and consider missing cut-offs between two observed cut-offs as interval censored. Jones et al. [ 18 ] proposed, in a Bayesian framework, a generalised nonlinear mixed model based on multinomial likelihood that employs a Box-Cox or logarithmic transformation to describe the underlying distribution of a continuous biomarker. Most recently, Hoyer and Kuss [ 19 ] extended Hoyer et al.’s method [ 17 ] by suggesting the family of generalized F distributions for describing the distribution of screening test scores.

Recently, Benedetti et al. [ 20 ] compared the performance of BREMs [ 13 ], Steinhauser et al. [ 16 ], and Jones et al. [ 18 ] methods when applied to data consisting of published primary study results with missing data for some cut-offs versus individual participant data (IPD) with complete cut-off data for a commonly used depression screening tool, the Patient Health Questionnaire-9 (PHQ-9; 45 studies, 15,020 participants, 1972 major depression cases). The PHQ-9 uses a standard cut-off of ≥10 to detect major depression, and missing cut-offs in primary studies tended to be scattered symmetrically around this standard cut-off. When applied to published data with missing cut-offs, the Steinhauser et al. [ 16 ] and Jones et al. [ 18 ] models performed better than the BREMs [ 13 ] in terms of their ability to recover the full receiver operating characteristics (ROC) curve – which unlike the SROC curve uses the separate cut-offs instead of the primary studies in the meta-analysis as a unit of analysis – from the full IPD. When all methods were applied to the full IPD, the Steinhauser et al. [ 16 ] and Jones et al. [ 18 ] methods produced similar areas under the curve (AUC) and ROC curves as the BREMs [ 13 ], but pooled sensitivity and specificity estimates were slightly lower than those from the BREMs [ 13 ].

The aim of the present study was to empirically compare three multiple cut-off models – the Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and recently proposed Hoyer and Kuss [ 19 ] (which was not included in Benedetti et al. [ 20 ]) models – to conducting BREMs [ 13 ] at each cut-off separately using data from primary studies that assessed the screening accuracy of the Edinburgh Postnatal Depression Scale (EPDS). Unlike the PHQ-9, the EPDS does not have a single standard cut-off, and cut-offs from ≥10 to ≥13 are sometimes used; therefore, the distribution of missing cut-offs may be less symmetrical around a single cut-off [ 3 ]. Unlike the study of Zapf et al. [ 21 ], that considered the Hoyer et al. [ 17 ] model, we aimed to [ 1 ] use the latest, generalized, and better-performing model of Hoyer and Kuss [ 19 ], and [ 2 ] compare the multiple cut-off methods applied to published individual study results with missing cut-offs data to the BREM applied to IPD with complete cut-off data, in the context of diagnostic accuracy studies of depression screening tools. First, to replicate standard meta-analytic practice and compare it to IPDMA, we fitted BREMs to published cut-off results and compared results with BREMs fitted to the full IPD dataset for all relevant cut-offs. Second, to compare the ability of the multiple cut-off methods to recover the ROC curve from the full IPD dataset, we compared the multiple cut-off models when applied to published primary study results with missing data for some cut-offs to BREMs applied to the full IPD with results for all cut-offs. Third, we compared the three multiple cut-off models and BREMs when applied to the full IPD to describe each model’s performance in the absence of missing cut-offs. Fourth, we fitted the three multiple cut-off models to both the full IPD dataset and to published primary study results and compared results across models to evaluate differences between the models due to data types.

This study uses data from an IPDMA of the accuracy of the EPDS for screening to detect major depression among pregnant and postpartum women [ 12 ]. A PROSPERO registration (CRD42015024785) and a published protocol [ 22 ] were available for the original IPDMA. The present study was not included in the original IPDMA protocol, but a separate protocol was prepared and posted on the Open Science Framework ( https://osf.io/5hf6t/ ) prior to study initiation. Because of the overlap of methods in the present study with methods from previous studies, we adopted those methods, including the description of our data and data collection methods [ 3 , 12 ] and descriptions of the statistical models we compared, which were described in Benedetti et al. [ 20 ] (except the Hoyer and Kuss model [ 19 ]). We followed guidance from the Text Recycling Research Project [ 23 ].

Identification of eligible studies for the main IPDMA

Eligibility criteria for the main IPDMA of the EPDS were based on how screening would occur in practice. In this article, the same eligibility standards as the main IPDMA of the EPDS were used [ 12 ], including administration of the EPDS and a validated diagnostic interview – that identified diagnostic classifications for current Major Depressive Disorder (MDD) or Major Depressive Episode (MDE) – within 2 weeks of each other. If the original data allowed for the identification of eligible participants, datasets where not all participants were eligible were included [ 12 ]. Our criteria for defining major depression also followed that of Levis et al. [ 12 ] and Benedetti et al. [ 20 ].

Search strategy and study selection

A medical librarian, using a peer-reviewed search strategy [ 24 ], searched Medline, Medline In-Process & Other Non-Indexed Citations and PsycINFO via OvidSP, and Web of Science via ISI Web of Knowledge from inception to October 3, 2018. The complete search strategy was published with the original IPDMA [ 12 ]. We also reviewed reference lists of relevant reviews and queried contributing authors about non-published studies. Search results were uploaded into RefWorks (RefWorks-COS, Bethesda, MD, USA). After de-duplication, unique citations were uploaded into DistillerSR (Evidence Partners, Ottawa, Canada) for storing and tracking search results.

Two investigators independently reviewed titles and abstracts for eligibility. If either reviewer deemed a study potentially eligible, full-text article review was done by two investigators, independently, with disagreements resolved by consensus, including a third investigator, as necessary.

Data contribution and synthesis

De-identified original data contributions from authors of suitable datasets were requested [ 12 ]. Data at the participant level included EPDS score and the presence or absence of major depression. We applied the supplied weights when datasets had necessary statistical weighting to account for sampling techniques, and we created the necessary weights based on inverse selection probabilities in cases where the original study did not weight [ 12 ].

Data used in the present study

Since the purpose of the present study was to compare statistical methods for multiple cut-off meta-analysis using published data versus IPD, we required that included studies for the present analysis published sensitivity and specificity for at least one cut-off in addition to meeting the inclusion and exclusion criteria for the main IPDMA. We did not consider any data from published studies for which the IPD could not be retrieved. Consistent with our previous work [ 3 ], to make the data close enough to the actual data used in the original reports, we excluded studies for which the difference in sample size or major depression cases between the published data and our IPD exceeded 10%. We also excluded studies if they reported diagnostic accuracy for a broader diagnostic category than major depression (e.g., any mood disorder) if diagnoses other than major depression comprised more than 10% of cases. For the eligible data, we constructed a dataset composed of 2 × 2 tables (true positives, false positives, true negatives, false negatives) for only published cut-offs for each study, and we refer to this as the published dataset . We refer to the dataset that included results for all cut-offs for each eligible study, rather than just published cut-offs, as the full IPD dataset .

Differences between primary study results, full IPD dataset , and published dataset

Because of the criteria for inclusion and exclusion criteria employed in our EPDS IPDMA [ 12 ], data that had previously been included in the published main studies occasionally differed from those used in the current analysis. First, rather than applying the eligibility standards for the EPDS IPDMA [ 12 ] at the study level, they were consistently applied to all participants. Due to this, a subset of the individuals in some of the original studies matched the inclusion requirements for the EPDS full IPD dataset . For instance, we only included data from individuals who completed the EPDS and reference standard within a two-week time frame, for adult women who completed assessments while pregnant or within a year of giving birth, and for individuals who were not recruited because they were undergoing psychiatric evaluation or treatment or suspected of having a depressive disorder. Participants who fulfilled these requirements were included from every primary study, while those who failed to, were not [ 12 ]. Second, we defined the outcome as “major depression.” Some original studies, nevertheless, provided accuracy scores for diagnoses of depression wider than major depression, including “major + minor depression” or “any depressive disorder.” Third, we created suitable weights based on inverse selection probabilities for cases where sampling techniques called for weighting, but the primary study did not. This happened, for example, when the diagnostic interview was given to all those who received positive screening results but only to a randomly selected group of individuals with negative screening results [ 12 ]. Fourth, we compared findings calculated using the raw datasets with published information on participants and diagnostic accuracy outcomes during our data validation procedure. We detected and fixed errors in conjunction with the primary research investigators where the primary data that we obtained from the investigators and the original publications conflicted [ 12 ]. After making the aforementioned changes and exclusions for the published dataset , we only estimated specificity and sensitivity for the cut-offs that were included in the original studies [ 20 ].

Statistical analyses

First, to replicate conventional meta-analytic practice, we fitted BREMs [ 13 ] to the published dataset , separately for each cut-off, and obtained pooled sensitivity and specificity with 95% confidence intervals (CIs). We evaluated results for all possible EPDS cut-offs (0 to 30) and presented results for those in a clinically relevant range (7 to 15) as we did in our main EPDS IPDMA [ 12 ]. We compared these results to BREMs using IPDMA with data from the full IPD dataset .

Second, we fitted the three multiple cut-off methods (i.e., the Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models) to the published dataset and compared to the BREMs [ 13 ] fitted to the full IPD dataset to evaluate how well each model recovered the ROC curve from the full IPD.

Third, we fitted the three multiple cut-off models [ 16 , 18 , 19 ] to the full IPD dataset and compared results across these models and the BREMs [ 13 ], also applied to the full IPD dataset , to assess whether any differences in results were due to differences in modelling approaches instead of differences in data type (published data with missing cut-offs versus full IPD).

Fourth, to evaluate whether differences in results were due to data types, we compared results across the three multiple cut-off models [ 16 , 18 , 19 ] applied to both the full IPD dataset and to the published dataset .

The BREM [ 13 ] is a two-stage random-effects meta-analytic approach that estimates pooled logit-transformed sensitivity and specificity simultaneously, accounting for the correlation between sensitivity and specificity across studies and for the precision by which sensitivity and specificity are estimated within studies. The BREM is fitted separately at each cut-off. It does not account for the correlation across cut-offs within a study or make any assumptions about the shape of the association between cut-offs and sensitivity or specificity. The AUC of the full ROC curve was obtained by numerical integration based on the trapezoidal rule, and a 95% CI for the AUC was estimated using bootstrap resampled data at the study and participant level [ 25 ].

The Steinhauser et al. [ 16 ] approach is a bivariate linear mixed-effects approach that models a study-specific logit-transformed proportion of negative test results (1 – sensitivity, specificity) at each cut-off through random-effects to account for the heterogeneity across studies in the meta-analysis. We used restricted maximum likelihood (REML) criteria [ 26 , 27 ] to choose among the eight linear mixed-effects models proposed by Steinhauser et al. [ 16 ], which differ in their random-effects structures. Accordingly, the “different random intercept and different random slope” model [ 16 ] was found to fit both the published dataset and the full IPD dataset well.

The Jones et al. [ 18 ] approach is a Bayesian random-effects model that describes the variability in the test results between cut-offs by the exact multinomial distribution. The model assumes the logistic distribution for the distribution of the Box-Cox or natural logarithm transformed test results in cases and non-cases group, and accounts for within-study correlation due to multiple cut-offs. To describe the variation in sensitivity and specificity across studies, the model assumes that the means and scale parameters of the test results in the case and non-case populations follow a quadrivariate normal distribution with a common mean vector of length four and a four-by-four variance-covariance matrix. We fitted the model to both the full IPD dataset and the published dataset by estimating the Box-Cox transformation parameters directly from the data instead of assuming the log-logistic distribution for the natural logarithm-transformed screening results since the 95% credible intervals for the Box-Cox transformation parameters did not include 0.

Hoyer and Kuss [ 19 ] use an accelerated failure time model by assuming positive test results (sensitivity, 1 – specificity) as the events of interest and the screening test scores as an interval-censored time variable. The family of generalized F distributions, which includes the Weibull, lognormal, log-logistic, generalized gamma, Burr III, Burr XII, and generalized log-logistic distribution, is used to describe the distribution of the logarithm of screening test scores. In the accelerated failure time framework, after log-transformation of the screening test scores, bivariate normally distributed random intercepts in the linear predictor are used to account for within-study correlation across screening test scores for different cut-offs and to account for the inherent correlation between sensitivity and specificity across studies. Sensitivity and specificity of a test are predicted from the survival functions of the respective distributions at a specified cut-off threshold. The Bayesian Information Criterion (BIC) [ 28 ] is used to choose the best-fitting model. Accordingly, the Burr III and the GF models were best fitting and used for the published dataset and the full IPD dataset , respectively.

For each method and at each step, we estimated cut-off-specific pooled sensitivity and specificity and corresponding 95% CIs and the AUC across the full range of EPDS cut-offs (0 to 30). We compared point estimates, 95% CI widths, and AUC between methods and datasets.

We fitted the BREMs [ 13 ], Steinhauser et al. [ 16 ], and Jones et al. [ 18 ] models in the R [ 29 ] programming language via RStudio [ 30 ] using the R packages lme4 [ 27 ], diagmeta [ 31 ], and R2WinBUGS [ 32 ], respectively. The Hoyer and Kuss [ 19 ] model was fitted in SAS using the NLMIXED procedure to obtain the maximum likelihood estimates of model parameters via the Gauss Hermite quadrature.

Search results and dataset inclusion

A total of 4434 unique titles and abstracts were identified from database searches; of these, 4056 were excluded after reviewing titles and abstracts and 257 after reviewing full texts, resulting in 121 eligible articles with data from 81 unique participant samples, of which 56 (69%) contributed datasets. Two additional studies were contributed by primary study authors, resulting in a total of 58 studies that provided participant data. We excluded 25 studies that did not publish accuracy results for any EPDS cut-off and 11 studies for which the difference in sample size or number of major depression cases between the published data and our IPD exceeded 10%, leaving data from a total of 22 primary studies that were included in the present study (38% of 58 identified studies that published accuracy results; see Fig.  1 ).

Flow diagram of study selection process

Description of included studies

The 22 studies included 4475 participants and 758 major depression cases in the full IPD dataset . These numbers vary by cut-off in the published dataset , which is a subset of the full IPD dataset with results only from cut-offs in the primary studies for which results were published (see Table  1 ). The aggregate distribution of published EPDS cut-offs by the primary studies included in the published dataset is depicted in Appendix Fig. A 1 . The overall distribution of EPDS scores among participants with and without major depression is shown in Appendix Table A 1 and Fig. A 2 .

Comparison of sensitivity and specificity

In Appendix Tables A 2 to A 5 we present the sensitivity and specificity estimates with their corresponding 95% CIs (Steinhauser et al. [ 16 ], Hoyer and Kuss [ 19 ], BREMs [ 13 ]) or credible intervals (Jones et al. [ 18 ] model) for both the published dataset and full IPD dataset for cut-offs 7 to 15.

Figure  2 depicts pooled sensitivity and specificity by cut-off when the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models were fitted to the published dataset and when the BREMs [ 13 ] were fitted to the full IPD dataset . The BREMs [ 13 ] fitted to the published dataset yielded lower sensitivity estimates for most cut-offs compared to the BREMs [ 13 ] fitted to the full IPD dataset , with mean absolute difference between the two models of 0.05 (range: 0.00 to 0.09). The right-hand panel of Fig.  2 shows that the specificity estimated by the BREMs [ 13 ] fitted to the published dataset was higher than that estimated by the BREMs [ 13 ] fitted to the full IPD dataset , and that the difference decreased as the cut-off increased (mean absolute difference: 0.06, range: 0.01 to 0.14).

Comparing the sensitivity (left) and specificity (right) estimates when the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models were fitted to the published data with when the BREMs [ 13 ] were fitted to the full IPD dataset

Compared to the BREMs [ 13 ] fitted to the full IPD dataset , the Steinhauser et al. [ 16 ] and Hoyer and Kuss [ 19 ] approaches applied to the published dataset had lower sensitivity estimates at lower cut-offs and the same or slightly higher estimates at higher cut-offs, with mean absolute difference of 0.02 (range: 0.00 to 0.05) and 0.02 (range: 0.00 to 0.04), respectively. On the other hand, the Jones et al. [ 18 ] model applied to the published dataset generated similar sensitivity estimates to the BREMs applied to the full IPD dataset across cut-offs (mean absolute difference: 0.01, range: 0.00 to 0.02). The Steinhauser et al. [ 16 ], Hoyer and Kuss [ 19 ], and Jones et al. [ 18 ] models fitted to the published dataset had higher specificity estimates at lower cut-offs but similar or lower estimates for higher cut-offs compared to those estimated by the BREMs [ 13 ] fitted to the full IPD dataset , with respective mean absolute differences of 0.01 (range: 0.00 to 0.03), 0.02 (range: 0.00 to 0.03), and 0.01 (range: 0.00 to 0.03).

Figure  3 compares the Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models when fitted to the full IPD dataset with the BREMs [ 13 ] fitted to the full IPD dataset . The Steinhauser et al. [ 16 ] model had lower sensitivity (mean absolute difference: 0.03, range: 0.02 to 0.04) and specificity (mean absolute difference: 0.02, range: 0.01 to 0.04) estimates for all cut-offs compared to the BREMs [ 13 ]. The sensitivity and specificity estimated by the Jones et al. [ 18 ] model were higher or similar at lower cut-offs and lower at higher cut-offs, with a mean absolute difference of 0.02 for sensitivity (range: 0.00 to 0.05) and 0.02 for specificity (range: 0.00 to 0.03). The Hoyer and Kuss [ 19 ] model generated estimates of sensitivity that were higher for all cut-offs (mean absolute difference: 0.03, range: 0.01 to 0.04) and estimates of specificity that were lower for all cut-offs (mean absolute difference: 0.06, range: 0.02 to 0.08) compared to estimates generated by the BREMs [ 13 ].

Comparing the sensitivity (left) and specificity (right) estimates when the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models were fitted to the full IPD data with when the BREMs [ 13 ] were fitted to the full IPD dataset

Compared to the Steinhauser et al. [ 16 ] model fitted to the full IPD dataset , the Steinhauser et al. [ 16 ] approach applied to the published dataset had similar sensitivity estimates at lower cut-offs but higher estimates at upper cut-offs (mean absolute difference: 0.02, range: 0.00 to 0.05), and higher specificity estimates for all cut-offs (mean absolute difference: 0.03, range: 0.00 to 0.06). Compared to the Jones et al. [ 18 ] model fitted to the full IPD dataset , the Jones et al. [ 18 ] model applied to the published dataset had lower sensitivity estimates at lower cut-offs and higher estimates at upper cut-offs (mean absolute difference: 0.02, range: 0.01 to 0.05), but similar specificity estimates (mean absolute difference: 0.00, range: 0.00 to 0.01). Compared to the Hoyer and Kuss [ 19 ] model fitted to the full IPD, the Hoyer and Kuss [ 19 ] model applied to the published dataset generated estimates of sensitivity that were lower for all cut-offs except ≥15 (mean absolute difference: 0.04, range: 0.01 to 0.06) and higher estimates of specificity for all cut-offs (mean absolute difference: 0.06, range: 0.05 to 0.07). See Appendix Tables A 3 to A 5 .

Comparison of confidence or credible interval width

As expected, the widths of the estimated 95% CIs for sensitivity and specificity using the full IPD dataset were narrower than those estimated using the published dataset for the BREMs [ 13 ], (mean absolute difference: 0.07, range: 0.01 to 0.12 for sensitivity; mean absolute difference: 0.02, range: 0.00 to 0.09 for specificity). All four modelling approaches had similar 95% CIs for sensitivity and specificity when applied to the full IPD dataset , with an increasing 95% CI width for sensitivity and decreasing 95% CI width for specificity as the cut-offs increased or the number of major depression cases decreased. Although estimated 95% CIs for sensitivity using the full IPD dataset were narrower than those estimated using the published dataset for the Steinhauser et al. [ 16 ] and Hoyer and Kuss [ 19 ] models (mean absolute difference: 0.05, range: 0.03 to 0.07 and mean absolute difference: 0.06, range: 0.04 to 0.09, respectively), both models produced similar estimated 95% CIs for specificity when the published dataset or the full IPD dataset was used, with a mean 95% CI width of ≤0.01 (range: 0.00 to 0.02 for Steinhauser et al. [ 16 ], range: 0.00 to 0.03 for Hoyer and Kuss [ 19 ]) across all cut-offs. The Jones et al. [ 18 ] model, however, yielded similar estimated credible intervals for sensitivity and specificity between the datasets, with a mean absolute difference across cut-offs of 0.002 (range: 0.00 to 0.02) and 0.01 (range: 0.00 to 0.02) for sensitivity and specificity, respectively. (See Appendix Figs. A 3 and A 4 ).

Comparison in terms of ROC curves and AUC

Figure  4 depicts the comparison of the ROC curves of the four modelling approaches when applied to the published dataset versus the BREMs [ 13 ] applied to the full IPD dataset (left panel) and when all approaches were applied to the full IPD dataset (right panel).

Comparing ROC curves when the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] approaches were fitted to the published data (left) and full IPD (right) with when the BREMs [ 13 ] were fitted to the full IPD dataset

The AUC of the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] methods when fitted to the published dataset were 0.90, 0.87, 0.94, and 0.82, respectively. The ROC curve from the BREMs [ 13 ] fitted to the published dataset largely deviated from that fitted to the full IPD dataset , whereas the ROC curves from the Steinhauser et al. [ 16 ] and Jones et al. [ 18 ] approaches fitted to the published dataset were similar to the BREMs [ 13 ] fitted to the full IPD dataset . The Hoyer and Kuss [ 19 ] approach resulted in a lower AUC (Fig.  4 , left panel).

A similar pattern of results was observed when the approaches were fitted to the full IPD dataset , though ROC curves were more spread out. The AUC of the BREMs [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] approaches when fitted to the full IPD dataset were 0.90, 0.86, 0.95, and 0.83, respectively. Compared to the ROC curve for the BREMs [ 13 ], the ROC curves for the Jones et al. [ 18 ] and Hoyer and Kuss [ 19 ] approaches were lower at lower cut-offs and slightly higher at higher cut-offs. The ROC curve for the Steinhauser et al. [ 16 ] approach remained lower than that for the BREMs [ 13 ] regardless of the cut-off thresholds (Fig. 4 , right panel).

We compared the performance of three recently developed multiple cut-off methods by Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] that account for missing cut-offs when meta-analyzing diagnostic test accuracy studies with multiple cut-offs. These methods do not require IPD, which is costly and labour-intensive to collect [ 33 ]. We compared them with BREMs [ 13 ] when each of the three multiple cut-off models was fitted to both a published dataset with missing cut-offs and using IPD from 22 studies on the diagnostic accuracy of the EPDS (the full IPD dataset ).

Most of the results we found were consistent with the findings of Benedetti et al. [ 20 ] The BREMs [ 13 ] fitted to the published dataset resulted in lower sensitivity and higher specificity estimates for most cut-offs, and a divergent ROC curve with similar AUC compared to results from the BREMs [ 13 ] fitted to the full IPD dataset (Fig. 2 and Table A 2 ), suggesting that results from the BREMs [ 13 ] fitted to published data are biased due to selective cut-off reporting [ 2 , 3 ].

Compared to the BREMs [ 13 ] fitted to the full IPD dataset , the Steinhauser et al. [ 16 ], Jones et al. [ 18 ], and Hoyer and Kuss [ 19 ] models fitted to the published dataset produced similar ROC curves; though, the Hoyer and Kuss [ 19 ] model had lower AUC, mainly due to estimating slightly lower sensitivity at lower cut-offs (Fig. 2 ). When fitting the three multiple cut-off models to the full IPD dataset , a similar pattern of results was observed (Fig.  3 ). Importantly, all models had similar 95% CIs for sensitivity and specificity, and the CI width increased with cut-off levels for sensitivity and decreased with an increasing cut-off for specificity, even the BREMs which treats each cut-off separately (Tables A 2 to A 5 ; Figs. A 3 and A 4 ).

The ROC curves estimated by the Hoyer and Kuss model [ 19 ] had considerably lower AUC than the Steinhauser et al. [ 16 ] and Jones et al. [ 18 ] methods (Fig. 4 ). While this may be due to the sensitivity of the model to starting values, we used an objective statistical approach to choose a starting value that yielded in the best model with the smallest BIC. Moreover, in the simulations presented in Hoyer and Kuss [ 19 ], when the Generalized F was the true model, the model as specified here underestimated sensitivity and overestimated specificity across cut-offs, similar to the pattern of results seen when this approach was applied to the full IPD dataset . For the published dataset , this approach estimated the lowest sensitivity at lower cut-offs and highest specificity at upper cut-offs.

The differences in results between the models when fitted to the full IPD dataset were likely due to the various assumptions each model makes. Each of the models discussed in this paper assume different distributions to describe the variation in the screening test results. While the recent methods account for the correlation across cut-offs between sensitivities and specificities, the BREM does not. Except the Jones et al. [ 18 ] model, which assumes four random-effects, the other models assume only two random-effects to describe the variation in sensitivities and specificities across studies and cut-offs. For example, as pointed out by Benedetti et al. [ 20 ], whereas, the Steinhauser et al. [ 16 ] model may fit the ROC curve at upper cut-offs where more major depression cases are observed as it assumes a parametric relationship between cut-offs and logit-transformed sensitivities, the Jones et al. [ 18 ] model, which additionally assumes the Box-Cox transformation estimated from the data, may recover the true ROC curve better.

The present study showed that recent methods for multiple cut-offs meta-analysis with missing cut-off information are important approaches that can produce reliable estimates in the absence of IPD, unlike standard BREMs [ 13 ] at each cut-off separately, which may produce misleading results when there is substantial missingness in reported results at different cut-offs.

We did not find substantial differences between our findings and those of Benedetti et al. [ 20 ], suggesting that the recent multiple cut-off models are robust to variations in data characteristics, although further research, including studies with simulated datasets, is needed. Whereas we fitted the models to the EPDS data that consisted of IPD from 22 studies, 4475 participants and 758 major depression cases (Table 1 ), Benedetti et al. [ 20 ] applied the models to the PHQ-9 data that comprised IPD from 45 studies, 15,020 participants and 972 major depression cases. There is also appreciable difference in the distribution of the published data for the cut-offs 7 to 15 (Table A 1 ; Fig. A 2 ), which were used in both studies. Whereas the distribution of missing cut-offs was scattered symmetrically around the standard cut-off of ≥10 for the PHQ-9, the distribution was less symmetrical around the commonly used cut-off of ≥13 for the EPDS (Fig. A 1 ).

Strengths of the present study include assessing the most recent approach of Hoyer and Kuss [ 19 ] in addition to those evaluated by Benedetti et al. [ 20 ] and the ability to compare results from a dataset with missing cut-offs to IPD that consisted of line-by-line participant data. Additionally, our ability to replicate the findings on Benedetti et al. [ 20 ] on a different dataset with differing characteristics supports the best-practice standards for developing knowledge through replication of existing studies using multiple empirical replication studies [ 34 ]. A main limitation is the lack of a simulation study upon which the methods can be examined using true population parameters instead of empirical data, although the in-progress simulation study as promised by Zapf et al. [ 21 ] is anticipated to shed some light on this end. Moreover, we could not include data from 36 (62%) of 58 identified studies that published accuracy results.

Despite the differences in model assumptions, all three recent methods for multiple cut-off diagnostic data meta-analysis, particularly the Jones et al. [ 18 ] model, satisfactorily recovered the ROC curve from the full IPD while being fitted to only the published data with missing cut-offs, which demonstrates the importance of such methods in the absence of IPD. Our results suggest that there is not a substantive disadvantage compared to applying the BREMs to the full IPD. Furthermore, our results suggest that multiple cut-off models are effective methods for meta-analysis of diagnostic test accuracy of depression screening tools when only published data are available, although our results may not hold in datasets with very different characteristics. However, we note that collecting full IPD allows additional analyses not possible when only aggregate data are collected (such as, e.g., conducting subgroup analyses). it is important to note that collecting IPD remains an attractive option. Beyond reducing bias from selective cut-off reporting, it can reduce heterogeneity among included studies as it allows for analysis based on predetermined inclusion/exclusion criteria, and it allows for subgroup analysis by important participant characteristics for which primary studies may not have reported results for, which would not be possible using the multiple cut-off models.

Availability of data and materials

The data that support the findings of this study are available upon reasonable request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions in agreements with individual data contributors.

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Acknowledgements

The DEPRESSD EPDS Group.

Ying Sun, 2 Chen He, 2 Ankur Krishnan, 2 Yin Wu, 2 Parash Mani Bhandari, 2 Dipika Neupane, 2 Mahrukh Imran, 2 Danielle B. Rice, 2 Marleine Azar, 2 Matthew J. Chiovitti, 2 Kira E. Riehm, 2 Jill T. Boruff, 11 Pim Cuijpers, 12 Simon Gilbody, 13 Lorie A. Kloda, 14 Scott B. Patten, 15 Roy C. Ziegelstein, 16 Sarah Markham, 17 Liane Comeau, 18 Nicholas D. Mitchell, 19 Simone N. Vigod, 20 Muideen O. Bakare, 21 Cheryl Tatano Beck, 22 Adomas Bunevicius, 23 Tiago Castro e Couto, 24 Genesis Chorwe-Sungani, 25 Nicolas Favez, 26 Sally Field, 27 Lluïsa Garcia-Esteve, 28 Simone Honikman, 29 Dina Sami Khalifa, 30 Jane Kohlhoff, 31  Laima Kusminskas, 32 Zoltán Kozinszky, 33  Sandra Nakić Radoš, 34 Susan J. Pawlby, 35 Tamsen J. Rochat, 36 Deborah J. Sharp, 37 Johanne Smith-Nielsen, 38 Kuan-Pin Su, 39 Meri Tadinac, 40 S. Darius Tandon, 41 Pavaani Thiagayson, 42 Annamária Töreki, 43  Anna Torres-Giménez, 44 Thandi van Heyningen, 45 Johann M. Vega-Dienstmaier. 46

11 Schulich Library of Physical Sciences, Life Sciences, and Engineering, McGill University, Montréal, Québec, Canada; 12 Department of Clinical, Neuro and Developmental Psychology, Amsterdam Public Health Research Institute, Vrije Universiteit Amsterdam, the Netherlands; 13 Hull York Medical School and the Department of Health Sciences, University of York, Heslington, York, UK; 14 Library, Concordia University, Montréal, Québec, Canada; 15 Departments of Community Health Sciences and Psychiatry, University of Calgary, Calgary, Canada; 16 Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, Maryland, USA; 17 Department of Biostatistics and Health Informatics, King’s College London, London, UK; 18 International Union for Health Promotion and Health Education, École de santé publique de l’Université de Montréal, Montréal, Québec, Canada; 19 Department of Psychiatry, University of Alberta, Edmonton, Alberta, Canada; 20 Women’s College Hospital and Research Institute, University of Toronto, Toronto, Ontario, Canada; 21 Muideen O. Bakare, Child and Adolescent Unit, Federal Neuropsychiatric Hospital, Enugu, Nigeria; 22 University of Connecticut School of Nursing, Mansfield, Connecticut, USA; 23 Neuroscience Institute, Lithuanian University of Health Sciences, Kaunas, Lithuania; 24 Federal University of Uberlândia, Brazil; 25 Department of Mental Health, School of Nursing, Kamuzu University of Health Sciences, Blantyre, Malawi; 26 Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland; 27 Perinatal Mental Health Project, Alan J. Flisher Centre for Public Mental Health, Department of Psychiatry and Mental Health, University of Cape Town, Cape Town, South Africa; 28 Perinatal Mental Health Unit CLINIC-BCN. Institut Clínic de Neurociències, Hospital Clínic, Barcelona, Spain; 29 Perinatal Mental Health Project, Alan J. Flisher Centre for Public Mental Health, Department of Psychiatry and Mental Health, University of Cape Town, Cape Town, South Africa; 30 Faculty of Health Sciences, Ahfad University for Women, Omdurman, Sudan; 31 School of Psychiatry, University of New South Wales, Kensington, Australia; 32 Private Practice, Hamburg, Germany; 33 Department of Obstetrics and Gynecology, Danderyd Hospital, Stockholm, Sweden; 34 Department of Psychology, Catholic University of Croatia, Zagreb, Croatia; 35 Institute of Psychiatry, Psychology & Neuroscience, King’s College London, London, UK; 36 MRC/Developmental Pathways to Health Research Unit, Faculty of Health Sciences, University of Witwatersrand, South Africa; 37 Centre for Academic Primary Care, Bristol Medical School, University of Bristol, UK; 38 Center for Early intervention and Family studies, Department of Psychology, University of Copenhagen, Denmark; 39 An-Nan Hospital, China Medical University and Mind-Body Interface Laboratory, China Medical University Hospital, Taiwan; 40 Department of Psychology, Faculty of Humanities and Social Sciences, University of Zagreb, Croatia; 41 Feinberg School of Medicine, Northwestern University, Chicago, Illinois, USA; 42 The Institute of Mental Health, Singapore; 43 Department of Emergency, University of Szeged, Hungary; 44 Perinatal Mental Health Unit CLINIC-BCN. Institut Clínic de Neurociències, Hospital Clínic, Barcelona, Spain; 45 Perinatal Mental Health Project, Alan J. Flisher Centre for Public Mental Health, Department of Psychiatry and Mental Health, University of Cape Town, Cape Town, South Africa; 46 Facultad de Medicina Alberto Hurtado, Universidad Peruana Cayetano Heredia, Lima, Perú.

This study was funded by the Canadian Institutes of Health Research (CIHR; KRS 140994, DA5 170278, PCG-155468, PBB 175359, PJT 178167). Dr. Negeri was supported by the Mitacs Accelerate Postdoctoral Fellowship. Drs. Levis and Wu were supported by Fonds de recherche du Québec – Santé (FRQ-S) Postdoctoral Training Fellowships. Dr. Thombs was supported by a Tier 1 Canada Research Chair. Dr. Benedetti was supported by a Fonds de recherche du Québec - Santé (FRQS) researcher salary award.

Ms. Rice was supported by a Vanier Canada Graduate Scholarship. The primary study by Alvarado et al. was supported by the Ministry of Health of Chile. The primary study by Beck et al. was supported by the Patrick and Catherine Weldon Donaghue Medical Research Foundation and the University of Connecticut Research Foundation. Prof. Robertas Bunevicius, MD, PhD (1958–2016) was Principal Investigator of the primary study by Bunevicius et al., but passed away and was unable to participate in this project. The primary study by Couto et al. was supported by the National Counsel of Technological and Scientific Development (CNPq) (Grant no. 444254/2014–5) and the Minas Gerais State Research Foundation (FAPEMIG) (Grant no. APQ-01954-14). The primary study by Chaudron et al. was supported by a grant from the National Institute of Mental Health (grant K23 MH64476). The primary study by Chorwe-Sungani et al. was supported by the University of Malawi through grant QZA-0484 NORHED 2013. The primary study by Tissot et al. was supported by the Swiss National Science Foundation (grant 32003B 125493). The primary study by van Heyningen et al. was supported by the Medical Research Council of South Africa (fund no. 415865), Cordaid Netherlands (Project 103/ 10002 G Sub 7) and the Truworths Community Foundation Trust, South Africa. Dr. van Heyningen was supported by the National Research Foundation of South Africa and the Harry Crossley Foundation. VHYTHE001/ 1232209. The primary study by Garcia-Esteve et al. was supported by grant 7/98 from the Ministerio de Trabajo y Asuntos Sociales, Women’s Institute, Spain. The primary study by Phillips et al. was supported by a scholarship from the National Health and Medical and Research Council (NHMRC). The primary study by Nakić Radoš et al. was supported by the Croatian Ministry of Science, Education, and Sports (134–0000000-2421). The primary study by Pawlby et al. was supported by a Medical Research Council UK Project Grant (number G89292999N). The primary study by Rochat et al. was supported by grants from the University of Oxford (HQ5035), the Tuixen Foundation (9940), the Wellcome Trust (082384/Z/07/Z and 071571), and the American Psychological Association. Dr. Rochat receives salary support from a Wellcome Trust Intermediate Fellowship (211374/Z/18/Z). The primary study by Smith-Nielsen et al. was supported by a grant from the charitable foundation Tryg Foundation (Grant ID no 107616). The primary study by Su et al. was supported by grants from the Department of Health (DOH94F044 and DOH95F022) and the China Medical University and Hospital (CMU94–105, DMR-92-92 and DMR94–46). The primary study by Tandon et al. was funded by the Thomas Wilson Sanitarium. The primary study by Vega-Dienstmaier et al. was supported by Tejada Family Foundation, Inc., and Peruvian-American Endowment, Inc. No other authors reported funding for primary studies or for their work on this study. No funder had any role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

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Zelalem F. Negeri

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Brooke Levis & Brett D. Thombs

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• , Lorie A. Kloda
• , Scott B. Patten
• , Roy C. Ziegelstein
• , Sarah Markham
• , Liane Comeau
• , Nicholas D. Mitchell
• , Simone N. Vigod
• , Muideen O. Bakare
• , Cheryl Tatano Beck
• , Adomas Bunevicius
• , Tiago Castro e Couto
• , Genesis Chorwe-Sungani
• , Nicolas Favez
• , Sally Field
• , Lluïsa Garcia-Esteve
• , Simone Honikman
• , Dina Sami Khalifa
• , Jane Kohlhoff
• , Laima Kusminskas
• , Zoltán Kozinszky
• , Sandra Nakić Radoš
• , Susan J. Pawlby
• , Tamsen J. Rochat
• , Deborah J. Sharp
• , Johanne Smith-Nielsen
• , Kuan-Pin Su
• , Meri Tadinac
• , S. Darius Tandon
• , Pavaani Thiagayson
• , Annamária Töreki
• , Anna Torres-Giménez
• , Thandi van Heyningen
•  & Johann M. Vega-Dienstmaier

Contributions

ZFN, BL, BDT, and AB contributed to the conception and design of the study, participated in the data analysis, and helped to draft the manuscript. JPAI contributed to the conception and design of the study and provided critical revisions to the manuscript. DEPRESSD EPDS Group authors contributed individual participant datasets, contributed to project conceptualization as DEPRESSD Steering Committee members or Knowledge Users, or contributed to the design and conduct of the main systematic review from which datasets were identified and obtained. All authors, including DEPRESSD EPDS Group authors, read and approved the final manuscript.

Corresponding author

Correspondence to Andrea Benedetti .

Ethics declarations

Ethics approval and consent to participate.

Since this study involves secondary analysis of de-identified previously collected data, the Research Ethics Committee of the Jewish General Hospital determined that research ethics approval was not required. For each included dataset, the primary study investigators confirmed that the original study received ethics approval and that all participants provided informed consent. All methods were carried out in accordance with the Declaration of Helsinki.

Consent for publication

Not Applicable.

Competing interests

All authors have completed the ICJME uniform disclosure form at www.icmje.org/coi_disclosure.pdf and declare: no support from any organization for the submitted work; no financial relationships with any organizations that might have an interest in the submitted work in the previous three years with the following exceptions: Dr. Vigod declares that she receives royalties from UpToDate, outside the submitted work. Dr. Beck declares that she receives royalties for her Postpartum Depression Screening Scale published by Western Psychological Services. All authors declare no other relationships or activities that could appear to have influenced the submitted work. No funder had any role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

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Supplementary Information

Additional file 1: table a1..

Distribution of EPDS scores by cut-off among participants with depression and without depression. Table A2. Estimated sensitivity and specificity, 95% confidence intervals (CI) and CI widths for each cut-off when BREM [ 13 ] was fitted to the published and full IPD dataset. Table A3. Estimated sensitivity and specificity, 95% confidence intervals (CI) and CI widths for each cut-off when Steinhauser et al. [ 16 ] model was fitted to the published and full IPD dataset. Table A4. Estimated sensitivity and specificity, 95% confidence intervals (CI) and CI widths for each cut-off when Jones et al. [ 18 ] model is fit to the published (top) and full IPD (bottom) dataset. Table A5. Estimated sensitivity and specificity, 95% confidence intervals (CI) and CI widths for each cut-off when Hoyer and Kuss [ 19 ] model is fit to the published (top) and full IPD (bottom) dataset. Figure A1. Distribution of published EPDS cut-offs by the number of primary studies included in the meta-analyses using the published dataset. Figure A2. Distribution of EPDS scores among participants with depression (red) and without depression (blue). Purple portions are part of both the blue and red distributions. Figure A3. Estimated sensitivity (left) and specificity (right) and 95% Confidence Interval (Credible Interval for Jones et al. [ 18 ]) by cut-off for the BREM [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ] and Hoyer and Kuss [ 19 ] methods applied to the full IPD dataset. Figure A4. Estimated sensitivity (left) and specificity (right) and 95% Confidence Interval (Credible Interval for Jones et al. [ 18 ]) by cut-off for the BREM [ 13 ], Steinhauser et al. [ 16 ], Jones et al. [ 18 ] and Hoyer and Kuss [ 19 ] methods applied to the published dataset.

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Negeri, Z.F., Levis, B., Ioannidis, J.P.A. et al. An empirical comparison of statistical methods for multiple cut-off diagnostic test accuracy meta-analysis of the Edinburgh postnatal depression scale (EPDS) depression screening tool using published results vs individual participant data. BMC Med Res Methodol 24 , 28 (2024). https://doi.org/10.1186/s12874-023-02134-w

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• Indian J Crit Care Med
• v.25(Suppl 2); 2021 May

An Introduction to Statistics: Choosing the Correct Statistical Test

Priya ranganathan.

1 Department of Anaesthesiology, Critical Care and Pain, Tata Memorial Centre, Homi Bhabha National Institute, Mumbai, Maharashtra, India

The choice of statistical test used for analysis of data from a research study is crucial in interpreting the results of the study. This article gives an overview of the various factors that determine the selection of a statistical test and lists some statistical testsused in common practice.

How to cite this article: Ranganathan P. An Introduction to Statistics: Choosing the Correct Statistical Test. Indian J Crit Care Med 2021;25(Suppl 2):S184–S186.

In a previous article in this series, we looked at different types of data and ways to summarise them. 1 At the end of the research study, statistical analyses are performed to test the hypothesis and either prove or disprove it. The choice of statistical test needs to be carefully performed since the use of incorrect tests could lead to misleading conclusions. Some key questions help us to decide the type of statistical test to be used for analysis of study data. 2

W hat is the R esearch H ypothesis ?

Sometimes, a study may just describe the characteristics of the sample, e.g., a prevalence study. Here, the statistical analysis involves only descriptive statistics . For example, Sridharan et al. aimed to analyze the clinical profile, species distribution, and susceptibility pattern of patients with invasive candidiasis. 3 They used descriptive statistics to express the characteristics of their study sample, including mean (and standard deviation) for normally distributed data, median (with interquartile range) for skewed data, and percentages for categorical data.

Studies may be conducted to test a hypothesis and derive inferences from the sample results to the population. This is known as inferential statistics . The goal of inferential statistics may be to assess differences between groups (comparison), establish an association between two variables (correlation), predict one variable from another (regression), or look for agreement between measurements (agreement). Studies may also look at time to a particular event, analyzed using survival analysis.

A re the C omparisons M atched (P aired ) or U nmatched (U npaired )?

Observations made on the same individual (before–after or comparing two sides of the body) are usually matched or paired . Comparisons made between individuals are usually unpaired or unmatched . Data are considered paired if the values in one set of data are likely to be influenced by the other set (as can happen in before and after readings from the same individual). Examples of paired data include serial measurements of procalcitonin in critically ill patients or comparison of pain relief during sequential administration of different analgesics in a patient with osteoarthritis.

W hat are the T ype of D ata B eing M easured ?

The test chosen to analyze data will depend on whether the data are categorical (and whether nominal or ordinal) or numerical (and whether skewed or normally distributed). Tests used to analyze normally distributed data are known as parametric tests and have a nonparametric counterpart that is used for data, which is distribution-free. 4 Parametric tests assume that the sample data are normally distributed and have the same characteristics as the population; nonparametric tests make no such assumptions. Parametric tests are more powerful and have a greater ability to pick up differences between groups (where they exist); in contrast, nonparametric tests are less efficient at identifying significant differences. Time-to-event data requires a special type of analysis, known as survival analysis.

H ow M any M easurements are B eing C ompared ?

The choice of the test differs depending on whether two or more than two measurements are being compared. This includes more than two groups (unmatched data) or more than two measurements in a group (matched data).

T ests for C omparison

( Table 1 lists the tests commonly used for comparing unpaired data, depending on the number of groups and type of data. As an example, Megahed and colleagues evaluated the role of early bronchoscopy in mechanically ventilated patients with aspiration pneumonitis. 5 Patients were randomized to receive either early bronchoscopy or conventional treatment. Between groups, comparisons were made using the unpaired t test for normally distributed continuous variables, the Mann–Whitney U -test for non-normal continuous variables, and the chi-square test for categorical variables. Chowhan et al. compared the efficacy of left ventricular outflow tract velocity time integral (LVOTVTI) and carotid artery velocity time integral (CAVTI) as predictors of fluid responsiveness in patients with sepsis and septic shock. 6 Patients were divided into three groups— sepsis, septic shock, and controls. Since there were three groups, comparisons of numerical variables were done using analysis of variance (for normally distributed data) or Kruskal–Wallis test (for skewed data).

Tests for comparison of unpaired data

A common error is to use multiple unpaired t -tests for comparing more than two groups; i.e., for a study with three treatment groups A, B, and C, it would be incorrect to run unpaired t -tests for group A vs B, B vs C, and C vs A. The correct technique of analysis is to run ANOVA and use post hoc tests (if ANOVA yields a significant result) to determine which group is different from the others.

( Table 2 lists the tests commonly used for comparing paired data, depending on the number of groups and type of data. As discussed above, it would be incorrect to use multiple paired t -tests to compare more than two measurements within a group. In the study by Chowhan, each parameter (LVOTVTI and CAVTI) was measured in the supine position and following passive leg raise. These represented paired readings from the same individual and comparison of prereading and postreading was performed using the paired t -test. 6 Verma et al. evaluated the role of physiotherapy on oxygen requirements and physiological parameters in patients with COVID-19. 7 Each patient had pretreatment and post-treatment data for heart rate and oxygen supplementation recorded on day 1 and day 14. Since data did not follow a normal distribution, they used Wilcoxon's matched pair test to compare the prevalues and postvalues of heart rate (numerical variable). McNemar's test was used to compare the presupplemental and postsupplemental oxygen status expressed as dichotomous data in terms of yes/no. In the study by Megahed, patients had various parameters such as sepsis-related organ failure assessment score, lung injury score, and clinical pulmonary infection score (CPIS) measured at baseline, on day 3 and day 7. 5 Within groups, comparisons were made using repeated measures ANOVA for normally distributed data and Friedman's test for skewed data.

Tests for comparison of paired data

T ests for A ssociation between V ariables

( Table 3 lists the tests used to determine the association between variables. Correlation determines the strength of the relationship between two variables; regression allows the prediction of one variable from another. Tyagi examined the correlation between ETCO 2 and PaCO 2 in patients with chronic obstructive pulmonary disease with acute exacerbation, who were mechanically ventilated. 8 Since these were normally distributed variables, the linear correlation between ETCO 2 and PaCO 2 was determined by Pearson's correlation coefficient. Parajuli et al. compared the acute physiology and chronic health evaluation II (APACHE II) and acute physiology and chronic health evaluation IV (APACHE IV) scores to predict intensive care unit mortality, both of which were ordinal data. Correlation between APACHE II and APACHE IV score was tested using Spearman's coefficient. 9 A study by Roshan et al. identified risk factors for the development of aspiration pneumonia following rapid sequence intubation. 10 Since the outcome was categorical binary data (aspiration pneumonia— yes/no), they performed a bivariate analysis to derive unadjusted odds ratios, followed by a multivariable logistic regression analysis to calculate adjusted odds ratios for risk factors associated with aspiration pneumonia.

Tests for assessing the association between variables

T ests for A greement between M easurements

( Table 4 outlines the tests used for assessing agreement between measurements. Gunalan evaluated concordance between the National Healthcare Safety Network surveillance criteria and CPIS for the diagnosis of ventilator-associated pneumonia. 11 Since both the scores are examples of ordinal data, Kappa statistics were calculated to assess the concordance between the two methods. In the previously quoted study by Tyagi, the agreement between ETCO 2 and PaCO 2 (both numerical variables) was represented using the Bland–Altman method. 8

Tests for assessing agreement between measurements

T ests for T ime-to -E vent D ata (S urvival A nalysis )

Time-to-event data represent a unique type of data where some participants have not experienced the outcome of interest at the time of analysis. Such participants are considered to be “censored” but are allowed to contribute to the analysis for the period of their follow-up. A detailed discussion on the analysis of time-to-event data is beyond the scope of this article. For analyzing time-to-event data, we use survival analysis (with the Kaplan–Meier method) and compare groups using the log-rank test. The risk of experiencing the event is expressed as a hazard ratio. Cox proportional hazards regression model is used to identify risk factors that are significantly associated with the event.

Hasanzadeh evaluated the impact of zinc supplementation on the development of ventilator-associated pneumonia (VAP) in adult mechanically ventilated trauma patients. 12 Survival analysis (Kaplan–Meier technique) was used to calculate the median time to development of VAP after ICU admission. The Cox proportional hazards regression model was used to calculate hazard ratios to identify factors significantly associated with the development of VAP.

The choice of statistical test used to analyze research data depends on the study hypothesis, the type of data, the number of measurements, and whether the data are paired or unpaired. Reviews of articles published in medical specialties such as family medicine, cytopathology, and pain have found several errors related to the use of descriptive and inferential statistics. 12 – 15 The statistical technique needs to be carefully chosen and specified in the protocol prior to commencement of the study, to ensure that the conclusions of the study are valid. This article has outlined the principles for selecting a statistical test, along with a list of tests used commonly. Researchers should seek help from statisticians while writing the research study protocol, to formulate the plan for statistical analysis.

Priya Ranganathan https://orcid.org/0000-0003-1004-5264

Source of support: Nil

Conflict of interest: None

R eferences

2024 Theses Doctoral

Statistically Efficient Methods for Computation-Aware Uncertainty Quantification and Rare-Event Optimization

He, Shengyi

The thesis covers two fundamental topics that are important across the disciplines of operations research, statistics and even more broadly, namely stochastic optimization and uncertainty quantification, with the common theme to address both statistical accuracy and computational constraints. Here, statistical accuracy encompasses the precision of estimated solutions in stochastic optimization, as well as the tightness or reliability of confidence intervals. Computational concerns arise from rare events or expensive models, necessitating efficient sampling methods or computation procedures. In the first half of this thesis, we study stochastic optimization that involves rare events, which arises in various contexts including risk-averse decision-making and training of machine learning models. Because of the presence of rare events, crude Monte Carlo methods can be prohibitively inefficient, as it takes a sample size reciprocal to the rare-event probability to obtain valid statistical information about the rare-event. To address this issue, we investigate the use of importance sampling (IS) to reduce the required sample size. IS is commonly used to handle rare events, and the idea is to sample from an alternative distribution that hits the rare event more frequently and adjusts the estimator with a likelihood ratio to retain unbiasedness. While IS has been long studied, most of its literature focuses on estimation problems and methodologies to obtain good IS in these contexts. Contrary to these studies, the first half of this thesis provides a systematic study on the efficient use of IS in stochastic optimization. In Chapter 2, we propose an adaptive procedure that converts an efficient IS for gradient estimation to an efficient IS procedure for stochastic optimization. Then, in Chapter 3, we provide an efficient IS for gradient estimation, which serves as the input for the procedure in Chapter 2. In the second half of this thesis, we study uncertainty quantification in the sense of constructing a confidence interval (CI) for target model quantities or prediction. We are interested in the setting of expensive black-box models, which means that we are confined to using a low number of model runs, and we also lack the ability to obtain auxiliary model information such as gradients. In this case, a classical method is batching, which divides data into a few batches and then constructs a CI based on the batched estimates. Another method is the recently proposed cheap bootstrap that is constructed on a few resamples in a similar manner as batching. These methods could save computation since they do not need an accurate variability estimator which requires sufficient model evaluations to obtain. Instead, they cancel out the variability when constructing pivotal statistics, and thus obtain asymptotically valid t-distribution-based CIs with only few batches or resamples. The second half of this thesis studies several theoretical aspects of these computation-aware CI construction methods. In Chapter 4, we study the statistical optimality on CI tightness among various computation-aware CIs. Then, in Chapter 5, we study the higher-order coverage errors of batching methods. Finally, Chapter 6 is a related investigation on the higher-order coverage and correction of distributionally robust optimization (DRO) as another CI construction tool, which assumes an amount of analytical information on the model but bears similarity to Chapter 5 in terms of analysis techniques.

• Operations research
• Stochastic processes--Mathematical models
• Mathematical optimization
• Bootstrap (Statistics)
• Sampling (Statistics)

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25+ Crucial Average Cost Per Hire Facts [2023]: All Cost Of Hiring Statistics

• Average Labor Cost Percent Of Sales
• Average Time to Reach Profitability At A Startup
• Office Space Per Employee
• Recruitment Statistics
• Employee Engagement Statistics
• Work-Life Balance Statistics
• BYOD Statistics
• Paternity Leave Statistics
• Onboarding Statistics
• Average Paid Maternity Leave In Us
• Average Cost Of A Bad Hire
• Employee Theft Statistics
• Paid Family Leave Statistics
• Cost Of Hiring Statistics
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• Social Media Recruitment Statistics
• Hiring Statistics
• Out Of Prison Employment Statistics

Research Summary. Hiring new employees with the appropriate experiences and qualifications is essential to the continued success and profitability of nearly every U.S. company. However, the average cost to hire an employee can be a huge factor when going through the process. After extensive research, our data analysis team concluded:

The average cost per hire is $4,700 .

It takes 36 to 42 days to fill the average position in the United States.

15% of Human Resources expenses are allocated towards recruitment efforts.

It costs up to 40% of an employee’s base salary to hire a new employee with benefits.

63% of hiring managers and talent acquisition specialists report that AI has positively changed how recruiting is handled at their company.

It takes, on average, three to eight months for a new hire to become fully productive at work.

General Cost of Hiring Statistics

In the United States, the median cost per hire is $1,633.

The median cost per hire is $2,792 less than the average cost per hire, which currently sits at $4,700. What this means is that some jobs cost a lot more to fill than a typical job, which skews the average cost of a new hire significantly.

To put it in perspective, 75% of hires cost less than $4,669 . In comparison, the average cost to hire an executive is $14,936 and the median cost is $5,000. These relatively small segments of employees eat up a disproportionate amount of recruiting and hiring expenses.

Average and Median Cost Per Hire for Executive and Non-Executive Positions

A vacancy in a company costs, on average, about $98 per day.

The average vacancy costs employers a staggering $4,129 over 42 days, the time it typically takes to fill an open position. This breaks down to just over $98 per day, plus the additional funds allocated towards recruitment.

On average, benefits cost employers 25% to 40% of a new employee’s base salary.

Salary and benefits packages are valued at 1.25 to 1.4 times a new employee’s base salary. Therefore, for an employee earning $50,000 annually, their benefits could cost a company anywhere from an additional $12,500 to $20,000 annually.

At small companies across the nation, the average cost of training is $1,105 per employee per year.

Small businesses, or companies with 100 to 999 employees, spend more than $1,000 per employee on training each year, $658 more than large companies.

For comparison, large companies with 10,000 employees or more spent about $447 per employee each year and midsize companies, with 1,000 to 9,999 employees, spent about $545.

Average Training Cost Per Employee

All training costs were calculated by taking both structured training costs and the time managers and employees spend training new hires into account.

It can take up to six months for a company to make up the money it spent on a new hire.

After investing in hiring a new, mid-level employee, HBS data suggests that it takes up to half a year to break even on their investment. The survey also concluded that new hires typically don’t reach their full productivity level until being on the job for more than 12 consecutive weeks.

Cost Per Hire Demographic Statistics

The cost of hiring and onboarding an entry-level employee is an estimated 180% less than the cost of hiring an executive-level employee.

Hiring an entry-level employee is estimated to cost about 20% of that employee’s salary. Meanwhile, hiring a mid-level employee typically runs up an average cost of $60,000, or 1 to 1.5 times the employee’s salary.

Hiring costs are the highest for executive-level employees. Data shows that it typically costs companies across the U.S. more than 200% of the new executive-level employee’s salary to complete the hiring and onboarding process.

Depending on the industry, it can take between 10 and 60 days to hire a new employee.

It typically takes approximately 60 days to hire a public sector employee, 30 days to hire a hospital or nonprofit employee, 20 days to hire a private sector employee, and 10 days to hire a franchise employee.

Hiring times also vary by state, city, and location. Average hiring times were 34.4 days in Washington , D.C., 25.3 days in Portland, Oregon , 23.7 days in San Francisco, California , 19.6 days in Austin, Texas , and 18.6 days in Miami, Florida .

Internal HR teams significantly increase a company’s cost per hire.

According to research, internal human resources teams can increase a firm’s hiring costs by 50% or more. An internal HR recruiter earning an annual salary of $51,000 increases hiring costs by at least $4,250 each month.

The majority of companies use reference checks to screen hourly, entry-level, middle management, executive candidates during the recruitment and selection processes.

Across the country, companies check references 74% of the time when screening executive level and middle management candidates, 69% of the time when screening non-management candidates, and 65% of the time when screening non-management hourly or non-exempt candidates.

Other popular screening methods include one-on-one interviews, phone screenings, behavioral interviews, in-person screenings, group interviews, and behavioral interviews , which are used by hiring managers and recruiters 68% to 54% of the time when assessing an applicant.

Executive search firms, in-house executive recruiters, and industry associations are the top three tools used to source executive candidates.

When recruiting employees for executive positions, data shows that 49% of surveyed firms use headhunters or executive search firms to find new talent, 28% use in-house executive recruiters to find new talent, and 23% of surveyed firms use industry associations to find new talent.

73% of companies in the United States use talent acquisition software.

The vast majority of U.S. businesses rely on talent acquisition software when recruiting new employees. Such software works to streamline the recruitment and hiring process, reduce the time and cost spent on hiring new employees, and enhance the onboarding experience.

Company websites, employee referrals, and free job boards are some of the most popular methods for employee recruitment in the U.S.

85% of surveyed companies recruit new employees through their company website, 90% of surveyed companies recruit new employees through referrals from current employees, and 71% of surveyed companies recruit new employees via free job boards.

Top Recruitment Methods in the U.S.

At most businesses across the United States, staff recruitment is the responsibility of an HR generalist.

Approximately 48% of HR generalists are responsible for recruiting for nonexecutive job openings, and 32% are responsible for recruiting for executive job openings.

Aside from HR generalists, new staff recruitment for non-executive roles is put in the hands of in-house recruiters 25% of the time, hiring managers 16% of the time, and third-party recruiters and staffing agencies 3% of the time.

Recruitment Trends and Predictions

The use of artificial intelligence as a recruitment tool is gaining popularity across the U.S.

According to recent research, 96% of hiring managers think that using AI, or artificial intelligence, can improve the recruitment and hiring process .

As the use of AI in HR departments across the nation continues to grow, it is primarily being used to improve talent acquisition and retention by enhancing sourcing, screening, hiring, onboarding, and more.

Human resources outsourcing is expected to grow at an annual rate of 4.9% over the next several years.

The HR outsourcing industry is expected to reach a market value of $45.8 billion by 2027, up by $13 billion from the 2020 market value of $32.8 billion. The increase in revenue represents a growth rate of nearly 5%.

Finding the right candidate in high-demand talent pools is one of the biggest challenges in recruiting today’s job candidates.

46% of hiring managers state that one of the biggest recruitment challenges is sourcing qualified candidates from high-demand talent pools. Other top challenges in today’s recruiting process include obstacles related to compensation and competition.

The majority of recruiters and hiring managers in the U.S. rely on software during the recruitment process.

The use of recruitment software is becoming more and more popular. Today, 51% of hiring managers use interview scheduling software to help streamline the recruitment process, and 26% are thinking about starting.

New Hire Statistics

Average productivity rates for new employees hover around 25% during the first 30 days of employment.

Data suggests that new hires have a 25% productivity rate in their first month on the job after completing new employee training. That number then increases to 50% in their second month of work and 75% in their third month on the job.

It takes three to eight months for an employee to become fully productive.

Across almost all professional industries, hiring experts estimate that it can take almost a year for a new hire to reach full productivity at work .

A bad hire could cost a company up to 300% of the employee’s salary.

According to the Harvard Business Review data, employee turnover costs range between 100% and 300% of the replaced employee’s salary. With about 23% of new hires turning over before their first year on the job, hiring the wrong person can quickly become costly.

Companies can lose $15,000 or more on hiring an employee who leaves after one year or less.

According to a report by Employee Benefits News, organizations that hire a full-time salary employee earning $45,000 annually lose about $15,000 when that employee leaves the company after one year or less. The cost is even higher for employees making more money, equalling at least 33% of their annual salary.

Average Cost Per Hire FAQ

What is cost per hire?

Cost per hire is the average amount of money a business spends on hiring a new employee. Cost per hire includes all HR and recruiting costs, including advertising, software, employee’s salaries, and more, involved in the onboarding process.

Cost per hire metrics are especially important as they allow companies to budget their recruiting expenses, evaluate their hiring process, and optimize their recruiting strategies.

How do you calculate cost per hire?

To calculate cost per hire, divide the total number of hires over a given period by the total recruitment cost over that same period. In other words:

Your total recruitment cost should take into account both internal recruiting costs and external recruiting costs.

What’s included in internal recruiting costs?

There are at least 6 factors included in internal recruiting costs. These include:

Candidate assessment costs

Employer branding

Internal recruiter salaries

Hiring managers’ salaries (or a portion thereof)

Travel expenses due to recruitment

Employee referral bonuses

Internal recruiting costs are typically the most expensive.

What’s included in external recruiting costs?

There are also at least 6 factors included in external recruiting costs. These include:

Job advertisement fees

External recruiter fees

Recruiting agency fees

Staffing agency/firm fees

Recruitment software

Recruiting event costs

What’s a good benchmark for cost per hire?

A good benchmark for cost per hire is between $3,000 and $5,000. However, it can be much lower depending on the size of your business and the nature of your business.

In the United States, the average cost per hire is $4,700. Many factors contribute to a company’s cost per hire, including industry, company size , and the level of the role being filled. As such, a good benchmark for cost per hire can range anywhere from $3,000 to $5,000, according to the Society of Human Resource Management.

What is a good cost per applicant?

What’s included in a recruiting budget?

There are 8 important elements included in a recruiting budget. These are those elements:

Job board/advertisement fees

Applicant tracking system sofware fees

Recruiter fees

Internal HR expenses

Expenses for branding, promotion, social media, etc.

Pre-employment screening and/or testing

Referral bonuses

Travel reimbursements

How much does it cost to advertise a job?

It costs between $0.10 and $5.00 per click to advertise a job, in most cases. Most job posting sites operate on a pay-per-click model, which means that you only pay them when a candidate is actually interested enough to click the job advertisement.

There are other models that include setting a maximum spend (once a certain amount of people click it, the posting will stop being advertised) so that you can manage your spending.

Is cost per hire important?

Yes, knowing your cost per hire is important. However, it is far more important to invest in top talent than to get the most hires for the least amount of money.

Effective onboarding and hiring processes are integral to businesses’ continued success and longevity in virtually every industry across the United States. With the nation’s average cost per hire hovering around $4,700, understanding hiring statistics is an important factor in reducing recruitment costs and increasing revenue and profitability.

Across the U.S., it takes between 36 and 42 days to make a new hire, so it’s no surprise that the vast majority of companies allocate roughly 15% of all HR expenses towards recruitment efforts. Although such efforts can be costly, sometimes adding up to more than 40% of an employee’s base salary, finding and hiring good employees is key.

With the increased use of artificial intelligence to enhance the hiring process, the future of recruitment looks bright. As a result, the likelihood of reducing HR costs and quickly finding qualified candidates is increasing substantially.

SHRM. “ SHRM Customized Talent Acquisition Benchmarking Report. ” Accessed on August 19, 2021.

SHRM. “ The Real Costs of Recruitment. ” Accessed on September 6, 2022.

Johnson Service Group. “ Are You Aware Of The Cost Of Vacancies? ” Accessed on August 19, 2021.

Investopedia. “ The Cost Of Hiring A New Employee. ” Accessed on August 19, 2021.

Harvard Business Review. “ Technology Can Save Onboarding From Itself. ” Accessed on August 20, 2021.

Forbes. “ The Cost Of Turnover Can Kill Your Business And Make Things Less Fun. ” Accessed on August 20, 2021.

PR Newswire. “ Global Human Resource Outsourcing (HRO) Industry. ” Accessed on August 20, 2021.

Ideal. “ The Rise Of AI In Talent Acquisition. ” Accessed on August 20, 2021.

Yello. “ Real Recruiters Share How HR Tech Has Helped Them Win The War On Talent. ” Accessed on August 20, 2021.

The Hire Talent. “ Hiring Costs At Every Level. ” Accessed on August 21, 2021.

SHRM. “ Average U.S. Hiring Time Increased By 10 Days Since 2010. ” Accessed on August 21, 2021.

Business Wire. “ It Can Take Eight Months Before New Starters Become Productive at Work. ” Accessed on February 16, 2023.

Office staff salaries

Zippia ’s research team connects data from disparate sources to break down statistics at the job and industry levels. Below you can dig deeper into the data on how much hiring costs for different positions or browse through Office and Administrative jobs .

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Overview | Jobs Salary

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Air cargo agent, browse office and administrative jobs.

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Elsie is an experienced writer, reporter, and content creator. As a leader in her field, Elsie is best known for her work as a Reporter for The Southampton Press, but she can also be credited with contributions to Long Island Pulse Magazine and Hamptons Online. She holds a Bachelor of Arts degree in journalism from Stony Brook University and currently resides in Franklin, Tennessee.

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Which social media platforms are most common, who uses each social media platform, find out more, social media fact sheet.

Many Americans use social media to connect with one another, engage with news content, share information and entertain themselves. Explore the patterns and trends shaping the social media landscape.

To better understand Americans’ social media use, Pew Research Center surveyed 5,733 U.S. adults from May 19 to Sept. 5, 2023. Ipsos conducted this National Public Opinion Reference Survey (NPORS) for the Center using address-based sampling and a multimode protocol that included both web and mail. This way nearly all U.S. adults have a chance of selection. The survey is weighted to be representative of the U.S. adult population by gender, race and ethnicity, education and other categories.

Polls from 2000 to 2021 were conducted via phone. For more on this mode shift, read our Q&A.

Here are the questions used for this analysis , along with responses, and  its methodology ­­­.

A note on terminology: Our May-September 2023 survey was already in the field when Twitter changed its name to “X.” The terms  Twitter  and  X  are both used in this report to refer to the same platform.

YouTube and Facebook are the most-widely used online platforms. About half of U.S. adults say they use Instagram, and smaller shares use sites or apps such as TikTok, LinkedIn, Twitter (X) and BeReal.

Note: The vertical line indicates a change in mode. Polls from 2012-2021 were conducted via phone. In 2023, the poll was conducted via web and mail. For more details on this shift, please read our Q&A . Refer to the topline for more information on how question wording varied over the years. Pre-2018 data is not available for YouTube, Snapchat or WhatsApp; pre-2019 data is not available for Reddit; pre-2021 data is not available for TikTok; pre-2023 data is not available for BeReal. Respondents who did not give an answer are not shown.

Source: Surveys of U.S. adults conducted 2012-2023.

Usage of the major online platforms varies by factors such as age, gender and level of formal education.

% of U.S. adults who say they ever use __ by …

• RACE & ETHNICITY
• POLITICAL AFFILIATION

This fact sheet was compiled by Research Assistant  Olivia Sidoti , with help from Research Analyst  Risa Gelles-Watnick , Research Analyst  Michelle Faverio , Digital Producer  Sara Atske , Associate Information Graphics Designer Kaitlyn Radde and Temporary Researcher  Eugenie Park .

Follow these links for more in-depth analysis of the impact of social media on American life.

• Americans’ Social Media Use  Jan. 31, 2024
• Americans’ Use of Mobile Technology and Home Broadband  Jan. 31 2024
• Q&A: How and why we’re changing the way we study tech adoption  Jan. 31, 2024

Find more reports and blog posts related to  internet and technology .

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