statistical analysis in research methodology example

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. 

If you are a science wizard and fascinated by the role of AI in statistical analysis, check out this amazing Caltech Post Graduate Program in AI & ML course in collaboration with Caltech. With a comprehensive syllabus and real-life projects, this course is one of the most popular courses and will help you with all that you need to know about Artificial Intelligence. 

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What Is Statistical Analysis?

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. 

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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What is Statistical Analysis? Types, Methods, Software, Examples

Appinio Research · 29.02.2024 · 31min read

Ever wondered how we make sense of vast amounts of data to make informed decisions? Statistical analysis is the answer. In our data-driven world, statistical analysis serves as a powerful tool to uncover patterns, trends, and relationships hidden within data. From predicting sales trends to assessing the effectiveness of new treatments, statistical analysis empowers us to derive meaningful insights and drive evidence-based decision-making across various fields and industries. In this guide, we'll explore the fundamentals of statistical analysis, popular methods, software tools, practical examples, and best practices to help you harness the power of statistics effectively. Whether you're a novice or an experienced analyst, this guide will equip you with the knowledge and skills to navigate the world of statistical analysis with confidence.

What is Statistical Analysis?

Statistical analysis is a methodical process of collecting, analyzing, interpreting, and presenting data to uncover patterns, trends, and relationships. It involves applying statistical techniques and methodologies to make sense of complex data sets and draw meaningful conclusions.

Importance of Statistical Analysis

Statistical analysis plays a crucial role in various fields and industries due to its numerous benefits and applications:

• Informed Decision Making : Statistical analysis provides valuable insights that inform decision-making processes in business, healthcare, government, and academia. By analyzing data, organizations can identify trends, assess risks, and optimize strategies for better outcomes.
• Evidence-Based Research : Statistical analysis is fundamental to scientific research, enabling researchers to test hypotheses, draw conclusions, and validate theories using empirical evidence. It helps researchers quantify relationships, assess the significance of findings, and advance knowledge in their respective fields.
• Quality Improvement : In manufacturing and quality management, statistical analysis helps identify defects, improve processes, and enhance product quality. Techniques such as Six Sigma and Statistical Process Control (SPC) are used to monitor performance, reduce variation, and achieve quality objectives.
• Risk Assessment : In finance, insurance, and investment, statistical analysis is used for risk assessment and portfolio management. By analyzing historical data and market trends, analysts can quantify risks, forecast outcomes, and make informed decisions to mitigate financial risks.
• Predictive Modeling : Statistical analysis enables predictive modeling and forecasting in various domains, including sales forecasting, demand planning, and weather prediction. By analyzing historical data patterns, predictive models can anticipate future trends and outcomes with reasonable accuracy.
• Healthcare Decision Support : In healthcare, statistical analysis is integral to clinical research, epidemiology, and healthcare management. It helps healthcare professionals assess treatment effectiveness, analyze patient outcomes, and optimize resource allocation for improved patient care.

Statistical Analysis Applications

Statistical analysis finds applications across diverse domains and disciplines, including:

• Business and Economics : Market research , financial analysis, econometrics, and business intelligence.
• Healthcare and Medicine : Clinical trials, epidemiological studies, healthcare outcomes research, and disease surveillance.
• Social Sciences : Survey research, demographic analysis, psychology experiments, and public opinion polls.
• Engineering : Reliability analysis, quality control, process optimization, and product design.
• Environmental Science : Environmental monitoring, climate modeling, and ecological research.
• Education : Educational research, assessment, program evaluation, and learning analytics.
• Government and Public Policy : Policy analysis, program evaluation, census data analysis, and public administration.
• Technology and Data Science : Machine learning, artificial intelligence, data mining, and predictive analytics.

These applications demonstrate the versatility and significance of statistical analysis in addressing complex problems and informing decision-making across various sectors and disciplines.

Fundamentals of Statistics

Understanding the fundamentals of statistics is crucial for conducting meaningful analyses. Let's delve into some essential concepts that form the foundation of statistical analysis.

Basic Concepts

Statistics is the science of collecting, organizing, analyzing, and interpreting data to make informed decisions or conclusions. To embark on your statistical journey, familiarize yourself with these fundamental concepts:

• Population vs. Sample : A population comprises all the individuals or objects of interest in a study, while a sample is a subset of the population selected for analysis. Understanding the distinction between these two entities is vital, as statistical analyses often rely on samples to draw conclusions about populations.
• Independent Variables : Variables that are manipulated or controlled in an experiment.
• Dependent Variables : Variables that are observed or measured in response to changes in independent variables.
• Parameters vs. Statistics : Parameters are numerical measures that describe a population, whereas statistics are numerical measures that describe a sample. For instance, the population mean is denoted by μ (mu), while the sample mean is denoted by x̄ (x-bar).

Descriptive Statistics

Descriptive statistics involve methods for summarizing and describing the features of a dataset. These statistics provide insights into the central tendency, variability, and distribution of the data. Standard measures of descriptive statistics include:

• Mean : The arithmetic average of a set of values, calculated by summing all values and dividing by the number of observations.
• Median : The middle value in a sorted list of observations.
• Mode : The value that appears most frequently in a dataset.
• Range : The difference between the maximum and minimum values in a dataset.
• Variance : The average of the squared differences from the mean.
• Standard Deviation : The square root of the variance, providing a measure of the average distance of data points from the mean.
• Graphical Techniques : Graphical representations, including histograms, box plots, and scatter plots, offer visual insights into the distribution and relationships within a dataset. These visualizations aid in identifying patterns, outliers, and trends.

Inferential Statistics

Inferential statistics enable researchers to draw conclusions or make predictions about populations based on sample data. These methods allow for generalizations beyond the observed data. Fundamental techniques in inferential statistics include:

• Null Hypothesis (H0) : The hypothesis that there is no significant difference or relationship.
• Alternative Hypothesis (H1) : The hypothesis that there is a significant difference or relationship.
• Confidence Intervals : Confidence intervals provide a range of plausible values for a population parameter. They offer insights into the precision of sample estimates and the uncertainty associated with those estimates.
• Regression Analysis : Regression analysis examines the relationship between one or more independent variables and a dependent variable. It allows for the prediction of the dependent variable based on the values of the independent variables.
• Sampling Methods : Sampling methods, such as simple random sampling, stratified sampling, and cluster sampling , are employed to ensure that sample data are representative of the population of interest. These methods help mitigate biases and improve the generalizability of results.

Probability Distributions

Probability distributions describe the likelihood of different outcomes in a statistical experiment. Understanding these distributions is essential for modeling and analyzing random phenomena. Some common probability distributions include:

• Normal Distribution : The normal distribution, also known as the Gaussian distribution, is characterized by a symmetric, bell-shaped curve. Many natural phenomena follow this distribution, making it widely applicable in statistical analysis.
• Binomial Distribution : The binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials. It is commonly used to model binary outcomes, such as success or failure, heads or tails.
• Poisson Distribution : The Poisson distribution models the number of events occurring in a fixed interval of time or space. It is often used to analyze rare or discrete events, such as the number of customer arrivals in a queue within a given time period.

Types of Statistical Analysis

Statistical analysis encompasses a diverse range of methods and approaches, each suited to different types of data and research questions. Understanding the various types of statistical analysis is essential for selecting the most appropriate technique for your analysis. Let's explore some common distinctions in statistical analysis methods.

Parametric vs. Non-parametric Analysis

Parametric and non-parametric analyses represent two broad categories of statistical methods, each with its own assumptions and applications.

• Parametric Analysis : Parametric methods assume that the data follow a specific probability distribution, often the normal distribution. These methods rely on estimating parameters (e.g., means, variances) from the data. Parametric tests typically provide more statistical power but require stricter assumptions. Examples of parametric tests include t-tests, ANOVA, and linear regression.
• Non-parametric Analysis : Non-parametric methods make fewer assumptions about the underlying distribution of the data. Instead of estimating parameters, non-parametric tests rely on ranks or other distribution-free techniques. Non-parametric tests are often used when data do not meet the assumptions of parametric tests or when dealing with ordinal or non-normal data. Examples of non-parametric tests include the Wilcoxon rank-sum test, Kruskal-Wallis test, and Spearman correlation.

Descriptive vs. Inferential Analysis

Descriptive and inferential analyses serve distinct purposes in statistical analysis, focusing on summarizing data and making inferences about populations, respectively.

• Descriptive Analysis : Descriptive statistics aim to describe and summarize the features of a dataset. These statistics provide insights into the central tendency, variability, and distribution of the data. Descriptive analysis techniques include measures of central tendency (e.g., mean, median, mode), measures of dispersion (e.g., variance, standard deviation), and graphical representations (e.g., histograms, box plots).
• Inferential Analysis : Inferential statistics involve making inferences or predictions about populations based on sample data. These methods allow researchers to generalize findings from the sample to the larger population. Inferential analysis techniques include hypothesis testing, confidence intervals, regression analysis, and sampling methods. These methods help researchers draw conclusions about population parameters, such as means, proportions, or correlations, based on sample data.

Exploratory vs. Confirmatory Analysis

Exploratory and confirmatory analyses represent two different approaches to data analysis, each serving distinct purposes in the research process.

• Exploratory Analysis : Exploratory data analysis (EDA) focuses on exploring data to discover patterns, relationships, and trends. EDA techniques involve visualizing data, identifying outliers, and generating hypotheses for further investigation. Exploratory analysis is particularly useful in the early stages of research when the goal is to gain insights and generate hypotheses rather than confirm specific hypotheses.
• Confirmatory Analysis : Confirmatory data analysis involves testing predefined hypotheses or theories based on prior knowledge or assumptions. Confirmatory analysis follows a structured approach, where hypotheses are tested using appropriate statistical methods. Confirmatory analysis is common in hypothesis-driven research, where the goal is to validate or refute specific hypotheses using empirical evidence. Techniques such as hypothesis testing, regression analysis, and experimental design are often employed in confirmatory analysis.

Methods of Statistical Analysis

Statistical analysis employs various methods to extract insights from data and make informed decisions. Let's explore some of the key methods used in statistical analysis and their applications.

Hypothesis Testing

Hypothesis testing is a fundamental concept in statistics, allowing researchers to make decisions about population parameters based on sample data. The process involves formulating null and alternative hypotheses, selecting an appropriate test statistic, determining the significance level, and interpreting the results. Standard hypothesis tests include:

• t-tests : Used to compare means between two groups.
• ANOVA (Analysis of Variance) : Extends the t-test to compare means across multiple groups.
• Chi-square test : Assessing the association between categorical variables.

Regression Analysis

Regression analysis explores the relationship between one or more independent variables and a dependent variable. It is widely used in predictive modeling and understanding the impact of variables on outcomes. Key types of regression analysis include:

• Simple Linear Regression : Examines the linear relationship between one independent variable and a dependent variable.
• Multiple Linear Regression : Extends simple linear regression to analyze the relationship between multiple independent variables and a dependent variable.
• Logistic Regression : Used for predicting binary outcomes or modeling probabilities.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups. It partitions the total variability in the data into components attributable to different sources, such as between-group differences and within-group variability. ANOVA is commonly used in experimental design and hypothesis testing scenarios.

Time Series Analysis

Time series analysis deals with analyzing data collected or recorded at successive time intervals. It helps identify patterns, trends, and seasonality in the data. Time series analysis techniques include:

• Trend Analysis : Identifying long-term trends or patterns in the data.
• Seasonal Decomposition : Separating the data into seasonal, trend, and residual components.
• Forecasting : Predicting future values based on historical data.

Survival Analysis

Survival analysis is used to analyze time-to-event data, such as time until death, failure, or occurrence of an event of interest. It is widely used in medical research, engineering, and social sciences to analyze survival probabilities and hazard rates over time.

Factor Analysis

Factor analysis is a statistical method used to identify underlying factors or latent variables that explain patterns of correlations among observed variables. It is commonly used in psychology, sociology, and market research to uncover underlying dimensions or constructs.

Cluster Analysis

Cluster analysis is a multivariate technique that groups similar objects or observations into clusters or segments based on their characteristics. It is widely used in market segmentation, image processing, and biological classification.

Principal Component Analysis (PCA)

PCA is a dimensionality reduction technique used to transform high-dimensional data into a lower-dimensional space while preserving most of the variability in the data. It identifies orthogonal axes (principal components) that capture the maximum variance in the data. PCA is useful for data visualization, feature selection, and data compression.

How to Choose the Right Statistical Analysis Method?

Selecting the appropriate statistical method is crucial for obtaining accurate and meaningful results from your data analysis.

Understanding Data Types and Distribution

Before choosing a statistical method, it's essential to understand the types of data you're working with and their distribution. Different statistical methods are suitable for different types of data:

• Continuous vs. Categorical Data : Determine whether your data are continuous (e.g., height, weight) or categorical (e.g., gender, race). Parametric methods such as t-tests and regression are typically used for continuous data, while non-parametric methods like chi-square tests are suitable for categorical data.
• Normality : Assess whether your data follows a normal distribution. Parametric methods often assume normality, so if your data are not normally distributed, non-parametric methods may be more appropriate.

Assessing Assumptions

Many statistical methods rely on certain assumptions about the data. Before applying a method, it's essential to assess whether these assumptions are met:

• Independence : Ensure that observations are independent of each other. Violations of independence assumptions can lead to biased results.
• Homogeneity of Variance : Verify that variances are approximately equal across groups, especially in ANOVA and regression analyses. Levene's test or Bartlett's test can be used to assess homogeneity of variance.
• Linearity : Check for linear relationships between variables, particularly in regression analysis. Residual plots can help diagnose violations of linearity assumptions.

Considering Research Objectives

Your research objectives should guide the selection of the appropriate statistical method.

• What are you trying to achieve with your analysis? : Determine whether you're interested in comparing groups, predicting outcomes, exploring relationships, or identifying patterns.
• What type of data are you analyzing? : Choose methods that are suitable for your data type and research questions.
• Are you testing specific hypotheses or exploring data for insights? : Confirmatory analyses involve testing predefined hypotheses, while exploratory analyses focus on discovering patterns or relationships in the data.

Consulting Statistical Experts

If you're unsure about the most appropriate statistical method for your analysis, don't hesitate to seek advice from statistical experts or consultants:

• Collaborate with Statisticians : Statisticians can provide valuable insights into the strengths and limitations of different statistical methods and help you select the most appropriate approach.
• Utilize Resources : Take advantage of online resources, forums, and statistical software documentation to learn about different methods and their applications.
• Peer Review : Consider seeking feedback from colleagues or peers familiar with statistical analysis to validate your approach and ensure rigor in your analysis.

By carefully considering these factors and consulting with experts when needed, you can confidently choose the suitable statistical method to address your research questions and obtain reliable results.

Statistical Analysis Software

Choosing the right software for statistical analysis is crucial for efficiently processing and interpreting your data. In addition to statistical analysis software, it's essential to consider tools for data collection, which lay the foundation for meaningful analysis.

What is Statistical Analysis Software?

Statistical software provides a range of tools and functionalities for data analysis, visualization, and interpretation. These software packages offer user-friendly interfaces and robust analytical capabilities, making them indispensable tools for researchers, analysts, and data scientists.

• Graphical User Interface (GUI) : Many statistical software packages offer intuitive GUIs that allow users to perform analyses using point-and-click interfaces. This makes statistical analysis accessible to users with varying levels of programming expertise.
• Scripting and Programming : Advanced users can leverage scripting and programming capabilities within statistical software to automate analyses, customize functions, and extend the software's functionality.
• Visualization : Statistical software often includes built-in visualization tools for creating charts, graphs, and plots to visualize data distributions, relationships, and trends.
• Data Management : These software packages provide features for importing, cleaning, and manipulating datasets, ensuring data integrity and consistency throughout the analysis process.

Popular Statistical Analysis Software

Several statistical software packages are widely used in various industries and research domains. Some of the most popular options include:

• R : R is a free, open-source programming language and software environment for statistical computing and graphics. It offers a vast ecosystem of packages for data manipulation, visualization, and analysis, making it a popular choice among statisticians and data scientists.
• Python : Python is a versatile programming language with robust libraries like NumPy, SciPy, and pandas for data analysis and scientific computing. Python's simplicity and flexibility make it an attractive option for statistical analysis, particularly for users with programming experience.
• SPSS : SPSS (Statistical Package for the Social Sciences) is a comprehensive statistical software package widely used in social science research, marketing, and healthcare. It offers a user-friendly interface and a wide range of statistical procedures for data analysis and reporting.
• SAS : SAS (Statistical Analysis System) is a powerful statistical software suite used for data management, advanced analytics, and predictive modeling. SAS is commonly employed in industries such as healthcare, finance, and government for data-driven decision-making.
• Stata : Stata is a statistical software package that provides tools for data analysis, manipulation, and visualization. It is popular in academic research, economics, and social sciences for its robust statistical capabilities and ease of use.
• MATLAB : MATLAB is a high-level programming language and environment for numerical computing and visualization. It offers built-in functions and toolboxes for statistical analysis, machine learning, and signal processing.

Data Collection Software

In addition to statistical analysis software, data collection software plays a crucial role in the research process. These tools facilitate data collection, management, and organization from various sources, ensuring data quality and reliability.

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How to Choose the Right Statistical Analysis Software?

When selecting software for statistical analysis and data collection, consider the following factors:

• Compatibility : Ensure the software is compatible with your operating system, hardware, and data formats.
• Usability : Choose software that aligns with your level of expertise and provides features that meet your analysis and data collection requirements.
• Integration : Consider whether the software integrates with other tools and platforms in your workflow, such as data visualization software or data storage systems.
• Cost and Licensing : Evaluate the cost of licensing or subscription fees, as well as any additional costs for training, support, or maintenance.

By carefully evaluating these factors and considering your specific analysis and data collection needs, you can select the right software tools to support your research objectives and drive meaningful insights from your data.

Statistical Analysis Examples

Understanding statistical analysis methods is best achieved through practical examples. Let's explore three examples that demonstrate the application of statistical techniques in real-world scenarios.

Example 1: Linear Regression

Scenario : A marketing analyst wants to understand the relationship between advertising spending and sales revenue for a product.

Data : The analyst collects data on monthly advertising expenditures (in dollars) and corresponding sales revenue (in dollars) over the past year.

Analysis : Using simple linear regression, the analyst fits a regression model to the data, where advertising spending is the independent variable (X) and sales revenue is the dependent variable (Y). The regression analysis estimates the linear relationship between advertising spending and sales revenue, allowing the analyst to predict sales based on advertising expenditures.

Result : The regression analysis reveals a statistically significant positive relationship between advertising spending and sales revenue. For every additional dollar spent on advertising, sales revenue increases by an estimated amount (slope coefficient). The analyst can use this information to optimize advertising budgets and forecast sales performance.

Example 2: Hypothesis Testing

Scenario : A pharmaceutical company develops a new drug intended to lower blood pressure. The company wants to determine whether the new drug is more effective than the existing standard treatment.

Data : The company conducts a randomized controlled trial (RCT) involving two groups of participants: one group receives the new drug, and the other receives the standard treatment. Blood pressure measurements are taken before and after the treatment period.

Analysis : The company uses hypothesis testing, specifically a two-sample t-test, to compare the mean reduction in blood pressure between the two groups. The null hypothesis (H0) states that there is no difference in the mean reduction in blood pressure between the two treatments, while the alternative hypothesis (H1) suggests that the new drug is more effective.

Result : The t-test results indicate a statistically significant difference in the mean reduction in blood pressure between the two groups. The company concludes that the new drug is more effective than the standard treatment in lowering blood pressure, based on the evidence from the RCT.

Example 3: ANOVA

Scenario : A researcher wants to compare the effectiveness of three different teaching methods on student performance in a mathematics course.

Data : The researcher conducts an experiment where students are randomly assigned to one of three groups: traditional lecture-based instruction, active learning, or flipped classroom. At the end of the semester, students' scores on a standardized math test are recorded.

Analysis : The researcher performs an analysis of variance (ANOVA) to compare the mean test scores across the three teaching methods. ANOVA assesses whether there are statistically significant differences in mean scores between the groups.

Result : The ANOVA results reveal a significant difference in mean test scores between the three teaching methods. Post-hoc tests, such as Tukey's HSD (Honestly Significant Difference), can be conducted to identify which specific teaching methods differ significantly from each other in terms of student performance.

These examples illustrate how statistical analysis techniques can be applied to address various research questions and make data-driven decisions in different fields. By understanding and applying these methods effectively, researchers and analysts can derive valuable insights from their data to inform decision-making and drive positive outcomes.

Statistical Analysis Best Practices

Statistical analysis is a powerful tool for extracting insights from data, but it's essential to follow best practices to ensure the validity, reliability, and interpretability of your results.

• Clearly Define Research Questions : Before conducting any analysis, clearly define your research questions or objectives . This ensures that your analysis is focused and aligned with the goals of your study.
• Choose Appropriate Methods : Select statistical methods suitable for your data type, research design , and objectives. Consider factors such as data distribution, sample size, and assumptions of the chosen method.
• Preprocess Data : Clean and preprocess your data to remove errors, outliers, and missing values. Data preprocessing steps may include data cleaning, normalization, and transformation to ensure data quality and consistency.
• Check Assumptions : Verify that the assumptions of the chosen statistical methods are met. Assumptions may include normality, homogeneity of variance, independence, and linearity. Conduct diagnostic tests or exploratory data analysis to assess assumptions.
• Transparent Reporting : Document your analysis procedures, including data preprocessing steps, statistical methods used, and any assumptions made. Transparent reporting enhances reproducibility and allows others to evaluate the validity of your findings.
• Consider Sample Size : Ensure that your sample size is sufficient to detect meaningful effects or relationships. Power analysis can help determine the minimum sample size required to achieve adequate statistical power.
• Interpret Results Cautiously : Interpret statistical results with caution and consider the broader context of your research. Be mindful of effect sizes, confidence intervals, and practical significance when interpreting findings.
• Validate Findings : Validate your findings through robustness checks, sensitivity analyses, or replication studies. Cross-validation and bootstrapping techniques can help assess the stability and generalizability of your results.
• Avoid P-Hacking and Data Dredging : Guard against p-hacking and data dredging by pre-registering hypotheses, conducting planned analyses, and avoiding selective reporting of results. Maintain transparency and integrity in your analysis process.

By following these best practices, you can conduct rigorous and reliable statistical analyses that yield meaningful insights and contribute to evidence-based decision-making in your field.

Conclusion for Statistical Analysis

Statistical analysis is a vital tool for making sense of data and guiding decision-making across diverse fields. By understanding the fundamentals of statistical analysis, including concepts like hypothesis testing, regression analysis, and data visualization, you gain the ability to extract valuable insights from complex datasets. Moreover, selecting the appropriate statistical methods, choosing the right software, and following best practices ensure the validity and reliability of your analyses. In today's data-driven world, the ability to conduct rigorous statistical analysis is a valuable skill that empowers individuals and organizations to make informed decisions and drive positive outcomes. Whether you're a researcher, analyst, or decision-maker, mastering statistical analysis opens doors to new opportunities for understanding the world around us and unlocking the potential of data to solve real-world problems.

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What is Data Analysis? Definition, Tools, Examples

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.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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74 Comments

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Absolutely!!! Thank you

Thank you very much for this post. It made me to understand how to do my data analysis.

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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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A tutorial on methodological studies: the what, when, how and why

• Lawrence Mbuagbaw   ORCID: orcid.org/0000-0001-5855-5461 1 , 2 , 3 ,
• Daeria O. Lawson 1 ,
• Livia Puljak 4 ,
• David B. Allison 5 &
• Lehana Thabane 1 , 2 , 6 , 7 , 8  

BMC Medical Research Methodology volume  20 , Article number:  226 ( 2020 ) Cite this article

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Methodological studies – studies that evaluate the design, analysis or reporting of other research-related reports – play an important role in health research. They help to highlight issues in the conduct of research with the aim of improving health research methodology, and ultimately reducing research waste.

We provide an overview of some of the key aspects of methodological studies such as what they are, and when, how and why they are done. We adopt a “frequently asked questions” format to facilitate reading this paper and provide multiple examples to help guide researchers interested in conducting methodological studies. Some of the topics addressed include: is it necessary to publish a study protocol? How to select relevant research reports and databases for a methodological study? What approaches to data extraction and statistical analysis should be considered when conducting a methodological study? What are potential threats to validity and is there a way to appraise the quality of methodological studies?

Appropriate reflection and application of basic principles of epidemiology and biostatistics are required in the design and analysis of methodological studies. This paper provides an introduction for further discussion about the conduct of methodological studies.

Peer Review reports

The field of meta-research (or research-on-research) has proliferated in recent years in response to issues with research quality and conduct [ 1 , 2 , 3 ]. As the name suggests, this field targets issues with research design, conduct, analysis and reporting. Various types of research reports are often examined as the unit of analysis in these studies (e.g. abstracts, full manuscripts, trial registry entries). Like many other novel fields of research, meta-research has seen a proliferation of use before the development of reporting guidance. For example, this was the case with randomized trials for which risk of bias tools and reporting guidelines were only developed much later – after many trials had been published and noted to have limitations [ 4 , 5 ]; and for systematic reviews as well [ 6 , 7 , 8 ]. However, in the absence of formal guidance, studies that report on research differ substantially in how they are named, conducted and reported [ 9 , 10 ]. This creates challenges in identifying, summarizing and comparing them. In this tutorial paper, we will use the term methodological study to refer to any study that reports on the design, conduct, analysis or reporting of primary or secondary research-related reports (such as trial registry entries and conference abstracts).

In the past 10 years, there has been an increase in the use of terms related to methodological studies (based on records retrieved with a keyword search [in the title and abstract] for “methodological review” and “meta-epidemiological study” in PubMed up to December 2019), suggesting that these studies may be appearing more frequently in the literature. See Fig.  1 .

Trends in the number studies that mention “methodological review” or “meta-

epidemiological study” in PubMed.

The methods used in many methodological studies have been borrowed from systematic and scoping reviews. This practice has influenced the direction of the field, with many methodological studies including searches of electronic databases, screening of records, duplicate data extraction and assessments of risk of bias in the included studies. However, the research questions posed in methodological studies do not always require the approaches listed above, and guidance is needed on when and how to apply these methods to a methodological study. Even though methodological studies can be conducted on qualitative or mixed methods research, this paper focuses on and draws examples exclusively from quantitative research.

The objectives of this paper are to provide some insights on how to conduct methodological studies so that there is greater consistency between the research questions posed, and the design, analysis and reporting of findings. We provide multiple examples to illustrate concepts and a proposed framework for categorizing methodological studies in quantitative research.

What is a methodological study?

Any study that describes or analyzes methods (design, conduct, analysis or reporting) in published (or unpublished) literature is a methodological study. Consequently, the scope of methodological studies is quite extensive and includes, but is not limited to, topics as diverse as: research question formulation [ 11 ]; adherence to reporting guidelines [ 12 , 13 , 14 ] and consistency in reporting [ 15 ]; approaches to study analysis [ 16 ]; investigating the credibility of analyses [ 17 ]; and studies that synthesize these methodological studies [ 18 ]. While the nomenclature of methodological studies is not uniform, the intents and purposes of these studies remain fairly consistent – to describe or analyze methods in primary or secondary studies. As such, methodological studies may also be classified as a subtype of observational studies.

Parallel to this are experimental studies that compare different methods. Even though they play an important role in informing optimal research methods, experimental methodological studies are beyond the scope of this paper. Examples of such studies include the randomized trials by Buscemi et al., comparing single data extraction to double data extraction [ 19 ], and Carrasco-Labra et al., comparing approaches to presenting findings in Grading of Recommendations, Assessment, Development and Evaluations (GRADE) summary of findings tables [ 20 ]. In these studies, the unit of analysis is the person or groups of individuals applying the methods. We also direct readers to the Studies Within a Trial (SWAT) and Studies Within a Review (SWAR) programme operated through the Hub for Trials Methodology Research, for further reading as a potential useful resource for these types of experimental studies [ 21 ]. Lastly, this paper is not meant to inform the conduct of research using computational simulation and mathematical modeling for which some guidance already exists [ 22 ], or studies on the development of methods using consensus-based approaches.

When should we conduct a methodological study?

Methodological studies occupy a unique niche in health research that allows them to inform methodological advances. Methodological studies should also be conducted as pre-cursors to reporting guideline development, as they provide an opportunity to understand current practices, and help to identify the need for guidance and gaps in methodological or reporting quality. For example, the development of the popular Preferred Reporting Items of Systematic reviews and Meta-Analyses (PRISMA) guidelines were preceded by methodological studies identifying poor reporting practices [ 23 , 24 ]. In these instances, after the reporting guidelines are published, methodological studies can also be used to monitor uptake of the guidelines.

These studies can also be conducted to inform the state of the art for design, analysis and reporting practices across different types of health research fields, with the aim of improving research practices, and preventing or reducing research waste. For example, Samaan et al. conducted a scoping review of adherence to different reporting guidelines in health care literature [ 18 ]. Methodological studies can also be used to determine the factors associated with reporting practices. For example, Abbade et al. investigated journal characteristics associated with the use of the Participants, Intervention, Comparison, Outcome, Timeframe (PICOT) format in framing research questions in trials of venous ulcer disease [ 11 ].

How often are methodological studies conducted?

There is no clear answer to this question. Based on a search of PubMed, the use of related terms (“methodological review” and “meta-epidemiological study”) – and therefore, the number of methodological studies – is on the rise. However, many other terms are used to describe methodological studies. There are also many studies that explore design, conduct, analysis or reporting of research reports, but that do not use any specific terms to describe or label their study design in terms of “methodology”. This diversity in nomenclature makes a census of methodological studies elusive. Appropriate terminology and key words for methodological studies are needed to facilitate improved accessibility for end-users.

Why do we conduct methodological studies?

Methodological studies provide information on the design, conduct, analysis or reporting of primary and secondary research and can be used to appraise quality, quantity, completeness, accuracy and consistency of health research. These issues can be explored in specific fields, journals, databases, geographical regions and time periods. For example, Areia et al. explored the quality of reporting of endoscopic diagnostic studies in gastroenterology [ 25 ]; Knol et al. investigated the reporting of p -values in baseline tables in randomized trial published in high impact journals [ 26 ]; Chen et al. describe adherence to the Consolidated Standards of Reporting Trials (CONSORT) statement in Chinese Journals [ 27 ]; and Hopewell et al. describe the effect of editors’ implementation of CONSORT guidelines on reporting of abstracts over time [ 28 ]. Methodological studies provide useful information to researchers, clinicians, editors, publishers and users of health literature. As a result, these studies have been at the cornerstone of important methodological developments in the past two decades and have informed the development of many health research guidelines including the highly cited CONSORT statement [ 5 ].

Where can we find methodological studies?

Methodological studies can be found in most common biomedical bibliographic databases (e.g. Embase, MEDLINE, PubMed, Web of Science). However, the biggest caveat is that methodological studies are hard to identify in the literature due to the wide variety of names used and the lack of comprehensive databases dedicated to them. A handful can be found in the Cochrane Library as “Cochrane Methodology Reviews”, but these studies only cover methodological issues related to systematic reviews. Previous attempts to catalogue all empirical studies of methods used in reviews were abandoned 10 years ago [ 29 ]. In other databases, a variety of search terms may be applied with different levels of sensitivity and specificity.

Some frequently asked questions about methodological studies

In this section, we have outlined responses to questions that might help inform the conduct of methodological studies.

Q: How should I select research reports for my methodological study?

A: Selection of research reports for a methodological study depends on the research question and eligibility criteria. Once a clear research question is set and the nature of literature one desires to review is known, one can then begin the selection process. Selection may begin with a broad search, especially if the eligibility criteria are not apparent. For example, a methodological study of Cochrane Reviews of HIV would not require a complex search as all eligible studies can easily be retrieved from the Cochrane Library after checking a few boxes [ 30 ]. On the other hand, a methodological study of subgroup analyses in trials of gastrointestinal oncology would require a search to find such trials, and further screening to identify trials that conducted a subgroup analysis [ 31 ].

The strategies used for identifying participants in observational studies can apply here. One may use a systematic search to identify all eligible studies. If the number of eligible studies is unmanageable, a random sample of articles can be expected to provide comparable results if it is sufficiently large [ 32 ]. For example, Wilson et al. used a random sample of trials from the Cochrane Stroke Group’s Trial Register to investigate completeness of reporting [ 33 ]. It is possible that a simple random sample would lead to underrepresentation of units (i.e. research reports) that are smaller in number. This is relevant if the investigators wish to compare multiple groups but have too few units in one group. In this case a stratified sample would help to create equal groups. For example, in a methodological study comparing Cochrane and non-Cochrane reviews, Kahale et al. drew random samples from both groups [ 34 ]. Alternatively, systematic or purposeful sampling strategies can be used and we encourage researchers to justify their selected approaches based on the study objective.

Q: How many databases should I search?

A: The number of databases one should search would depend on the approach to sampling, which can include targeting the entire “population” of interest or a sample of that population. If you are interested in including the entire target population for your research question, or drawing a random or systematic sample from it, then a comprehensive and exhaustive search for relevant articles is required. In this case, we recommend using systematic approaches for searching electronic databases (i.e. at least 2 databases with a replicable and time stamped search strategy). The results of your search will constitute a sampling frame from which eligible studies can be drawn.

Alternatively, if your approach to sampling is purposeful, then we recommend targeting the database(s) or data sources (e.g. journals, registries) that include the information you need. For example, if you are conducting a methodological study of high impact journals in plastic surgery and they are all indexed in PubMed, you likely do not need to search any other databases. You may also have a comprehensive list of all journals of interest and can approach your search using the journal names in your database search (or by accessing the journal archives directly from the journal’s website). Even though one could also search journals’ web pages directly, using a database such as PubMed has multiple advantages, such as the use of filters, so the search can be narrowed down to a certain period, or study types of interest. Furthermore, individual journals’ web sites may have different search functionalities, which do not necessarily yield a consistent output.

Q: Should I publish a protocol for my methodological study?

A: A protocol is a description of intended research methods. Currently, only protocols for clinical trials require registration [ 35 ]. Protocols for systematic reviews are encouraged but no formal recommendation exists. The scientific community welcomes the publication of protocols because they help protect against selective outcome reporting, the use of post hoc methodologies to embellish results, and to help avoid duplication of efforts [ 36 ]. While the latter two risks exist in methodological research, the negative consequences may be substantially less than for clinical outcomes. In a sample of 31 methodological studies, 7 (22.6%) referenced a published protocol [ 9 ]. In the Cochrane Library, there are 15 protocols for methodological reviews (21 July 2020). This suggests that publishing protocols for methodological studies is not uncommon.

Authors can consider publishing their study protocol in a scholarly journal as a manuscript. Advantages of such publication include obtaining peer-review feedback about the planned study, and easy retrieval by searching databases such as PubMed. The disadvantages in trying to publish protocols includes delays associated with manuscript handling and peer review, as well as costs, as few journals publish study protocols, and those journals mostly charge article-processing fees [ 37 ]. Authors who would like to make their protocol publicly available without publishing it in scholarly journals, could deposit their study protocols in publicly available repositories, such as the Open Science Framework ( https://osf.io/ ).

Q: How to appraise the quality of a methodological study?

A: To date, there is no published tool for appraising the risk of bias in a methodological study, but in principle, a methodological study could be considered as a type of observational study. Therefore, during conduct or appraisal, care should be taken to avoid the biases common in observational studies [ 38 ]. These biases include selection bias, comparability of groups, and ascertainment of exposure or outcome. In other words, to generate a representative sample, a comprehensive reproducible search may be necessary to build a sampling frame. Additionally, random sampling may be necessary to ensure that all the included research reports have the same probability of being selected, and the screening and selection processes should be transparent and reproducible. To ensure that the groups compared are similar in all characteristics, matching, random sampling or stratified sampling can be used. Statistical adjustments for between-group differences can also be applied at the analysis stage. Finally, duplicate data extraction can reduce errors in assessment of exposures or outcomes.

Q: Should I justify a sample size?

A: In all instances where one is not using the target population (i.e. the group to which inferences from the research report are directed) [ 39 ], a sample size justification is good practice. The sample size justification may take the form of a description of what is expected to be achieved with the number of articles selected, or a formal sample size estimation that outlines the number of articles required to answer the research question with a certain precision and power. Sample size justifications in methodological studies are reasonable in the following instances:

Comparing two groups

Determining a proportion, mean or another quantifier

Determining factors associated with an outcome using regression-based analyses

For example, El Dib et al. computed a sample size requirement for a methodological study of diagnostic strategies in randomized trials, based on a confidence interval approach [ 40 ].

Q: What should I call my study?

A: Other terms which have been used to describe/label methodological studies include “ methodological review ”, “methodological survey” , “meta-epidemiological study” , “systematic review” , “systematic survey”, “meta-research”, “research-on-research” and many others. We recommend that the study nomenclature be clear, unambiguous, informative and allow for appropriate indexing. Methodological study nomenclature that should be avoided includes “ systematic review” – as this will likely be confused with a systematic review of a clinical question. “ Systematic survey” may also lead to confusion about whether the survey was systematic (i.e. using a preplanned methodology) or a survey using “ systematic” sampling (i.e. a sampling approach using specific intervals to determine who is selected) [ 32 ]. Any of the above meanings of the words “ systematic” may be true for methodological studies and could be potentially misleading. “ Meta-epidemiological study” is ideal for indexing, but not very informative as it describes an entire field. The term “ review ” may point towards an appraisal or “review” of the design, conduct, analysis or reporting (or methodological components) of the targeted research reports, yet it has also been used to describe narrative reviews [ 41 , 42 ]. The term “ survey ” is also in line with the approaches used in many methodological studies [ 9 ], and would be indicative of the sampling procedures of this study design. However, in the absence of guidelines on nomenclature, the term “ methodological study ” is broad enough to capture most of the scenarios of such studies.

Q: Should I account for clustering in my methodological study?

A: Data from methodological studies are often clustered. For example, articles coming from a specific source may have different reporting standards (e.g. the Cochrane Library). Articles within the same journal may be similar due to editorial practices and policies, reporting requirements and endorsement of guidelines. There is emerging evidence that these are real concerns that should be accounted for in analyses [ 43 ]. Some cluster variables are described in the section: “ What variables are relevant to methodological studies?”

A variety of modelling approaches can be used to account for correlated data, including the use of marginal, fixed or mixed effects regression models with appropriate computation of standard errors [ 44 ]. For example, Kosa et al. used generalized estimation equations to account for correlation of articles within journals [ 15 ]. Not accounting for clustering could lead to incorrect p -values, unduly narrow confidence intervals, and biased estimates [ 45 ].

Q: Should I extract data in duplicate?

A: Yes. Duplicate data extraction takes more time but results in less errors [ 19 ]. Data extraction errors in turn affect the effect estimate [ 46 ], and therefore should be mitigated. Duplicate data extraction should be considered in the absence of other approaches to minimize extraction errors. However, much like systematic reviews, this area will likely see rapid new advances with machine learning and natural language processing technologies to support researchers with screening and data extraction [ 47 , 48 ]. However, experience plays an important role in the quality of extracted data and inexperienced extractors should be paired with experienced extractors [ 46 , 49 ].

Q: Should I assess the risk of bias of research reports included in my methodological study?

A : Risk of bias is most useful in determining the certainty that can be placed in the effect measure from a study. In methodological studies, risk of bias may not serve the purpose of determining the trustworthiness of results, as effect measures are often not the primary goal of methodological studies. Determining risk of bias in methodological studies is likely a practice borrowed from systematic review methodology, but whose intrinsic value is not obvious in methodological studies. When it is part of the research question, investigators often focus on one aspect of risk of bias. For example, Speich investigated how blinding was reported in surgical trials [ 50 ], and Abraha et al., investigated the application of intention-to-treat analyses in systematic reviews and trials [ 51 ].

Q: What variables are relevant to methodological studies?

A: There is empirical evidence that certain variables may inform the findings in a methodological study. We outline some of these and provide a brief overview below:

Country: Countries and regions differ in their research cultures, and the resources available to conduct research. Therefore, it is reasonable to believe that there may be differences in methodological features across countries. Methodological studies have reported loco-regional differences in reporting quality [ 52 , 53 ]. This may also be related to challenges non-English speakers face in publishing papers in English.

Authors’ expertise: The inclusion of authors with expertise in research methodology, biostatistics, and scientific writing is likely to influence the end-product. Oltean et al. found that among randomized trials in orthopaedic surgery, the use of analyses that accounted for clustering was more likely when specialists (e.g. statistician, epidemiologist or clinical trials methodologist) were included on the study team [ 54 ]. Fleming et al. found that including methodologists in the review team was associated with appropriate use of reporting guidelines [ 55 ].

Source of funding and conflicts of interest: Some studies have found that funded studies report better [ 56 , 57 ], while others do not [ 53 , 58 ]. The presence of funding would indicate the availability of resources deployed to ensure optimal design, conduct, analysis and reporting. However, the source of funding may introduce conflicts of interest and warrant assessment. For example, Kaiser et al. investigated the effect of industry funding on obesity or nutrition randomized trials and found that reporting quality was similar [ 59 ]. Thomas et al. looked at reporting quality of long-term weight loss trials and found that industry funded studies were better [ 60 ]. Kan et al. examined the association between industry funding and “positive trials” (trials reporting a significant intervention effect) and found that industry funding was highly predictive of a positive trial [ 61 ]. This finding is similar to that of a recent Cochrane Methodology Review by Hansen et al. [ 62 ]

Journal characteristics: Certain journals’ characteristics may influence the study design, analysis or reporting. Characteristics such as journal endorsement of guidelines [ 63 , 64 ], and Journal Impact Factor (JIF) have been shown to be associated with reporting [ 63 , 65 , 66 , 67 ].

Study size (sample size/number of sites): Some studies have shown that reporting is better in larger studies [ 53 , 56 , 58 ].

Year of publication: It is reasonable to assume that design, conduct, analysis and reporting of research will change over time. Many studies have demonstrated improvements in reporting over time or after the publication of reporting guidelines [ 68 , 69 ].

Type of intervention: In a methodological study of reporting quality of weight loss intervention studies, Thabane et al. found that trials of pharmacologic interventions were reported better than trials of non-pharmacologic interventions [ 70 ].

Interactions between variables: Complex interactions between the previously listed variables are possible. High income countries with more resources may be more likely to conduct larger studies and incorporate a variety of experts. Authors in certain countries may prefer certain journals, and journal endorsement of guidelines and editorial policies may change over time.

Q: Should I focus only on high impact journals?

A: Investigators may choose to investigate only high impact journals because they are more likely to influence practice and policy, or because they assume that methodological standards would be higher. However, the JIF may severely limit the scope of articles included and may skew the sample towards articles with positive findings. The generalizability and applicability of findings from a handful of journals must be examined carefully, especially since the JIF varies over time. Even among journals that are all “high impact”, variations exist in methodological standards.

Q: Can I conduct a methodological study of qualitative research?

A: Yes. Even though a lot of methodological research has been conducted in the quantitative research field, methodological studies of qualitative studies are feasible. Certain databases that catalogue qualitative research including the Cumulative Index to Nursing & Allied Health Literature (CINAHL) have defined subject headings that are specific to methodological research (e.g. “research methodology”). Alternatively, one could also conduct a qualitative methodological review; that is, use qualitative approaches to synthesize methodological issues in qualitative studies.

Q: What reporting guidelines should I use for my methodological study?

A: There is no guideline that covers the entire scope of methodological studies. One adaptation of the PRISMA guidelines has been published, which works well for studies that aim to use the entire target population of research reports [ 71 ]. However, it is not widely used (40 citations in 2 years as of 09 December 2019), and methodological studies that are designed as cross-sectional or before-after studies require a more fit-for purpose guideline. A more encompassing reporting guideline for a broad range of methodological studies is currently under development [ 72 ]. However, in the absence of formal guidance, the requirements for scientific reporting should be respected, and authors of methodological studies should focus on transparency and reproducibility.

Q: What are the potential threats to validity and how can I avoid them?

A: Methodological studies may be compromised by a lack of internal or external validity. The main threats to internal validity in methodological studies are selection and confounding bias. Investigators must ensure that the methods used to select articles does not make them differ systematically from the set of articles to which they would like to make inferences. For example, attempting to make extrapolations to all journals after analyzing high-impact journals would be misleading.

Many factors (confounders) may distort the association between the exposure and outcome if the included research reports differ with respect to these factors [ 73 ]. For example, when examining the association between source of funding and completeness of reporting, it may be necessary to account for journals that endorse the guidelines. Confounding bias can be addressed by restriction, matching and statistical adjustment [ 73 ]. Restriction appears to be the method of choice for many investigators who choose to include only high impact journals or articles in a specific field. For example, Knol et al. examined the reporting of p -values in baseline tables of high impact journals [ 26 ]. Matching is also sometimes used. In the methodological study of non-randomized interventional studies of elective ventral hernia repair, Parker et al. matched prospective studies with retrospective studies and compared reporting standards [ 74 ]. Some other methodological studies use statistical adjustments. For example, Zhang et al. used regression techniques to determine the factors associated with missing participant data in trials [ 16 ].

With regard to external validity, researchers interested in conducting methodological studies must consider how generalizable or applicable their findings are. This should tie in closely with the research question and should be explicit. For example. Findings from methodological studies on trials published in high impact cardiology journals cannot be assumed to be applicable to trials in other fields. However, investigators must ensure that their sample truly represents the target sample either by a) conducting a comprehensive and exhaustive search, or b) using an appropriate and justified, randomly selected sample of research reports.

Even applicability to high impact journals may vary based on the investigators’ definition, and over time. For example, for high impact journals in the field of general medicine, Bouwmeester et al. included the Annals of Internal Medicine (AIM), BMJ, the Journal of the American Medical Association (JAMA), Lancet, the New England Journal of Medicine (NEJM), and PLoS Medicine ( n  = 6) [ 75 ]. In contrast, the high impact journals selected in the methodological study by Schiller et al. were BMJ, JAMA, Lancet, and NEJM ( n  = 4) [ 76 ]. Another methodological study by Kosa et al. included AIM, BMJ, JAMA, Lancet and NEJM ( n  = 5). In the methodological study by Thabut et al., journals with a JIF greater than 5 were considered to be high impact. Riado Minguez et al. used first quartile journals in the Journal Citation Reports (JCR) for a specific year to determine “high impact” [ 77 ]. Ultimately, the definition of high impact will be based on the number of journals the investigators are willing to include, the year of impact and the JIF cut-off [ 78 ]. We acknowledge that the term “generalizability” may apply differently for methodological studies, especially when in many instances it is possible to include the entire target population in the sample studied.

Finally, methodological studies are not exempt from information bias which may stem from discrepancies in the included research reports [ 79 ], errors in data extraction, or inappropriate interpretation of the information extracted. Likewise, publication bias may also be a concern in methodological studies, but such concepts have not yet been explored.

A proposed framework

In order to inform discussions about methodological studies, the development of guidance for what should be reported, we have outlined some key features of methodological studies that can be used to classify them. For each of the categories outlined below, we provide an example. In our experience, the choice of approach to completing a methodological study can be informed by asking the following four questions:

What is the aim?

Methodological studies that investigate bias

A methodological study may be focused on exploring sources of bias in primary or secondary studies (meta-bias), or how bias is analyzed. We have taken care to distinguish bias (i.e. systematic deviations from the truth irrespective of the source) from reporting quality or completeness (i.e. not adhering to a specific reporting guideline or norm). An example of where this distinction would be important is in the case of a randomized trial with no blinding. This study (depending on the nature of the intervention) would be at risk of performance bias. However, if the authors report that their study was not blinded, they would have reported adequately. In fact, some methodological studies attempt to capture both “quality of conduct” and “quality of reporting”, such as Richie et al., who reported on the risk of bias in randomized trials of pharmacy practice interventions [ 80 ]. Babic et al. investigated how risk of bias was used to inform sensitivity analyses in Cochrane reviews [ 81 ]. Further, biases related to choice of outcomes can also be explored. For example, Tan et al investigated differences in treatment effect size based on the outcome reported [ 82 ].

Methodological studies that investigate quality (or completeness) of reporting

Methodological studies may report quality of reporting against a reporting checklist (i.e. adherence to guidelines) or against expected norms. For example, Croituro et al. report on the quality of reporting in systematic reviews published in dermatology journals based on their adherence to the PRISMA statement [ 83 ], and Khan et al. described the quality of reporting of harms in randomized controlled trials published in high impact cardiovascular journals based on the CONSORT extension for harms [ 84 ]. Other methodological studies investigate reporting of certain features of interest that may not be part of formally published checklists or guidelines. For example, Mbuagbaw et al. described how often the implications for research are elaborated using the Evidence, Participants, Intervention, Comparison, Outcome, Timeframe (EPICOT) format [ 30 ].

Methodological studies that investigate the consistency of reporting

Sometimes investigators may be interested in how consistent reports of the same research are, as it is expected that there should be consistency between: conference abstracts and published manuscripts; manuscript abstracts and manuscript main text; and trial registration and published manuscript. For example, Rosmarakis et al. investigated consistency between conference abstracts and full text manuscripts [ 85 ].

Methodological studies that investigate factors associated with reporting

In addition to identifying issues with reporting in primary and secondary studies, authors of methodological studies may be interested in determining the factors that are associated with certain reporting practices. Many methodological studies incorporate this, albeit as a secondary outcome. For example, Farrokhyar et al. investigated the factors associated with reporting quality in randomized trials of coronary artery bypass grafting surgery [ 53 ].

Methodological studies that investigate methods

Methodological studies may also be used to describe methods or compare methods, and the factors associated with methods. Muller et al. described the methods used for systematic reviews and meta-analyses of observational studies [ 86 ].

Methodological studies that summarize other methodological studies

Some methodological studies synthesize results from other methodological studies. For example, Li et al. conducted a scoping review of methodological reviews that investigated consistency between full text and abstracts in primary biomedical research [ 87 ].

Methodological studies that investigate nomenclature and terminology

Some methodological studies may investigate the use of names and terms in health research. For example, Martinic et al. investigated the definitions of systematic reviews used in overviews of systematic reviews (OSRs), meta-epidemiological studies and epidemiology textbooks [ 88 ].

Other types of methodological studies

In addition to the previously mentioned experimental methodological studies, there may exist other types of methodological studies not captured here.

What is the design?

Methodological studies that are descriptive

Most methodological studies are purely descriptive and report their findings as counts (percent) and means (standard deviation) or medians (interquartile range). For example, Mbuagbaw et al. described the reporting of research recommendations in Cochrane HIV systematic reviews [ 30 ]. Gohari et al. described the quality of reporting of randomized trials in diabetes in Iran [ 12 ].

Methodological studies that are analytical

Some methodological studies are analytical wherein “analytical studies identify and quantify associations, test hypotheses, identify causes and determine whether an association exists between variables, such as between an exposure and a disease.” [ 89 ] In the case of methodological studies all these investigations are possible. For example, Kosa et al. investigated the association between agreement in primary outcome from trial registry to published manuscript and study covariates. They found that larger and more recent studies were more likely to have agreement [ 15 ]. Tricco et al. compared the conclusion statements from Cochrane and non-Cochrane systematic reviews with a meta-analysis of the primary outcome and found that non-Cochrane reviews were more likely to report positive findings. These results are a test of the null hypothesis that the proportions of Cochrane and non-Cochrane reviews that report positive results are equal [ 90 ].

What is the sampling strategy?

Methodological studies that include the target population

Methodological reviews with narrow research questions may be able to include the entire target population. For example, in the methodological study of Cochrane HIV systematic reviews, Mbuagbaw et al. included all of the available studies ( n  = 103) [ 30 ].

Methodological studies that include a sample of the target population

Many methodological studies use random samples of the target population [ 33 , 91 , 92 ]. Alternatively, purposeful sampling may be used, limiting the sample to a subset of research-related reports published within a certain time period, or in journals with a certain ranking or on a topic. Systematic sampling can also be used when random sampling may be challenging to implement.

What is the unit of analysis?

Methodological studies with a research report as the unit of analysis

Many methodological studies use a research report (e.g. full manuscript of study, abstract portion of the study) as the unit of analysis, and inferences can be made at the study-level. However, both published and unpublished research-related reports can be studied. These may include articles, conference abstracts, registry entries etc.

Methodological studies with a design, analysis or reporting item as the unit of analysis

Some methodological studies report on items which may occur more than once per article. For example, Paquette et al. report on subgroup analyses in Cochrane reviews of atrial fibrillation in which 17 systematic reviews planned 56 subgroup analyses [ 93 ].

This framework is outlined in Fig.  2 .

A proposed framework for methodological studies

Conclusions

Methodological studies have examined different aspects of reporting such as quality, completeness, consistency and adherence to reporting guidelines. As such, many of the methodological study examples cited in this tutorial are related to reporting. However, as an evolving field, the scope of research questions that can be addressed by methodological studies is expected to increase.

In this paper we have outlined the scope and purpose of methodological studies, along with examples of instances in which various approaches have been used. In the absence of formal guidance on the design, conduct, analysis and reporting of methodological studies, we have provided some advice to help make methodological studies consistent. This advice is grounded in good contemporary scientific practice. Generally, the research question should tie in with the sampling approach and planned analysis. We have also highlighted the variables that may inform findings from methodological studies. Lastly, we have provided suggestions for ways in which authors can categorize their methodological studies to inform their design and analysis.

Availability of data and materials

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Abbreviations

Consolidated Standards of Reporting Trials

Evidence, Participants, Intervention, Comparison, Outcome, Timeframe

Grading of Recommendations, Assessment, Development and Evaluations

Participants, Intervention, Comparison, Outcome, Timeframe

Preferred Reporting Items of Systematic reviews and Meta-Analyses

Studies Within a Review

Studies Within a Trial

Chalmers I, Glasziou P. Avoidable waste in the production and reporting of research evidence. Lancet. 2009;374(9683):86–9.

PubMed   Google Scholar  

Chan AW, Song F, Vickers A, Jefferson T, Dickersin K, Gotzsche PC, Krumholz HM, Ghersi D, van der Worp HB. Increasing value and reducing waste: addressing inaccessible research. Lancet. 2014;383(9913):257–66.

PubMed   PubMed Central   Google Scholar  

Ioannidis JP, Greenland S, Hlatky MA, Khoury MJ, Macleod MR, Moher D, Schulz KF, Tibshirani R. Increasing value and reducing waste in research design, conduct, and analysis. Lancet. 2014;383(9912):166–75.

Higgins JP, Altman DG, Gotzsche PC, Juni P, Moher D, Oxman AD, Savovic J, Schulz KF, Weeks L, Sterne JA. The Cochrane Collaboration's tool for assessing risk of bias in randomised trials. BMJ. 2011;343:d5928.

Moher D, Schulz KF, Altman DG. The CONSORT statement: revised recommendations for improving the quality of reports of parallel-group randomised trials. Lancet. 2001;357.

Liberati A, Altman DG, Tetzlaff J, Mulrow C, Gotzsche PC, Ioannidis JP, Clarke M, Devereaux PJ, Kleijnen J, Moher D. The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: explanation and elaboration. PLoS Med. 2009;6(7):e1000100.

Shea BJ, Hamel C, Wells GA, Bouter LM, Kristjansson E, Grimshaw J, Henry DA, Boers M. AMSTAR is a reliable and valid measurement tool to assess the methodological quality of systematic reviews. J Clin Epidemiol. 2009;62(10):1013–20.

Shea BJ, Reeves BC, Wells G, Thuku M, Hamel C, Moran J, Moher D, Tugwell P, Welch V, Kristjansson E, et al. AMSTAR 2: a critical appraisal tool for systematic reviews that include randomised or non-randomised studies of healthcare interventions, or both. Bmj. 2017;358:j4008.

Lawson DO, Leenus A, Mbuagbaw L. Mapping the nomenclature, methodology, and reporting of studies that review methods: a pilot methodological review. Pilot Feasibility Studies. 2020;6(1):13.

Puljak L, Makaric ZL, Buljan I, Pieper D. What is a meta-epidemiological study? Analysis of published literature indicated heterogeneous study designs and definitions. J Comp Eff Res. 2020.

Abbade LPF, Wang M, Sriganesh K, Jin Y, Mbuagbaw L, Thabane L. The framing of research questions using the PICOT format in randomized controlled trials of venous ulcer disease is suboptimal: a systematic survey. Wound Repair Regen. 2017;25(5):892–900.

Gohari F, Baradaran HR, Tabatabaee M, Anijidani S, Mohammadpour Touserkani F, Atlasi R, Razmgir M. Quality of reporting randomized controlled trials (RCTs) in diabetes in Iran; a systematic review. J Diabetes Metab Disord. 2015;15(1):36.

Wang M, Jin Y, Hu ZJ, Thabane A, Dennis B, Gajic-Veljanoski O, Paul J, Thabane L. The reporting quality of abstracts of stepped wedge randomized trials is suboptimal: a systematic survey of the literature. Contemp Clin Trials Commun. 2017;8:1–10.

Shanthanna H, Kaushal A, Mbuagbaw L, Couban R, Busse J, Thabane L: A cross-sectional study of the reporting quality of pilot or feasibility trials in high-impact anesthesia journals Can J Anaesthesia 2018, 65(11):1180–1195.

Kosa SD, Mbuagbaw L, Borg Debono V, Bhandari M, Dennis BB, Ene G, Leenus A, Shi D, Thabane M, Valvasori S, et al. Agreement in reporting between trial publications and current clinical trial registry in high impact journals: a methodological review. Contemporary Clinical Trials. 2018;65:144–50.

Zhang Y, Florez ID, Colunga Lozano LE, Aloweni FAB, Kennedy SA, Li A, Craigie S, Zhang S, Agarwal A, Lopes LC, et al. A systematic survey on reporting and methods for handling missing participant data for continuous outcomes in randomized controlled trials. J Clin Epidemiol. 2017;88:57–66.

CAS   PubMed   Google Scholar  

Hernández AV, Boersma E, Murray GD, Habbema JD, Steyerberg EW. Subgroup analyses in therapeutic cardiovascular clinical trials: are most of them misleading? Am Heart J. 2006;151(2):257–64.

Samaan Z, Mbuagbaw L, Kosa D, Borg Debono V, Dillenburg R, Zhang S, Fruci V, Dennis B, Bawor M, Thabane L. A systematic scoping review of adherence to reporting guidelines in health care literature. J Multidiscip Healthc. 2013;6:169–88.

Buscemi N, Hartling L, Vandermeer B, Tjosvold L, Klassen TP. Single data extraction generated more errors than double data extraction in systematic reviews. J Clin Epidemiol. 2006;59(7):697–703.

Carrasco-Labra A, Brignardello-Petersen R, Santesso N, Neumann I, Mustafa RA, Mbuagbaw L, Etxeandia Ikobaltzeta I, De Stio C, McCullagh LJ, Alonso-Coello P. Improving GRADE evidence tables part 1: a randomized trial shows improved understanding of content in summary-of-findings tables with a new format. J Clin Epidemiol. 2016;74:7–18.

The Northern Ireland Hub for Trials Methodology Research: SWAT/SWAR Information [ https://www.qub.ac.uk/sites/TheNorthernIrelandNetworkforTrialsMethodologyResearch/SWATSWARInformation/ ]. Accessed 31 Aug 2020.

Chick S, Sánchez P, Ferrin D, Morrice D. How to conduct a successful simulation study. In: Proceedings of the 2003 winter simulation conference: 2003; 2003. p. 66–70.

Google Scholar  

Mulrow CD. The medical review article: state of the science. Ann Intern Med. 1987;106(3):485–8.

Sacks HS, Reitman D, Pagano D, Kupelnick B. Meta-analysis: an update. Mount Sinai J Med New York. 1996;63(3–4):216–24.

CAS   Google Scholar  

Areia M, Soares M, Dinis-Ribeiro M. Quality reporting of endoscopic diagnostic studies in gastrointestinal journals: where do we stand on the use of the STARD and CONSORT statements? Endoscopy. 2010;42(2):138–47.

Knol M, Groenwold R, Grobbee D. P-values in baseline tables of randomised controlled trials are inappropriate but still common in high impact journals. Eur J Prev Cardiol. 2012;19(2):231–2.

Chen M, Cui J, Zhang AL, Sze DM, Xue CC, May BH. Adherence to CONSORT items in randomized controlled trials of integrative medicine for colorectal Cancer published in Chinese journals. J Altern Complement Med. 2018;24(2):115–24.

Hopewell S, Ravaud P, Baron G, Boutron I. Effect of editors' implementation of CONSORT guidelines on the reporting of abstracts in high impact medical journals: interrupted time series analysis. BMJ. 2012;344:e4178.

The Cochrane Methodology Register Issue 2 2009 [ https://cmr.cochrane.org/help.htm ]. Accessed 31 Aug 2020.

Mbuagbaw L, Kredo T, Welch V, Mursleen S, Ross S, Zani B, Motaze NV, Quinlan L. Critical EPICOT items were absent in Cochrane human immunodeficiency virus systematic reviews: a bibliometric analysis. J Clin Epidemiol. 2016;74:66–72.

Barton S, Peckitt C, Sclafani F, Cunningham D, Chau I. The influence of industry sponsorship on the reporting of subgroup analyses within phase III randomised controlled trials in gastrointestinal oncology. Eur J Cancer. 2015;51(18):2732–9.

Setia MS. Methodology series module 5: sampling strategies. Indian J Dermatol. 2016;61(5):505–9.

Wilson B, Burnett P, Moher D, Altman DG, Al-Shahi Salman R. Completeness of reporting of randomised controlled trials including people with transient ischaemic attack or stroke: a systematic review. Eur Stroke J. 2018;3(4):337–46.

Kahale LA, Diab B, Brignardello-Petersen R, Agarwal A, Mustafa RA, Kwong J, Neumann I, Li L, Lopes LC, Briel M, et al. Systematic reviews do not adequately report or address missing outcome data in their analyses: a methodological survey. J Clin Epidemiol. 2018;99:14–23.

De Angelis CD, Drazen JM, Frizelle FA, Haug C, Hoey J, Horton R, Kotzin S, Laine C, Marusic A, Overbeke AJPM, et al. Is this clinical trial fully registered?: a statement from the International Committee of Medical Journal Editors*. Ann Intern Med. 2005;143(2):146–8.

Ohtake PJ, Childs JD. Why publish study protocols? Phys Ther. 2014;94(9):1208–9.

Rombey T, Allers K, Mathes T, Hoffmann F, Pieper D. A descriptive analysis of the characteristics and the peer review process of systematic review protocols published in an open peer review journal from 2012 to 2017. BMC Med Res Methodol. 2019;19(1):57.

Grimes DA, Schulz KF. Bias and causal associations in observational research. Lancet. 2002;359(9302):248–52.

Porta M (ed.): A dictionary of epidemiology, 5th edn. Oxford: Oxford University Press, Inc.; 2008.

El Dib R, Tikkinen KAO, Akl EA, Gomaa HA, Mustafa RA, Agarwal A, Carpenter CR, Zhang Y, Jorge EC, Almeida R, et al. Systematic survey of randomized trials evaluating the impact of alternative diagnostic strategies on patient-important outcomes. J Clin Epidemiol. 2017;84:61–9.

Helzer JE, Robins LN, Taibleson M, Woodruff RA Jr, Reich T, Wish ED. Reliability of psychiatric diagnosis. I. a methodological review. Arch Gen Psychiatry. 1977;34(2):129–33.

Chung ST, Chacko SK, Sunehag AL, Haymond MW. Measurements of gluconeogenesis and Glycogenolysis: a methodological review. Diabetes. 2015;64(12):3996–4010.

CAS   PubMed   PubMed Central   Google Scholar  

Sterne JA, Juni P, Schulz KF, Altman DG, Bartlett C, Egger M. Statistical methods for assessing the influence of study characteristics on treatment effects in 'meta-epidemiological' research. Stat Med. 2002;21(11):1513–24.

Moen EL, Fricano-Kugler CJ, Luikart BW, O’Malley AJ. Analyzing clustered data: why and how to account for multiple observations nested within a study participant? PLoS One. 2016;11(1):e0146721.

Zyzanski SJ, Flocke SA, Dickinson LM. On the nature and analysis of clustered data. Ann Fam Med. 2004;2(3):199–200.

Mathes T, Klassen P, Pieper D. Frequency of data extraction errors and methods to increase data extraction quality: a methodological review. BMC Med Res Methodol. 2017;17(1):152.

Bui DDA, Del Fiol G, Hurdle JF, Jonnalagadda S. Extractive text summarization system to aid data extraction from full text in systematic review development. J Biomed Inform. 2016;64:265–72.

Bui DD, Del Fiol G, Jonnalagadda S. PDF text classification to leverage information extraction from publication reports. J Biomed Inform. 2016;61:141–8.

Maticic K, Krnic Martinic M, Puljak L. Assessment of reporting quality of abstracts of systematic reviews with meta-analysis using PRISMA-A and discordance in assessments between raters without prior experience. BMC Med Res Methodol. 2019;19(1):32.

Speich B. Blinding in surgical randomized clinical trials in 2015. Ann Surg. 2017;266(1):21–2.

Abraha I, Cozzolino F, Orso M, Marchesi M, Germani A, Lombardo G, Eusebi P, De Florio R, Luchetta ML, Iorio A, et al. A systematic review found that deviations from intention-to-treat are common in randomized trials and systematic reviews. J Clin Epidemiol. 2017;84:37–46.

Zhong Y, Zhou W, Jiang H, Fan T, Diao X, Yang H, Min J, Wang G, Fu J, Mao B. Quality of reporting of two-group parallel randomized controlled clinical trials of multi-herb formulae: A survey of reports indexed in the Science Citation Index Expanded. Eur J Integrative Med. 2011;3(4):e309–16.

Farrokhyar F, Chu R, Whitlock R, Thabane L. A systematic review of the quality of publications reporting coronary artery bypass grafting trials. Can J Surg. 2007;50(4):266–77.

Oltean H, Gagnier JJ. Use of clustering analysis in randomized controlled trials in orthopaedic surgery. BMC Med Res Methodol. 2015;15:17.

Fleming PS, Koletsi D, Pandis N. Blinded by PRISMA: are systematic reviewers focusing on PRISMA and ignoring other guidelines? PLoS One. 2014;9(5):e96407.

Balasubramanian SP, Wiener M, Alshameeri Z, Tiruvoipati R, Elbourne D, Reed MW. Standards of reporting of randomized controlled trials in general surgery: can we do better? Ann Surg. 2006;244(5):663–7.

de Vries TW, van Roon EN. Low quality of reporting adverse drug reactions in paediatric randomised controlled trials. Arch Dis Child. 2010;95(12):1023–6.

Borg Debono V, Zhang S, Ye C, Paul J, Arya A, Hurlburt L, Murthy Y, Thabane L. The quality of reporting of RCTs used within a postoperative pain management meta-analysis, using the CONSORT statement. BMC Anesthesiol. 2012;12:13.

Kaiser KA, Cofield SS, Fontaine KR, Glasser SP, Thabane L, Chu R, Ambrale S, Dwary AD, Kumar A, Nayyar G, et al. Is funding source related to study reporting quality in obesity or nutrition randomized control trials in top-tier medical journals? Int J Obes. 2012;36(7):977–81.

Thomas O, Thabane L, Douketis J, Chu R, Westfall AO, Allison DB. Industry funding and the reporting quality of large long-term weight loss trials. Int J Obes. 2008;32(10):1531–6.

Khan NR, Saad H, Oravec CS, Rossi N, Nguyen V, Venable GT, Lillard JC, Patel P, Taylor DR, Vaughn BN, et al. A review of industry funding in randomized controlled trials published in the neurosurgical literature-the elephant in the room. Neurosurgery. 2018;83(5):890–7.

Hansen C, Lundh A, Rasmussen K, Hrobjartsson A. Financial conflicts of interest in systematic reviews: associations with results, conclusions, and methodological quality. Cochrane Database Syst Rev. 2019;8:Mr000047.

Kiehna EN, Starke RM, Pouratian N, Dumont AS. Standards for reporting randomized controlled trials in neurosurgery. J Neurosurg. 2011;114(2):280–5.

Liu LQ, Morris PJ, Pengel LH. Compliance to the CONSORT statement of randomized controlled trials in solid organ transplantation: a 3-year overview. Transpl Int. 2013;26(3):300–6.

Bala MM, Akl EA, Sun X, Bassler D, Mertz D, Mejza F, Vandvik PO, Malaga G, Johnston BC, Dahm P, et al. Randomized trials published in higher vs. lower impact journals differ in design, conduct, and analysis. J Clin Epidemiol. 2013;66(3):286–95.

Lee SY, Teoh PJ, Camm CF, Agha RA. Compliance of randomized controlled trials in trauma surgery with the CONSORT statement. J Trauma Acute Care Surg. 2013;75(4):562–72.

Ziogas DC, Zintzaras E. Analysis of the quality of reporting of randomized controlled trials in acute and chronic myeloid leukemia, and myelodysplastic syndromes as governed by the CONSORT statement. Ann Epidemiol. 2009;19(7):494–500.

Alvarez F, Meyer N, Gourraud PA, Paul C. CONSORT adoption and quality of reporting of randomized controlled trials: a systematic analysis in two dermatology journals. Br J Dermatol. 2009;161(5):1159–65.

Mbuagbaw L, Thabane M, Vanniyasingam T, Borg Debono V, Kosa S, Zhang S, Ye C, Parpia S, Dennis BB, Thabane L. Improvement in the quality of abstracts in major clinical journals since CONSORT extension for abstracts: a systematic review. Contemporary Clin trials. 2014;38(2):245–50.

Thabane L, Chu R, Cuddy K, Douketis J. What is the quality of reporting in weight loss intervention studies? A systematic review of randomized controlled trials. Int J Obes. 2007;31(10):1554–9.

Murad MH, Wang Z. Guidelines for reporting meta-epidemiological methodology research. Evidence Based Med. 2017;22(4):139.

METRIC - MEthodological sTudy ReportIng Checklist: guidelines for reporting methodological studies in health research [ http://www.equator-network.org/library/reporting-guidelines-under-development/reporting-guidelines-under-development-for-other-study-designs/#METRIC ]. Accessed 31 Aug 2020.

Jager KJ, Zoccali C, MacLeod A, Dekker FW. Confounding: what it is and how to deal with it. Kidney Int. 2008;73(3):256–60.

Parker SG, Halligan S, Erotocritou M, Wood CPJ, Boulton RW, Plumb AAO, Windsor ACJ, Mallett S. A systematic methodological review of non-randomised interventional studies of elective ventral hernia repair: clear definitions and a standardised minimum dataset are needed. Hernia. 2019.

Bouwmeester W, Zuithoff NPA, Mallett S, Geerlings MI, Vergouwe Y, Steyerberg EW, Altman DG, Moons KGM. Reporting and methods in clinical prediction research: a systematic review. PLoS Med. 2012;9(5):1–12.

Schiller P, Burchardi N, Niestroj M, Kieser M. Quality of reporting of clinical non-inferiority and equivalence randomised trials--update and extension. Trials. 2012;13:214.

Riado Minguez D, Kowalski M, Vallve Odena M, Longin Pontzen D, Jelicic Kadic A, Jeric M, Dosenovic S, Jakus D, Vrdoljak M, Poklepovic Pericic T, et al. Methodological and reporting quality of systematic reviews published in the highest ranking journals in the field of pain. Anesth Analg. 2017;125(4):1348–54.

Thabut G, Estellat C, Boutron I, Samama CM, Ravaud P. Methodological issues in trials assessing primary prophylaxis of venous thrombo-embolism. Eur Heart J. 2005;27(2):227–36.

Puljak L, Riva N, Parmelli E, González-Lorenzo M, Moja L, Pieper D. Data extraction methods: an analysis of internal reporting discrepancies in single manuscripts and practical advice. J Clin Epidemiol. 2020;117:158–64.

Ritchie A, Seubert L, Clifford R, Perry D, Bond C. Do randomised controlled trials relevant to pharmacy meet best practice standards for quality conduct and reporting? A systematic review. Int J Pharm Pract. 2019.

Babic A, Vuka I, Saric F, Proloscic I, Slapnicar E, Cavar J, Pericic TP, Pieper D, Puljak L. Overall bias methods and their use in sensitivity analysis of Cochrane reviews were not consistent. J Clin Epidemiol. 2019.

Tan A, Porcher R, Crequit P, Ravaud P, Dechartres A. Differences in treatment effect size between overall survival and progression-free survival in immunotherapy trials: a Meta-epidemiologic study of trials with results posted at ClinicalTrials.gov. J Clin Oncol. 2017;35(15):1686–94.

Croitoru D, Huang Y, Kurdina A, Chan AW, Drucker AM. Quality of reporting in systematic reviews published in dermatology journals. Br J Dermatol. 2020;182(6):1469–76.

Khan MS, Ochani RK, Shaikh A, Vaduganathan M, Khan SU, Fatima K, Yamani N, Mandrola J, Doukky R, Krasuski RA: Assessing the Quality of Reporting of Harms in Randomized Controlled Trials Published in High Impact Cardiovascular Journals. Eur Heart J Qual Care Clin Outcomes 2019.

Rosmarakis ES, Soteriades ES, Vergidis PI, Kasiakou SK, Falagas ME. From conference abstract to full paper: differences between data presented in conferences and journals. FASEB J. 2005;19(7):673–80.

Mueller M, D’Addario M, Egger M, Cevallos M, Dekkers O, Mugglin C, Scott P. Methods to systematically review and meta-analyse observational studies: a systematic scoping review of recommendations. BMC Med Res Methodol. 2018;18(1):44.

Li G, Abbade LPF, Nwosu I, Jin Y, Leenus A, Maaz M, Wang M, Bhatt M, Zielinski L, Sanger N, et al. A scoping review of comparisons between abstracts and full reports in primary biomedical research. BMC Med Res Methodol. 2017;17(1):181.

Krnic Martinic M, Pieper D, Glatt A, Puljak L. Definition of a systematic review used in overviews of systematic reviews, meta-epidemiological studies and textbooks. BMC Med Res Methodol. 2019;19(1):203.

Analytical study [ https://medical-dictionary.thefreedictionary.com/analytical+study ]. Accessed 31 Aug 2020.

Tricco AC, Tetzlaff J, Pham B, Brehaut J, Moher D. Non-Cochrane vs. Cochrane reviews were twice as likely to have positive conclusion statements: cross-sectional study. J Clin Epidemiol. 2009;62(4):380–6 e381.

Schalken N, Rietbergen C. The reporting quality of systematic reviews and Meta-analyses in industrial and organizational psychology: a systematic review. Front Psychol. 2017;8:1395.

Ranker LR, Petersen JM, Fox MP. Awareness of and potential for dependent error in the observational epidemiologic literature: A review. Ann Epidemiol. 2019;36:15–9 e12.

Paquette M, Alotaibi AM, Nieuwlaat R, Santesso N, Mbuagbaw L. A meta-epidemiological study of subgroup analyses in cochrane systematic reviews of atrial fibrillation. Syst Rev. 2019;8(1):241.

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Lawrence Mbuagbaw, Daeria O. Lawson & Lehana Thabane

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Lawrence Mbuagbaw

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Livia Puljak

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David B. Allison

Departments of Paediatrics and Anaesthesia, McMaster University, Hamilton, ON, Canada

Lehana Thabane

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Mbuagbaw, L., Lawson, D.O., Puljak, L. et al. A tutorial on methodological studies: the what, when, how and why. BMC Med Res Methodol 20 , 226 (2020). https://doi.org/10.1186/s12874-020-01107-7

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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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How to write statistical analysis section in medical research

Alok kumar dwivedi.

Department of Molecular and Translational Medicine, Division of Biostatistics and Epidemiology, Texas Tech University Health Sciences Center El Paso, El Paso, Texas, USA

Associated Data

jim-2022-002479supp001.pdf

Data sharing not applicable as no datasets generated and/or analyzed for this study.

Reporting of statistical analysis is essential in any clinical and translational research study. However, medical research studies sometimes report statistical analysis that is either inappropriate or insufficient to attest to the accuracy and validity of findings and conclusions. Published works involving inaccurate statistical analyses and insufficient reporting influence the conduct of future scientific studies, including meta-analyses and medical decisions. Although the biostatistical practice has been improved over the years due to the involvement of statistical reviewers and collaborators in research studies, there remain areas of improvement for transparent reporting of the statistical analysis section in a study. Evidence-based biostatistics practice throughout the research is useful for generating reliable data and translating meaningful data to meaningful interpretation and decisions in medical research. Most existing research reporting guidelines do not provide guidance for reporting methods in the statistical analysis section that helps in evaluating the quality of findings and data interpretation. In this report, we highlight the global and critical steps to be reported in the statistical analysis of grants and research articles. We provide clarity and the importance of understanding study objective types, data generation process, effect size use, evidence-based biostatistical methods use, and development of statistical models through several thematic frameworks. We also provide published examples of adherence or non-adherence to methodological standards related to each step in the statistical analysis and their implications. We believe the suggestions provided in this report can have far-reaching implications for education and strengthening the quality of statistical reporting and biostatistical practice in medical research.

Introduction

Biostatistics is the overall approach to how we realistically and feasibly execute a research idea to produce meaningful data and translate data to meaningful interpretation and decisions. In this era of evidence-based medicine and practice, basic biostatistical knowledge becomes essential for critically appraising research articles and implementing findings for better patient management, improving healthcare, and research planning. 1 However, it may not be sufficient for the proper execution and reporting of statistical analyses in studies. 2 3 Three things are required for statistical analyses, namely knowledge of the conceptual framework of variables, research design, and evidence-based applications of statistical analysis with statistical software. 4 5 The conceptual framework provides possible biological and clinical pathways between independent variables and outcomes with role specification of variables. The research design provides a protocol of study design and data generation process (DGP), whereas the evidence-based statistical analysis approach provides guidance for selecting and implementing approaches after evaluating data with the research design. 2 5 Ocaña-Riola 6 reported a substantial percentage of articles from high-impact medical journals contained errors in statistical analysis or data interpretation. These errors in statistical analyses and interpretation of results do not only impact the reliability of research findings but also influence the medical decision-making and planning and execution of other related studies. A survey of consulting biostatisticians in the USA reported that researchers frequently request biostatisticians for performing inappropriate statistical analyses and inappropriate reporting of data. 7 This implies that there is a need to enforce standardized reporting of the statistical analysis section in medical research which can also help rreviewers and investigators to improve the methodological standards of the study.

Biostatistical practice in medicine has been improving over the years due to continuous efforts in promoting awareness and involving expert services on biostatistics, epidemiology, and research design in clinical and translational research. 8–11 Despite these efforts, the quality of reporting of statistical analysis in research studies has often been suboptimal. 12 13 We noticed that none of the methods reporting documents were developed using evidence-based biostatistics (EBB) theory and practice. The EBB practice implies that the selection of statistical analysis methods for statistical analyses and the steps of results reporting and interpretation should be grounded based on the evidence generated in the scientific literature and according to the study objective type and design. 5 Previous works have not properly elucidated the importance of understanding EBB concepts and related reporting in the write-up of statistical analyses. As a result, reviewers sometimes ask to present data or execute analyses that do not match the study objective type. 14 We summarize the statistical analysis steps to be reported in the statistical analysis section based on review and thematic frameworks.

We identified articles describing statistical reporting problems in medicine using different search terms ( online supplemental table 1 ). Based on these studies, we prioritized commonly reported statistical errors in analytical strategies and developed essential components to be reported in the statistical analysis section of research grants and studies. We also clarified the purpose and the overall implication of reporting each step in statistical analyses through various examples.

Supplementary data

Although biostatistical inputs are critical for the entire research study ( online supplemental table 2 ), biostatistical consultations were mostly used for statistical analyses only 15 . Even though the conduct of statistical analysis mismatched with the study objective and DGP was identified as the major problem in articles submitted to high-impact medical journals. 16 In addition, multivariable analyses were often inappropriately conducted and reported in published studies. 17 18 In light of these statistical errors, we describe the reporting of the following components in the statistical analysis section of the study.

Step 1: specify study objective type and outcomes (overall approach)

The study objective type provides the role of important variables for a specified outcome in statistical analyses and the overall approach of the model building and model reporting steps in a study. In the statistical framework, the problems are classified into descriptive and inferential/analytical/confirmatory objectives. In the epidemiological framework, the analytical and prognostic problems are broadly classified into association, explanatory, and predictive objectives. 19 These study objectives ( figure 1 ) may be classified into six categories: (1) exploratory, (2) association, (3) causal, (4) intervention, (5) prediction and (6) clinical decision models in medical research. 20

Comparative assessments of developing and reporting of study objective types and models. Association measures include odds ratio, risk ratio, or hazard ratio. AUC, area under the curve; C, confounder; CI, confidence interval; E, exposure; HbA1C: hemoglobin A1c; M, mediator; MFT, model fit test; MST, model specification test; PI, predictive interval; R 2 , coefficient of determinant; X, independent variable; Y, outcome.

The exploratory objective type is a specific type of determinant study and is commonly known as risk factors or correlates study in medical research. In an exploratory study, all covariates are considered equally important for the outcome of interest in the study. The goal of the exploratory study is to present the results of a model which gives higher accuracy after satisfying all model-related assumptions. In the association study, the investigator identifies predefined exposures of interest for the outcome, and variables other than exposures are also important for the interpretation and considered as covariates. The goal of an association study is to present the adjusted association of exposure with outcome. 20 In the causal objective study, the investigator is interested in determining the impact of exposure(s) on outcome using the conceptual framework. In this study objective, all variables should have a predefined role (exposures, confounders, mediators, covariates, and predictors) in a conceptual framework. A study with a causal objective is known as an explanatory or a confirmatory study in medical research. The goal is to present the direct or indirect effects of exposure(s) on an outcome after assessing the model’s fitness in the conceptual framework. 19 21 The objective of an interventional study is to determine the effect of an intervention on outcomes and is often known as randomized or non-randomized clinical trials in medical research. In the intervention objective model, all variables other than the intervention are treated as nuisance variables for primary analyses. The goal is to present the direct effect of the intervention on the outcomes by eliminating biases. 22–24 In the predictive study, the goal is to determine an optimum set of variables that can predict the outcome, particularly in external settings. The clinical decision models are a special case of prognostic models in which high dimensional data at various levels are used for risk stratification, classification, and prediction. In this model, all variables are considered input features. The goal is to present a decision tool that has high accuracy in training, testing, and validation data sets. 20 25 Biostatisticians or applied researchers should properly discuss the intention of the study objective type before proceeding with statistical analyses. In addition, it would be a good idea to prepare a conceptual model framework regardless of study objective type to understand study concepts.

A study 26 showed a favorable effect of the beta-blocker intervention on survival outcome in patients with advanced human epidermal growth factor receptor (HER2)-negative breast cancer without adjusting for all the potential confounding effects (age or menopausal status and Eastern Cooperative Oncology Performance Status) in primary analyses or validation analyses or using a propensity score-adjusted analysis, which is an EBB preferred method for analyzing non-randomized studies. 27 Similarly, another study had the goal of developing a predictive model for prediction of Alzheimer’s disease progression. 28 However, this study did not internally or externally validate the performance of the model as per the requirement of a predictive objective study. In another study, 29 investigators were interested in determining an association between metabolic syndrome and hepatitis C virus. However, the authors did not clearly specify the outcome in the analysis and produced conflicting associations with different analyses. 30 Thus, the outcome should be clearly specified as per the study objective type.

Step 2: specify effect size measure according to study design (interpretation and practical value)

The study design provides information on the selection of study participants and the process of data collection conditioned on either exposure or outcome ( figure 2 ). The appropriate use of effect size measure, tabular presentation of results, and the level of evidence are mostly determined by the study design. 31 32 In cohort or clinical trial study designs, the participants are selected based on exposure status and are followed up for the development of the outcome. These study designs can provide multiple outcomes, produce incidence or incidence density, and are preferred to be analyzed with risk ratio (RR) or hazards models. In a case–control study, the selection of participants is conditioned on outcome status. This type of study can have only one outcome and is preferred to be analyzed with an odds ratio (OR) model. In a cross-sectional study design, there is no selection restriction on outcomes or exposures. All data are collected simultaneously and can be analyzed with a prevalence ratio model, which is mathematically equivalent to the RR model. 33 The reporting of effect size measure also depends on the study objective type. For example, predictive models typically require reporting of regression coefficients or weight of variables in the model instead of association measures, which are required in other objective types. There are agreements and disagreements between OR and RR measures. Due to the constancy and symmetricity properties of OR, some researchers prefer to use OR in studies with common events. Similarly, the collapsibility and interpretability properties of RR make it more appealing to use in studies with common events. 34 To avoid variable practice and interpretation issues with OR, it is recommended to use RR models in all studies except for case–control and nested case–control studies, where OR approximates RR and thus OR models should be used. Otherwise, investigators may report sufficient data to compute any ratio measure. Biostatisticians should educate investigators on the proper interpretation of ratio measures in the light of study design and their reporting. 34 35

Effect size according to study design.

Investigators sometimes either inappropriately label their study design 36 37 or report effect size measures not aligned with the study design, 38 39 leading to difficulty in results interpretation and evaluation of the level of evidence. The proper labeling of study design and the appropriate use of effect size measure have substantial implications for results interpretation, including the conduct of systematic review and meta-analysis. 40 A study 31 reviewed the frequency of reporting OR instead of RR in cohort studies and randomized clinical trials (RCTs) and found that one-third of the cohort studies used an OR model, whereas 5% of RCTs used an OR model. The majority of estimated ORs from these studies had a 20% or higher deviation from the corresponding RR.

Step 3: specify study hypothesis, reporting of p values, and interval estimates (interpretation and decision)

The clinical hypothesis provides information for evaluating formal claims specified in the study objectives, while the statistical hypothesis provides information about the population parameters/statistics being used to test the formal claims. The inference about the study hypothesis is typically measured by p value and confidence interval (CI). A smaller p value indicates that the data support against the null hypothesis. Since the p value is a conditional probability, it can never tell about the acceptance or rejection of the null hypothesis. Therefore, multiple alternative strategies of p values have been proposed to strengthen the credibility of conclusions. 41 42 Adaption of these alternative strategies is only needed in the explanatory objective studies. Although exact p values are recommended to be reported in research studies, p values do not provide any information about the effect size. Compared with p values, the CI provides a confidence range of the effect size that contains the true effect size if the study were repeated and can be used to determine whether the results are statistically significant or not. 43 Both p value and 95% CI provide complementary information and thus need to be specified in the statistical analysis section. 24 44

Researchers often test one or more comparisons or hypotheses. Accordingly, the side and the level of significance for considering results to be statistically significant may change. Furthermore, studies may include more than one primary outcome that requires an adjustment in the level of significance for multiplicity. All studies should provide the interval estimate of the effect size/regression coefficient in the primary analyses. Since the interpretation of data analysis depends on the study hypothesis, researchers are required to specify the level of significance along with the side (one-sided or two-sided) of the p value in the test for considering statistically significant results, adjustment of the level of significance due to multiple comparisons or multiplicity, and reporting of interval estimates of the effect size in the statistical analysis section. 45

A study 46 showed a significant effect of fluoxetine on relapse rates in obsessive-compulsive disorder based on a one-sided p value of 0.04. Clearly, there was no reason for using a one-sided p value as opposed to a two-sided p value. A review of the appropriate use of multiple test correction methods in multiarm clinical trials published in major medical journals in 2012 identified over 50% of the articles did not perform multiple-testing correction. 47 Similar to controlling a familywise error rate due to multiple comparisons, adjustment of the false discovery rate is also critical in studies involving multiple related outcomes. A review of RCTs for depression between 2007 and 2008 from six journals reported that only limited studies (5.8%) accounted for multiplicity in the analyses due to multiple outcomes. 48

Step 4: account for DGP in the statistical analysis (accuracy)

The study design also requires the specification of the selection of participants and outcome measurement processes in different design settings. We referred to this specific design feature as DGP. Understanding DGP helps in determining appropriate modeling of outcome distribution in statistical analyses and setting up model premises and units of analysis. 4 DGP ( figure 3 ) involves information on data generation and data measures, including the number of measurements after random selection, complex selection, consecutive selection, pragmatic selection, or systematic selection. Specifically, DGP depends on a sampling setting (participants are selected using survey sampling methods and one subject may represent multiple participants in the population), clustered setting (participants are clustered through a recruitment setting or hierarchical setting or multiple hospitals), pragmatic setting (participants are selected through mixed approaches), or systematic review setting (participants are selected from published studies). DGP also depends on the measurements of outcomes in an unpaired setting (measured on one occasion only in independent groups), paired setting (measured on more than one occasion or participants are matched on certain subject characteristics), or mixed setting (measured on more than one occasion but interested in comparing independent groups). It also involves information regarding outcomes or exposure generation processes using quantitative or categorical variables, quantitative values using labs or validated instruments, and self-reported or administered tests yielding a variety of data distributions, including individual distribution, mixed-type distribution, mixed distributions, and latent distributions. Due to different DGPs, study data may include messy or missing data, incomplete/partial measurements, time-varying measurements, surrogate measures, latent measures, imbalances, unknown confounders, instrument variables, correlated responses, various levels of clustering, qualitative data, or mixed data outcomes, competing events, individual and higher-level variables, etc. The performance of statistical analysis, appropriate estimation of standard errors of estimates and subsequently computation of p values, the generalizability of findings, and the graphical display of data rely on DGP. Accounting for DGP in the analyses requires proper communication between investigators and biostatisticians about each aspect of participant selection and data collection, including measurements, occasions of measurements, and instruments used in the research study.

Common features of the data generation process.

A study 49 compared the intake of fresh fruit and komatsuna juice with the intake of commercial vegetable juice on metabolic parameters in middle-aged men using an RCT. The study was criticized for many reasons, but primarily for incorrect statistical methods not aligned with the study DGP. 50 Similarly, another study 51 highlighted that 80% of published studies using the Korean National Health and Nutrition Examination Survey did not incorporate survey sampling structure in statistical analyses, producing biased estimates and inappropriate findings. Likewise, another study 52 highlighted the need for maintaining methodological standards while analyzing data from the National Inpatient Sample. A systematic review 53 identified that over 50% of studies did not specify whether a paired t-test or an unpaired t-test was performed in statistical analysis in the top 25% of physiology journals, indicating poor transparency in reporting of statistical analysis as per the data type. Another study 54 also highlighted the data displaying errors not aligned with DGP. As per DGP, delay in treatment initiation of patients with cancer defined from the onset of symptom to treatment initiation should be analyzed into three components: patient/primary delay, secondary delay, and tertiary delay. 55 Similarly, the number of cancerous nodes should be analyzed with count data models. 56 However, several studies did not analyze such data according to DGP. 57 58

Step 5: apply EBB methods specific to study design features and DGP (efficiency and robustness)

The continuous growth in the development of robust statistical methods for dealing with a specific problem produced various methods to analyze specific data types. Since multiple methods are available for handling a specific problem yet with varying performances, heterogeneous practices among applied researchers have been noticed. Variable practices could also be due to a lack of consensus on statistical methods in literature, unawareness, and the unavailability of standardized statistical guidelines. 2 5 59 However, it becomes sometimes difficult to differentiate whether a specific method was used due to its robustness, lack of awareness, lack of accessibility of statistical software to apply an alternative appropriate method, intention to produce expected results, or ignorance of model diagnostics. To avoid heterogeneous practices, the selection of statistical methodology and their reporting at each stage of data analysis should be conducted using methods according to EBB practice. 5 Since it is hard for applied researchers to optimally select statistical methodology at each step, we encourage investigators to involve biostatisticians at the very early stage in basic, clinical, population, translational, and database research. We also appeal to biostatisticians to develop guidelines, checklists, and educational tools to promote the concept of EBB. As an effort, we developed the statistical analysis and methods in biomedical research (SAMBR) guidelines for applied researchers to use EBB methods for data analysis. 5 The EBB practice is essential for applying recent cutting-edge robust methodologies to yield accurate and unbiased results. The efficiency of statistical methodologies depends on the assumptions and DGP. Therefore, investigators may attempt to specify the choice of specific models in the primary analysis as per the EBB.

Although details of evidence-based preferred methods are provided in the SAMBR checklists for each study design/objective, 5 we have presented a simplified version of evidence-based preferred methods for common statistical analysis ( online supplemental table 3 ). Several examples are available in the literature where inefficient methods not according to EBB practice have been used. 31 57 60

Step 6: report variable selection method in the multivariable analysis according to study objective type (unbiased)

Multivariable analysis can be used for association, prediction or classification or risk stratification, adjustment, propensity score development, and effect size estimation. 61 Some biological, clinical, behavioral, and environmental factors may directly associate or influence the relationship between exposure and outcome. Therefore, almost all health studies require multivariable analyses for accurate and unbiased interpretations of findings ( figure 1 ). Analysts should develop an adjusted model if the sample size permits. It is a misconception that the analysis of RCT does not require adjusted analysis. Analysis of RCT may require adjustment for prognostic variables. 23 The foremost step in model building is the entry of variables after finalizing the appropriate parametric or non-parametric regression model. In the exploratory model building process due to no preference of exposures, a backward automated approach after including any variables that are significant at 25% in the unadjusted analysis can be used for variable selection. 62 63 In the association model, a manual selection of covariates based on the relevance of the variables should be included in a fully adjusted model. 63 In a causal model, clinically guided methods should be used for variable selection and their adjustments. 20 In a non-randomized interventional model, efforts should be made to eliminate confounding effects through propensity score methods and the final propensity score-adjusted multivariable model may adjust any prognostic variables, while a randomized study simply should adjust any prognostic variables. 27 Maintaining the event per variable (EVR) is important to avoid overfitting in any type of modeling; therefore, screening of variables may be required in some association and explanatory studies, which may be accomplished using a backward stepwise method that needs to be clarified in the statistical analyses. 10 In a predictive study, a model with an optimum set of variables producing the highest accuracy should be used. The optimum set of variables may be screened with the random forest method or bootstrap or machine learning methods. 64 65 Different methods of variable selection and adjustments may lead to different results. The screening process of variables and their adjustments in the final multivariable model should be clearly mentioned in the statistical analysis section.

A study 66 evaluating the effect of hydroxychloroquine (HDQ) showed unfavorable events (intubation or death) in patients who received HDQ compared with those who did not (hazard ratio (HR): 2.37, 95% CI 1.84 to 3.02) in an unadjusted analysis. However, the propensity score-adjusted analyses as appropriate with the interventional objective model showed no significant association between HDQ use and unfavorable events (HR: 1.04, 95% CI 0.82 to 1.32), which was also confirmed in multivariable and other propensity score-adjusted analyses. This study clearly suggests that results interpretation should be based on a multivariable analysis only in observational studies if feasible. A recent study 10 noted that approximately 6% of multivariable analyses based on either logistic or Cox regression used an inappropriate selection method of variables in medical research. This practice was more commonly noted in studies that did not involve an expert biostatistician. Another review 61 of 316 articles from high-impact Chinese medical journals revealed that 30.7% of articles did not report the selection of variables in multivariable models. Indeed, this inappropriate practice could have been identified more commonly if classified according to the study objective type. 18 In RCTs, it is uncommon to report an adjusted analysis based on prognostic variables, even though an adjusted analysis may produce an efficient estimate compared with an unadjusted analysis. A study assessing the effect of preemptive intervention on development outcomes showed a significant effect of an intervention on reducing autism spectrum disorder symptoms. 67 However, this study was criticized by Ware 68 for not reporting non-significant results in unadjusted analyses. If possible, unadjusted estimates should also be reported in any study, particularly in RCTs. 23 68

Step 7: provide evidence for exploring effect modifiers (applicability)

Any variable that modifies the effect of exposure on the outcome is called an effect modifier or modifier or an interacting variable. Exploring the effect modifiers in multivariable analyses helps in (1) determining the applicability/generalizability of findings in the overall or specific subpopulation, (2) generating ideas for new hypotheses, (3) explaining uninterpretable findings between unadjusted and adjusted analyses, (4) guiding to present combined or separate models for each specific subpopulation, and (5) explaining heterogeneity in treatment effect. Often, investigators present adjusted stratified results according to the presence or absence of an effect modifier. If the exposure interacts with multiple variables statistically or conceptually in the model, then the stratified findings (subgroup) according to each effect modifier may be presented. Otherwise, stratified analysis substantially reduces the power of the study due to the lower sample size in each stratum and may produce significant results by inflating type I error. 69 Therefore, a multivariable analysis involving an interaction term as opposed to a stratified analysis may be presented in the presence of an effect modifier. 70 Sometimes, a quantitative variable may emerge as a potential effect modifier for exposure and an outcome relationship. In such a situation, the quantitative variable should not be categorized unless a clinically meaningful threshold is not available in the study. In fact, the practice of categorizing quantitative variables should be avoided in the analysis unless a clinically meaningful cut-off is available or a hypothesis requires for it. 71 In an exploratory objective type, any possible interaction may be obtained in a study; however, the interpretation should be guided based on clinical implications. Similarly, some objective models may have more than one exposure or intervention and the association of each exposure according to the level of other exposure should be presented through adjusted analyses as suggested in the presence of interaction effects. 70

A review of 428 articles from MEDLINE on the quality of reporting from statistical analyses of three (linear, logistic, and Cox) commonly used regression models reported that only 18.5% of the published articles provided interaction analyses, 17 even though interaction analyses can provide a lot of useful information.

Step 8: assessment of assumptions, specifically the distribution of outcome, linearity, multicollinearity, sparsity, and overfitting (reliability)

The assessment and reporting of model diagnostics are important in assessing the efficiency, validity, and usefulness of the model. Model diagnostics include satisfying model-specific assumptions and the assessment of sparsity, linearity, distribution of outcome, multicollinearity, and overfitting. 61 72 Model-specific assumptions such as normal residuals, heteroscedasticity and independence of errors in linear regression, proportionality in Cox regression, proportionality odds assumption in ordinal logistic regression, and distribution fit in other types of continuous and count models are required. In addition, sparsity should also be examined prior to selecting an appropriate model. Sparsity indicates many zero observations in the data set. 73 In the presence of sparsity, the effect size is difficult to interpret. Except for machine learning models, most of the parametric and semiparametric models require a linear relationship between independent variables and a functional form of an outcome. Linearity should be assessed using a multivariable polynomial in all model objectives. 62 Similarly, the appropriate choice of the distribution of outcome is required for model building in all study objective models. Multicollinearity assessment is also useful in all objective models. Assessment of EVR in multivariable analysis can be used to avoid the overfitting issue of a multivariable model. 18

Some review studies highlighted that 73.8%–92% of the articles published in MEDLINE had not assessed the model diagnostics of the multivariable regression models. 17 61 72 Contrary to the monotonically, linearly increasing relationship between systolic blood pressure (SBP) and mortality established using the Framingham’s study, 74 Port et al 75 reported a non-linear relationship between SBP and all-cause mortality or cardiovascular deaths by reanalysis of the Framingham’s study data set. This study identified a different threshold for treating hypertension, indicating the role of linearity assessment in multivariable models. Although a non-Gaussian distribution model may be required for modeling patient delay outcome data in cancer, 55 a study analyzed patient delay data using an ordinary linear regression model. 57 An investigation of the development of predictive models and their reporting in medical journals identified that 53% of the articles had fewer EVR than the recommended EVR, indicating over half of the published articles may have an overfitting model. 18 Another study 76 attempted to identify the anthropometric variables associated with non-insulin-dependent diabetes and found that none of the anthropometric variables were significant after adjusting for waist circumference, age, and sex, indicating the presence of collinearity. A study reported detailed sparse data problems in published studies and potential solutions. 73

Step 9: report type of primary and sensitivity analyses (consistency)

Numerous considerations and assumptions are made throughout the research processes that require assessment, evaluation, and validation. Some assumptions, executions, and errors made at the beginning of the study data collection may not be fixable 13 ; however, additional information collected during the study and data processing, including data distribution obtained at the end of the study, may facilitate additional considerations that need to be verified in the statistical analyses. Consistencies in the research findings via modifications in the outcome or exposure definition, study population, accounting for missing data, model-related assumptions, variables and their forms, and accounting for adherence to protocol in the models can be evaluated and reported in research studies using sensitivity analyses. 77 The purpose and type of supporting analyses need to be specified clearly in the statistical analyses to differentiate the main findings from the supporting findings. Sensitivity analyses are different from secondary or interim or subgroup analyses. 78 Data analyses for secondary outcomes are often referred to as secondary analyses, while data analyses of an ongoing study are called interim analyses and data analyses according to groups based on patient characteristics are known as subgroup analyses.

Almost all studies require some form of sensitivity analysis to validate the findings under different conditions. However, it is often underutilized in medical journals. Only 18%–20.3% of studies reported some forms of sensitivity analyses. 77 78 A review of nutritional trials from high-quality journals reflected that 17% of the conclusions were reported inappropriately using findings from sensitivity analyses not based on the primary/main analyses. 77

Step 10: provide methods for summarizing, displaying, and interpreting data (transparency and usability)

Data presentation includes data summary, data display, and data from statistical model analyses. The primary purpose of the data summary is to understand the distribution of outcome status and other characteristics in the total sample and by primary exposure status or outcome status. Column-wise data presentation should be preferred according to exposure status in all study designs, while row-wise data presentation for the outcome should be preferred in all study designs except for a case–control study. 24 32 Summary statistics should be used to provide maximum information on data distribution aligned with DGP and variable type. The purpose of results presentation primarily from regression analyses or statistical models is to convey results interpretation and implications of findings. The results should be presented according to the study objective type. Accordingly, the reporting of unadjusted and adjusted associations of each factor with the outcome may be preferred in the determinant objective model, while unadjusted and adjusted effects of primary exposure on the outcome may be preferred in the explanatory objective model. In prognostic models, the final predictive models may be presented in such a way that users can use models to predict an outcome. In the exploratory objective model, a final multivariable model should be reported with R 2 or area under the curve (AUC). In the association and interventional models, the assessment of internal validation is critically important through various sensitivity and validation analyses. A model with better fit indices (in terms of R 2 or AUC, Akaike information criterion, Bayesian information criterion, fit index, root mean square error) should be finalized and reported in the causal model objective study. In the predictive objective type, the model performance in terms of R 2 or AUC in training and validation data sets needs to be reported ( figure 1 ). 20 21 There are multiple purposes of data display, including data distribution using bar diagram or histogram or frequency polygons or box plots, comparisons using cluster bar diagram or scatter dot plot or stacked bar diagram or Kaplan-Meier plot, correlation or model assessment using scatter plot or scatter matrix, clustering or pattern using heatmap or line plots, the effect of predictors with fitted models using marginsplot, and comparative evaluation of effect sizes from regression models using forest plot. Although the key purpose of data display is to highlight critical issues or findings in the study, data display should essentially follow DGP and variable types and should be user-friendly. 54 79 Data interpretation heavily relies on the effect size measure along with study design and specified hypotheses. Sometimes, variables require standardization for descriptive comparison of effect sizes among exposures or interpreting small effect size, or centralization for interpreting intercept or avoiding collinearity due to interaction terms, or transformation for achieving model-related assumptions. 80 Appropriate methods of data reporting and interpretation aligned with study design, study hypothesis, and effect size measure should be specified in the statistical analysis section of research studies.

Published articles from reputed journals inappropriately summarized a categorized variable with mean and range, 81 summarized a highly skewed variable with mean and standard deviation, 57 and treated a categorized variable as a continuous variable in regression analyses. 82 Similarly, numerous examples from published studies reporting inappropriate graphical display or inappropriate interpretation of data not aligned with DGP or variable types are illustrated in a book published by Bland and Peacock. 83 84 A study used qualitative data on MRI but inappropriately presented with a Box-Whisker plot. 81 Another study reported unusually high OR for an association between high breast parenchymal enhancement and breast cancer in both premenopausal and postmenopausal women. 85 This reporting makes suspicious findings and may include sparse data bias. 86 A poor tabular presentation without proper scaling or standardization of a variable, missing CI for some variables, missing unit and sample size, and inconsistent reporting of decimal places could be easily noticed in table 4 of a published study. 29 Some published predictive models 87 do not report intercept or baseline survival estimates to use their predictive models in clinical use. Although a direct comparison of effect sizes obtained from the same model may be avoided if the units are different among variables, 35 a study had an objective to compare effect sizes across variables but the authors performed comparisons without standardization of variables or using statistical tests. 88

A sample for writing statistical analysis section in medical journals/research studies

Our primary study objective type was to develop a (select from figure 1 ) model to assess the relationship of risk factors (list critical variables or exposures) with outcomes (specify type from continuous/discrete/count/binary/polytomous/time-to-event). To address this objective, we conducted a (select from figure 2 or any other) study design to test the hypotheses of (equality or superiority or non-inferiority or equivalence or futility) or develop prediction. Accordingly, the other variables were adjusted or considered as (specify role of variables from confounders, covariates, or predictors or independent variables) as reflected in the conceptual framework. In the unadjusted or preliminary analyses as per the (select from figure 3 or any other design features) DGP, (specify EBB preferred tests from online supplemental table 3 or any other appropriate tests) were used for (specify variables and types) in unadjusted analyses. According to the EBB practice for the outcome (specify type) and DGP of (select from figure 3 or any other), we used (select from online supplemental table 1 or specify a multivariable approach) as the primary model in the multivariable analysis. We used (select from figure 1 ) variable selection method in the multivariable analysis and explored the interaction effects between (specify variables). The model diagnostics including (list all applicable, including model-related assumptions, linearity, or multicollinearity or overfitting or distribution of outcome or sparsity) were also assessed using (specify appropriate methods) respectively. In such exploration, we identified (specify diagnostic issues if any) and therefore the multivariable models were developed using (specify potential methods used to handle diagnostic issues). The other outcomes were analyzed with (list names of multivariable approaches with respective outcomes). All the models used the same procedure (or specify from figure 1 ) for variable selection, exploration of interaction effects, and model diagnostics using (specify statistical approaches) depending on the statistical models. As per the study design, hypothesis, and multivariable analysis, the results were summarized with effect size (select as appropriate or from figure 2 ) along with (specify 95% CI or other interval estimates) and considered statistically significant using (specify the side of p value or alternatives) at (specify the level of significance) due to (provide reasons for choosing a significance level). We presented unadjusted and/or adjusted estimates of primary outcome according to (list primary exposures or variables). Additional analyses were conducted for (specific reasons from step 9) using (specify methods) to validate findings obtained in the primary analyses. The data were summarized with (list summary measures and appropriate graphs from step 10), whereas the final multivariable model performance was summarized with (fit indices if applicable from step 10). We also used (list graphs) as appropriate with DGP (specify from figure 3 ) to present the critical findings or highlight (specify data issues) using (list graphs/methods) in the study. The exposures or variables were used in (specify the form of the variables) and therefore the effect or association of (list exposures or variables) on outcome should be interpreted in terms of changes in (specify interpretation unit) exposures/variables. List all other additional analyses if performed (with full details of all models in a supplementary file along with statistical codes if possible).

Concluding remarks

We highlighted 10 essential steps to be reported in the statistical analysis section of any analytical study ( figure 4 ). Adherence to minimum reporting of the steps specified in this report may enforce investigators to understand concepts and approach biostatisticians timely to apply these concepts in their study to improve the overall quality of methodological standards in grant proposals and research studies. The order of reporting information in statistical analyses specified in this report is not mandatory; however, clear reporting of analytical steps applicable to the specific study type should be mentioned somewhere in the manuscript. Since the entire approach of statistical analyses is dependent on the study objective type and EBB practice, proper execution and reporting of statistical models can be taught to the next generation of statisticians by the study objective type in statistical education courses. In fact, some disciplines ( figure 5 ) are strictly aligned with specific study objective types. Bioinformaticians are oriented in studying determinant and prognostic models toward precision medicine, while epidemiologists are oriented in studying association and causal models, particularly in population-based observational and pragmatic settings. Data scientists are heavily involved in prediction and classification models in personalized medicine. A common thing across disciplines is using biostatistical principles and computation tools to address any research question. Sometimes, one discipline expert does the part of others. 89 We strongly recommend using a team science approach that includes an epidemiologist, biostatistician, data scientist, and bioinformatician depending on the study objectives and needs. Clear reporting of data analyses as per the study objective type should be encouraged among all researchers to minimize heterogeneous practices and improve scientific quality and outcomes. In addition, we also encourage investigators to strictly follow transparent reporting and quality assessment guidelines according to the study design ( https://www.equator-network.org/ ) to improve the overall quality of the study, accordingly STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) for observational studies, CONSORT (Consolidated Standards of Reporting Trials) for clinical trials, STARD (Standards for Reporting Diagnostic Accuracy Studies) for diagnostic studies, TRIPOD (Transparent Reporting of a multivariable prediction model for Individual Prognosis OR Diagnosis) for prediction modeling, and ARRIVE (Animal Research: Reporting of In Vivo Experiments) for preclinical studies. The steps provided in this document for writing the statistical analysis section is essentially different from other guidance documents, including SAMBR. 5 SAMBR provides a guidance document for selecting evidence-based preferred methods of statistical analysis according to different study designs, while this report suggests the global reporting of essential information in the statistical analysis section according to study objective type. In this guidance report, our suggestion strictly pertains to the reporting of methods in the statistical analysis section and their implications on the interpretation of results. Our document does not provide guidance on the reporting of sample size or results or statistical analysis section for meta-analysis. The examples and reviews reported in this study may be used to emphasize the concepts and related implications in medical research.

Summary of reporting steps, purpose, and evaluation measures in the statistical analysis section.

Role of interrelated disciplines according to study objective type.

Acknowledgments

The author would like to thank the reviewers for their careful review and insightful suggestions.

Contributors: AKD developed the concept and design and wrote the manuscript.

Funding: The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

Competing interests: AKD is a Journal of Investigative Medicine Editorial Board member. No other competing interests declared.

Provenance and peer review: Commissioned; externally peer reviewed.

Supplemental material: This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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• Knowledge Base

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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