example of quantitative research results

How To Write The Results/Findings Chapter

For quantitative studies (dissertations & theses).

By: Derek Jansen (MBA). Expert Reviewed By: Kerryn Warren (PhD) | July 2021

So, you’ve completed your quantitative data analysis and it’s time to report on your findings. But where do you start? In this post, we’ll walk you through the results chapter (also called the findings or analysis chapter), step by step, so that you can craft this section of your dissertation or thesis with confidence. If you’re looking for information regarding the results chapter for qualitative studies, you can find that here .

Overview: Quantitative Results Chapter

• What exactly the results/findings/analysis chapter is
• What you need to include in your results chapter
• How to structure your results chapter
• A few tips and tricks for writing top-notch chapter

What exactly is the results chapter?

The results chapter (also referred to as the findings or analysis chapter) is one of the most important chapters of your dissertation or thesis because it shows the reader what you’ve found in terms of the quantitative data you’ve collected. It presents the data using a clear text narrative, supported by tables, graphs and charts. In doing so, it also highlights any potential issues (such as outliers or unusual findings) you’ve come across.

But how’s that different from the discussion chapter?

Well, in the results chapter, you only present your statistical findings. Only the numbers, so to speak – no more, no less. Contrasted to this, in the discussion chapter , you interpret your findings and link them to prior research (i.e. your literature review), as well as your research objectives and research questions . In other words, the results chapter presents and describes the data, while the discussion chapter interprets the data.

Let’s look at an example.

In your results chapter, you may have a plot that shows how respondents to a survey  responded: the numbers of respondents per category, for instance. You may also state whether this supports a hypothesis by using a p-value from a statistical test. But it is only in the discussion chapter where you will say why this is relevant or how it compares with the literature or the broader picture. So, in your results chapter, make sure that you don’t present anything other than the hard facts – this is not the place for subjectivity.

It’s worth mentioning that some universities prefer you to combine the results and discussion chapters. Even so, it is good practice to separate the results and discussion elements within the chapter, as this ensures your findings are fully described. Typically, though, the results and discussion chapters are split up in quantitative studies. If you’re unsure, chat with your research supervisor or chair to find out what their preference is.

What should you include in the results chapter?

Following your analysis, it’s likely you’ll have far more data than are necessary to include in your chapter. In all likelihood, you’ll have a mountain of SPSS or R output data, and it’s your job to decide what’s most relevant. You’ll need to cut through the noise and focus on the data that matters.

This doesn’t mean that those analyses were a waste of time – on the contrary, those analyses ensure that you have a good understanding of your dataset and how to interpret it. However, that doesn’t mean your reader or examiner needs to see the 165 histograms you created! Relevance is key.

How do I decide what’s relevant?

At this point, it can be difficult to strike a balance between what is and isn’t important. But the most important thing is to ensure your results reflect and align with the purpose of your study .  So, you need to revisit your research aims, objectives and research questions and use these as a litmus test for relevance. Make sure that you refer back to these constantly when writing up your chapter so that you stay on track.

As a general guide, your results chapter will typically include the following:

• Some demographic data about your sample
• Reliability tests (if you used measurement scales)
• Descriptive statistics
• Inferential statistics (if your research objectives and questions require these)
• Hypothesis tests (again, if your research objectives and questions require these)

We’ll discuss each of these points in more detail in the next section.

Importantly, your results chapter needs to lay the foundation for your discussion chapter . This means that, in your results chapter, you need to include all the data that you will use as the basis for your interpretation in the discussion chapter.

For example, if you plan to highlight the strong relationship between Variable X and Variable Y in your discussion chapter, you need to present the respective analysis in your results chapter – perhaps a correlation or regression analysis.

Need a helping hand?

How do I write the results chapter?

There are multiple steps involved in writing up the results chapter for your quantitative research. The exact number of steps applicable to you will vary from study to study and will depend on the nature of the research aims, objectives and research questions . However, we’ll outline the generic steps below.

Step 1 – Revisit your research questions

The first step in writing your results chapter is to revisit your research objectives and research questions . These will be (or at least, should be!) the driving force behind your results and discussion chapters, so you need to review them and then ask yourself which statistical analyses and tests (from your mountain of data) would specifically help you address these . For each research objective and research question, list the specific piece (or pieces) of analysis that address it.

At this stage, it’s also useful to think about the key points that you want to raise in your discussion chapter and note these down so that you have a clear reminder of which data points and analyses you want to highlight in the results chapter. Again, list your points and then list the specific piece of analysis that addresses each point. 

Next, you should draw up a rough outline of how you plan to structure your chapter . Which analyses and statistical tests will you present and in what order? We’ll discuss the “standard structure” in more detail later, but it’s worth mentioning now that it’s always useful to draw up a rough outline before you start writing (this advice applies to any chapter).

Step 2 – Craft an overview introduction

As with all chapters in your dissertation or thesis, you should start your quantitative results chapter by providing a brief overview of what you’ll do in the chapter and why . For example, you’d explain that you will start by presenting demographic data to understand the representativeness of the sample, before moving onto X, Y and Z.

This section shouldn’t be lengthy – a paragraph or two maximum. Also, it’s a good idea to weave the research questions into this section so that there’s a golden thread that runs through the document.

Step 3 – Present the sample demographic data

The first set of data that you’ll present is an overview of the sample demographics – in other words, the demographics of your respondents.

For example:

• What age range are they?
• How is gender distributed?
• How is ethnicity distributed?
• What areas do the participants live in?

The purpose of this is to assess how representative the sample is of the broader population. This is important for the sake of the generalisability of the results. If your sample is not representative of the population, you will not be able to generalise your findings. This is not necessarily the end of the world, but it is a limitation you’ll need to acknowledge.

Of course, to make this representativeness assessment, you’ll need to have a clear view of the demographics of the population. So, make sure that you design your survey to capture the correct demographic information that you will compare your sample to.

But what if I’m not interested in generalisability?

Well, even if your purpose is not necessarily to extrapolate your findings to the broader population, understanding your sample will allow you to interpret your findings appropriately, considering who responded. In other words, it will help you contextualise your findings . For example, if 80% of your sample was aged over 65, this may be a significant contextual factor to consider when interpreting the data. Therefore, it’s important to understand and present the demographic data.

 Step 4 – Review composite measures and the data “shape”.

Before you undertake any statistical analysis, you’ll need to do some checks to ensure that your data are suitable for the analysis methods and techniques you plan to use. If you try to analyse data that doesn’t meet the assumptions of a specific statistical technique, your results will be largely meaningless. Therefore, you may need to show that the methods and techniques you’ll use are “allowed”.

Most commonly, there are two areas you need to pay attention to:

#1: Composite measures

The first is when you have multiple scale-based measures that combine to capture one construct – this is called a composite measure .  For example, you may have four Likert scale-based measures that (should) all measure the same thing, but in different ways. In other words, in a survey, these four scales should all receive similar ratings. This is called “ internal consistency ”.

Internal consistency is not guaranteed though (especially if you developed the measures yourself), so you need to assess the reliability of each composite measure using a test. Typically, Cronbach’s Alpha is a common test used to assess internal consistency – i.e., to show that the items you’re combining are more or less saying the same thing. A high alpha score means that your measure is internally consistent. A low alpha score means you may need to consider scrapping one or more of the measures.

#2: Data shape

The second matter that you should address early on in your results chapter is data shape. In other words, you need to assess whether the data in your set are symmetrical (i.e. normally distributed) or not, as this will directly impact what type of analyses you can use. For many common inferential tests such as T-tests or ANOVAs (we’ll discuss these a bit later), your data needs to be normally distributed. If it’s not, you’ll need to adjust your strategy and use alternative tests.

To assess the shape of the data, you’ll usually assess a variety of descriptive statistics (such as the mean, median and skewness), which is what we’ll look at next.

Step 5 – Present the descriptive statistics

Now that you’ve laid the foundation by discussing the representativeness of your sample, as well as the reliability of your measures and the shape of your data, you can get started with the actual statistical analysis. The first step is to present the descriptive statistics for your variables.

For scaled data, this usually includes statistics such as:

• The mean – this is simply the mathematical average of a range of numbers.
• The median – this is the midpoint in a range of numbers when the numbers are arranged in order.
• The mode – this is the most commonly repeated number in the data set.
• Standard deviation – this metric indicates how dispersed a range of numbers is. In other words, how close all the numbers are to the mean (the average).
• Skewness – this 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 (this is called a normal or parametric distribution), or do they lean to the left or right (this is called a non-normal or non-parametric distribution).
• Kurtosis – this metric indicates whether the data are heavily or lightly-tailed, relative to the normal distribution. In other words, how peaked or flat the distribution is.

A large table that indicates all the above for multiple variables can be a very effective way to present your data economically. You can also use colour coding to help make the data more easily digestible.

For categorical data, where you show the percentage of people who chose or fit into a category, for instance, you can either just plain describe the percentages or numbers of people who responded to something or use graphs and charts (such as bar graphs and pie charts) to present your data in this section of the chapter.

When using figures, make sure that you label them simply and clearly , so that your reader can easily understand them. There’s nothing more frustrating than a graph that’s missing axis labels! Keep in mind that although you’ll be presenting charts and graphs, your text content needs to present a clear narrative that can stand on its own. In other words, don’t rely purely on your figures and tables to convey your key points: highlight the crucial trends and values in the text. Figures and tables should complement the writing, not carry it .

Depending on your research aims, objectives and research questions, you may stop your analysis at this point (i.e. descriptive statistics). However, if your study requires inferential statistics, then it’s time to deep dive into those .

Step 6 – Present the inferential statistics

Inferential statistics are used to make generalisations about a population , whereas descriptive statistics focus purely on the sample . Inferential statistical techniques, broadly speaking, can be broken down into two groups .

First, there are those that compare measurements between groups , such as t-tests (which measure differences between two groups) and ANOVAs (which measure differences between multiple groups). Second, there are techniques that assess the relationships between variables , such as correlation analysis and regression analysis. Within each of these, some tests can be used for normally distributed (parametric) data and some tests are designed specifically for use on non-parametric data.

There are a seemingly endless number of tests that you can use to crunch your data, so it’s easy to run down a rabbit hole and end up with piles of test data. Ultimately, the most important thing is to make sure that you adopt the tests and techniques that allow you to achieve your research objectives and answer your research questions .

In this section of the results chapter, you should try to make use of figures and visual components as effectively as possible. For example, if you present a correlation table, use colour coding to highlight the significance of the correlation values, or scatterplots to visually demonstrate what the trend is. The easier you make it for your reader to digest your findings, the more effectively you’ll be able to make your arguments in the next chapter.

Step 7 – Test your hypotheses

If your study requires it, the next stage is hypothesis testing. A hypothesis is a statement , often indicating a difference between groups or relationship between variables, that can be supported or rejected by a statistical test. However, not all studies will involve hypotheses (again, it depends on the research objectives), so don’t feel like you “must” present and test hypotheses just because you’re undertaking quantitative research.

The basic process for hypothesis testing is as follows:

• Specify your null hypothesis (for example, “The chemical psilocybin has no effect on time perception).
• Specify your alternative hypothesis (e.g., “The chemical psilocybin has an effect on time perception)
• Set your significance level (this is usually 0.05)
• Calculate your statistics and find your p-value (e.g., p=0.01)
• Draw your conclusions (e.g., “The chemical psilocybin does have an effect on time perception”)

Finally, if the aim of your study is to develop and test a conceptual framework , this is the time to present it, following the testing of your hypotheses. While you don’t need to develop or discuss these findings further in the results chapter, indicating whether the tests (and their p-values) support or reject the hypotheses is crucial.

Step 8 – Provide a chapter summary

To wrap up your results chapter and transition to the discussion chapter, you should provide a brief summary of the key findings . “Brief” is the keyword here – much like the chapter introduction, this shouldn’t be lengthy – a paragraph or two maximum. Highlight the findings most relevant to your research objectives and research questions, and wrap it up.

Some final thoughts, tips and tricks

Now that you’ve got the essentials down, here are a few tips and tricks to make your quantitative results chapter shine:

• When writing your results chapter, report your findings in the past tense . You’re talking about what you’ve found in your data, not what you are currently looking for or trying to find.
• Structure your results chapter systematically and sequentially . If you had two experiments where findings from the one generated inputs into the other, report on them in order.
• Make your own tables and graphs rather than copying and pasting them from statistical analysis programmes like SPSS. Check out the DataIsBeautiful reddit for some inspiration.
• Once you’re done writing, review your work to make sure that you have provided enough information to answer your research questions , but also that you didn’t include superfluous information.

If you’ve got any questions about writing up the quantitative results chapter, please leave a comment below. If you’d like 1-on-1 assistance with your quantitative analysis and discussion, check out our hands-on coaching service , or book a free consultation with a friendly coach.

Psst… there’s more (for free)

This post is part of our dissertation mini-course, which covers everything you need to get started with your dissertation, thesis or research project. 

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Home Market Research

Quantitative Research: What It Is, Practices & Methods

Quantitative research involves analyzing and gathering numerical data to uncover trends, calculate averages, evaluate relationships, and derive overarching insights. It’s used in various fields, including the natural and social sciences. Quantitative data analysis employs statistical techniques for processing and interpreting numeric data.

Research designs in the quantitative realm outline how data will be collected and analyzed with methods like experiments and surveys. Qualitative methods complement quantitative research by focusing on non-numerical data, adding depth to understanding. Data collection methods can be qualitative or quantitative, depending on research goals. Researchers often use a combination of both approaches to gain a comprehensive understanding of phenomena.

What is Quantitative Research?

Quantitative research is a systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical, or computational techniques. Quantitative research collects statistically significant information from existing and potential customers using sampling methods and sending out online surveys , online polls , and questionnaires , for example.

One of the main characteristics of this type of research is that the results can be depicted in numerical form. After carefully collecting structured observations and understanding these numbers, it’s possible to predict the future of a product or service, establish causal relationships or Causal Research , and make changes accordingly. Quantitative research primarily centers on the analysis of numerical data and utilizes inferential statistics to derive conclusions that can be extrapolated to the broader population.

An example of a quantitative research study is the survey conducted to understand how long a doctor takes to tend to a patient when the patient walks into the hospital. A patient satisfaction survey can be administered to ask questions like how long a doctor takes to see a patient, how often a patient walks into a hospital, and other such questions, which are dependent variables in the research. This kind of research method is often employed in the social sciences, and it involves using mathematical frameworks and theories to effectively present data, ensuring that the results are logical, statistically sound, and unbiased.

Data collection in quantitative research uses a structured method and is typically conducted on larger samples representing the entire population. Researchers use quantitative methods to collect numerical data, which is then subjected to statistical analysis to determine statistically significant findings. This approach is valuable in both experimental research and social research, as it helps in making informed decisions and drawing reliable conclusions based on quantitative data.

Quantitative Research Characteristics

Quantitative research has several unique characteristics that make it well-suited for specific projects. Let’s explore the most crucial of these characteristics so that you can consider them when planning your next research project:

• Structured tools: Quantitative research relies on structured tools such as surveys, polls, or questionnaires to gather quantitative data . Using such structured methods helps collect in-depth and actionable numerical data from the survey respondents, making it easier to perform data analysis.
• Sample size: Quantitative research is conducted on a significant sample size  representing the target market . Appropriate Survey Sampling methods, a fundamental aspect of quantitative research methods, must be employed when deriving the sample to fortify the research objective and ensure the reliability of the results.
• Close-ended questions: Closed-ended questions , specifically designed to align with the research objectives, are a cornerstone of quantitative research. These questions facilitate the collection of quantitative data and are extensively used in data collection processes.
• Prior studies: Before collecting feedback from respondents, researchers often delve into previous studies related to the research topic. This preliminary research helps frame the study effectively and ensures the data collection process is well-informed.
• Quantitative data: Typically, quantitative data is represented using tables, charts, graphs, or other numerical forms. This visual representation aids in understanding the collected data and is essential for rigorous data analysis, a key component of quantitative research methods.
• Generalization of results: One of the strengths of quantitative research is its ability to generalize results to the entire population. It means that the findings derived from a sample can be extrapolated to make informed decisions and take appropriate actions for improvement based on numerical data analysis.

Quantitative Research Methods

Quantitative research methods are systematic approaches used to gather and analyze numerical data to understand and draw conclusions about a phenomenon or population. Here are the quantitative research methods:

• Primary quantitative research methods
• Secondary quantitative research methods

Primary Quantitative Research Methods

Primary quantitative research is the most widely used method of conducting market research. The distinct feature of primary research is that the researcher focuses on collecting data directly rather than depending on data collected from previously done research. Primary quantitative research design can be broken down into three further distinctive tracks and the process flow. They are:

A. Techniques and Types of Studies

There are multiple types of primary quantitative research. They can be distinguished into the four following distinctive methods, which are:

01. Survey Research

Survey Research is fundamental for all quantitative outcome research methodologies and studies. Surveys are used to ask questions to a sample of respondents, using various types such as online polls, online surveys, paper questionnaires, web-intercept surveys , etc. Every small and big organization intends to understand what their customers think about their products and services, how well new features are faring in the market, and other such details.

By conducting survey research, an organization can ask multiple survey questions , collect data from a pool of customers, and analyze this collected data to produce numerical results. It is the first step towards collecting data for any research. You can use single ease questions . A single-ease question is a straightforward query that elicits a concise and uncomplicated response.

This type of research can be conducted with a specific target audience group and also can be conducted across multiple groups along with comparative analysis . A prerequisite for this type of research is that the sample of respondents must have randomly selected members. This way, a researcher can easily maintain the accuracy of the obtained results as a huge variety of respondents will be addressed using random selection. 

Traditionally, survey research was conducted face-to-face or via phone calls. Still, with the progress made by online mediums such as email or social media, survey research has also spread to online mediums.There are two types of surveys , either of which can be chosen based on the time in hand and the kind of data required:

Cross-sectional surveys: Cross-sectional surveys are observational surveys conducted in situations where the researcher intends to collect data from a sample of the target population at a given point in time. Researchers can evaluate various variables at a particular time. Data gathered using this type of survey is from people who depict similarity in all variables except the variables which are considered for research . Throughout the survey, this one variable will stay constant.

• Cross-sectional surveys are popular with retail, SMEs, and healthcare industries. Information is garnered without modifying any parameters in the variable ecosystem.
• Multiple samples can be analyzed and compared using a cross-sectional survey research method.
• Multiple variables can be evaluated using this type of survey research.
• The only disadvantage of cross-sectional surveys is that the cause-effect relationship of variables cannot be established as it usually evaluates variables at a particular time and not across a continuous time frame.

Longitudinal surveys: Longitudinal surveys are also observational surveys , but unlike cross-sectional surveys, longitudinal surveys are conducted across various time durations to observe a change in respondent behavior and thought processes. This time can be days, months, years, or even decades. For instance, a researcher planning to analyze the change in buying habits of teenagers over 5 years will conduct longitudinal surveys.

• In cross-sectional surveys, the same variables were evaluated at a given time, and in longitudinal surveys, different variables can be analyzed at different intervals.
• Longitudinal surveys are extensively used in the field of medicine and applied sciences. Apart from these two fields, they are also used to observe a change in the market trend analysis , analyze customer satisfaction, or gain feedback on products/services.
• In situations where the sequence of events is highly essential, longitudinal surveys are used.
• Researchers say that when research subjects need to be thoroughly inspected before concluding, they rely on longitudinal surveys.

02. Correlational Research

A comparison between two entities is invariable. Correlation research is conducted to establish a relationship between two closely-knit entities and how one impacts the other, and what changes are eventually observed. This research method is carried out to give value to naturally occurring relationships, and a minimum of two different groups are required to conduct this quantitative research method successfully. Without assuming various aspects, a relationship between two groups or entities must be established.

Researchers use this quantitative research design to correlate two or more variables using mathematical analysis methods. Patterns, relationships, and trends between variables are concluded as they exist in their original setup. The impact of one of these variables on the other is observed, along with how it changes the relationship between the two variables. Researchers tend to manipulate one of the variables to attain the desired results.

Ideally, it is advised not to make conclusions merely based on correlational research. This is because it is not mandatory that if two variables are in sync that they are interrelated.

Example of Correlational Research Questions :

• The relationship between stress and depression.
• The equation between fame and money.
• The relation between activities in a third-grade class and its students.

03. Causal-comparative Research

This research method mainly depends on the factor of comparison. Also called quasi-experimental research , this quantitative research method is used by researchers to conclude the cause-effect equation between two or more variables, where one variable is dependent on the other independent variable. The independent variable is established but not manipulated, and its impact on the dependent variable is observed. These variables or groups must be formed as they exist in the natural setup. As the dependent and independent variables will always exist in a group, it is advised that the conclusions are carefully established by keeping all the factors in mind.

Causal-comparative research is not restricted to the statistical analysis of two variables but extends to analyzing how various variables or groups change under the influence of the same changes. This research is conducted irrespective of the type of relationship that exists between two or more variables. Statistical analysis plan is used to present the outcome using this quantitative research method.

Example of Causal-Comparative Research Questions:

• The impact of drugs on a teenager. The effect of good education on a freshman. The effect of substantial food provision in the villages of Africa.

04. Experimental Research

Also known as true experimentation, this research method relies on a theory. As the name suggests, experimental research is usually based on one or more theories. This theory has yet to be proven before and is merely a supposition. In experimental research, an analysis is done around proving or disproving the statement. This research method is used in natural sciences. Traditional research methods are more effective than modern techniques.

There can be multiple theories in experimental research. A theory is a statement that can be verified or refuted.

After establishing the statement, efforts are made to understand whether it is valid or invalid. This quantitative research method is mainly used in natural or social sciences as various statements must be proved right or wrong.

• Traditional research methods are more effective than modern techniques.
• Systematic teaching schedules help children who struggle to cope with the course.
• It is a boon to have responsible nursing staff for ailing parents.

B. Data Collection Methodologies

The second major step in primary quantitative research is data collection. Data collection can be divided into sampling methods and data collection using surveys and polls.

01. Data Collection Methodologies: Sampling Methods

There are two main sampling methods for quantitative research: Probability and Non-probability sampling .

Probability sampling: A theory of probability is used to filter individuals from a population and create samples in probability sampling . Participants of a sample are chosen by random selection processes. Each target audience member has an equal opportunity to be selected in the sample.

There are four main types of probability sampling:

• Simple random sampling: As the name indicates, simple random sampling is nothing but a random selection of elements for a sample. This sampling technique is implemented where the target population is considerably large.
• Stratified random sampling: In the stratified random sampling method , a large population is divided into groups (strata), and members of a sample are chosen randomly from these strata. The various segregated strata should ideally not overlap one another.
• Cluster sampling: Cluster sampling is a probability sampling method using which the main segment is divided into clusters, usually using geographic segmentation and demographic segmentation parameters.
• Systematic sampling: Systematic sampling is a technique where the starting point of the sample is chosen randomly, and all the other elements are chosen using a fixed interval. This interval is calculated by dividing the population size by the target sample size.

Non-probability sampling: Non-probability sampling is where the researcher’s knowledge and experience are used to create samples. Because of the researcher’s involvement, not all the target population members have an equal probability of being selected to be a part of a sample.

There are five non-probability sampling models:

• Convenience sampling: In convenience sampling , elements of a sample are chosen only due to one prime reason: their proximity to the researcher. These samples are quick and easy to implement as there is no other parameter of selection involved.
• Consecutive sampling: Consecutive sampling is quite similar to convenience sampling, except for the fact that researchers can choose a single element or a group of samples and conduct research consecutively over a significant period and then perform the same process with other samples.
• Quota sampling: Using quota sampling , researchers can select elements using their knowledge of target traits and personalities to form strata. Members of various strata can then be chosen to be a part of the sample as per the researcher’s understanding.
• Snowball sampling: Snowball sampling is conducted with target audiences who are difficult to contact and get information. It is popular in cases where the target audience for analysis research is rare to put together.
• Judgmental sampling: Judgmental sampling is a non-probability sampling method where samples are created only based on the researcher’s experience and research skill .

02. Data collection methodologies: Using surveys & polls

Once the sample is determined, then either surveys or polls can be distributed to collect the data for quantitative research.

Using surveys for primary quantitative research

A survey is defined as a research method used for collecting data from a pre-defined group of respondents to gain information and insights on various topics of interest. The ease of survey distribution and the wide number of people it can reach depending on the research time and objective makes it one of the most important aspects of conducting quantitative research.

Fundamental levels of measurement – nominal, ordinal, interval, and ratio scales

Four measurement scales are fundamental to creating a multiple-choice question in a survey. They are nominal, ordinal, interval, and ratio measurement scales without the fundamentals of which no multiple-choice questions can be created. Hence, it is crucial to understand these measurement levels to develop a robust survey.

Use of different question types

To conduct quantitative research, close-ended questions must be used in a survey. They can be a mix of multiple question types, including multiple-choice questions like semantic differential scale questions , rating scale questions , etc.

Survey Distribution and Survey Data Collection

In the above, we have seen the process of building a survey along with the research design to conduct primary quantitative research. Survey distribution to collect data is the other important aspect of the survey process. There are different ways of survey distribution. Some of the most commonly used methods are:

• Email: Sending a survey via email is the most widely used and effective survey distribution method. This method’s response rate is high because the respondents know your brand. You can use the QuestionPro email management feature to send out and collect survey responses.
• Buy respondents: Another effective way to distribute a survey and conduct primary quantitative research is to use a sample. Since the respondents are knowledgeable and are on the panel by their own will, responses are much higher.
• Embed survey on a website: Embedding a survey on a website increases a high number of responses as the respondent is already in close proximity to the brand when the survey pops up.
• Social distribution: Using social media to distribute the survey aids in collecting a higher number of responses from the people that are aware of the brand.
• QR code: QuestionPro QR codes store the URL for the survey. You can print/publish this code in magazines, signs, business cards, or on just about any object/medium.
• SMS survey: The SMS survey is a quick and time-effective way to collect a high number of responses.
• Offline Survey App: The QuestionPro App allows users to circulate surveys quickly, and the responses can be collected both online and offline.

Survey example

An example of a survey is a short customer satisfaction (CSAT) survey that can quickly be built and deployed to collect feedback about what the customer thinks about a brand and how satisfied and referenceable the brand is.

Using polls for primary quantitative research

Polls are a method to collect feedback using close-ended questions from a sample. The most commonly used types of polls are election polls and exit polls . Both of these are used to collect data from a large sample size but using basic question types like multiple-choice questions.

C. Data Analysis Techniques

The third aspect of primary quantitative research design is data analysis . After collecting raw data, there must be an analysis of this data to derive statistical inferences from this research. It is important to relate the results to the research objective and establish the statistical relevance of the results.

Remember to consider aspects of research that were not considered for the data collection process and report the difference between what was planned vs. what was actually executed.

It is then required to select precise Statistical Analysis Methods , such as SWOT, Conjoint, Cross-tabulation, etc., to analyze the quantitative data.

• SWOT analysis: SWOT Analysis stands for the acronym of Strengths, Weaknesses, Opportunities, and Threat analysis. Organizations use this statistical analysis technique to evaluate their performance internally and externally to develop effective strategies for improvement.
• Conjoint Analysis: Conjoint Analysis is a market analysis method to learn how individuals make complicated purchasing decisions. Trade-offs are involved in an individual’s daily activities, and these reflect their ability to decide from a complex list of product/service options.
• Cross-tabulation: Cross-tabulation is one of the preliminary statistical market analysis methods which establishes relationships, patterns, and trends within the various parameters of the research study.
• TURF Analysis: TURF Analysis , an acronym for Totally Unduplicated Reach and Frequency Analysis, is executed in situations where the reach of a favorable communication source is to be analyzed along with the frequency of this communication. It is used for understanding the potential of a target market.

Inferential statistics methods such as confidence interval, the margin of error, etc., can then be used to provide results.

Secondary Quantitative Research Methods

Secondary quantitative research or desk research is a research method that involves using already existing data or secondary data. Existing data is summarized and collated to increase the overall effectiveness of the research.

This research method involves collecting quantitative data from existing data sources like the internet, government resources, libraries, research reports, etc. Secondary quantitative research helps to validate the data collected from primary quantitative research and aid in strengthening or proving, or disproving previously collected data.

The following are five popularly used secondary quantitative research methods:

• Data available on the internet: With the high penetration of the internet and mobile devices, it has become increasingly easy to conduct quantitative research using the internet. Information about most research topics is available online, and this aids in boosting the validity of primary quantitative data.
• Government and non-government sources: Secondary quantitative research can also be conducted with the help of government and non-government sources that deal with market research reports. This data is highly reliable and in-depth and hence, can be used to increase the validity of quantitative research design.
• Public libraries: Now a sparingly used method of conducting quantitative research, it is still a reliable source of information, though. Public libraries have copies of important research that was conducted earlier. They are a storehouse of valuable information and documents from which information can be extracted.
• Educational institutions: Educational institutions conduct in-depth research on multiple topics, and hence, the reports that they publish are an important source of validation in quantitative research.
• Commercial information sources: Local newspapers, journals, magazines, radio, and TV stations are great sources to obtain data for secondary quantitative research. These commercial information sources have in-depth, first-hand information on market research, demographic segmentation, and similar subjects.

Quantitative Research Examples

Some examples of quantitative research are:

• A customer satisfaction template can be used if any organization would like to conduct a customer satisfaction (CSAT) survey . Through this kind of survey, an organization can collect quantitative data and metrics on the goodwill of the brand or organization in the customer’s mind based on multiple parameters such as product quality, pricing, customer experience, etc. This data can be collected by asking a net promoter score (NPS) question , matrix table questions, etc. that provide data in the form of numbers that can be analyzed and worked upon.
• Another example of quantitative research is an organization that conducts an event, collecting feedback from attendees about the value they see from the event. By using an event survey , the organization can collect actionable feedback about the satisfaction levels of customers during various phases of the event such as the sales, pre and post-event, the likelihood of recommending the organization to their friends and colleagues, hotel preferences for the future events and other such questions.

What are the Advantages of Quantitative Research?

There are many advantages to quantitative research. Some of the major advantages of why researchers use this method in market research are:

Collect Reliable and Accurate Data:

Quantitative research is a powerful method for collecting reliable and accurate quantitative data. Since data is collected, analyzed, and presented in numbers, the results obtained are incredibly reliable and objective. Numbers do not lie and offer an honest and precise picture of the conducted research without discrepancies. In situations where a researcher aims to eliminate bias and predict potential conflicts, quantitative research is the method of choice.

Quick Data Collection:

Quantitative research involves studying a group of people representing a larger population. Researchers use a survey or another quantitative research method to efficiently gather information from these participants, making the process of analyzing the data and identifying patterns faster and more manageable through the use of statistical analysis. This advantage makes quantitative research an attractive option for projects with time constraints.

Wider Scope of Data Analysis:

Quantitative research, thanks to its utilization of statistical methods, offers an extensive range of data collection and analysis. Researchers can delve into a broader spectrum of variables and relationships within the data, enabling a more thorough comprehension of the subject under investigation. This expanded scope is precious when dealing with complex research questions that require in-depth numerical analysis.

Eliminate Bias:

One of the significant advantages of quantitative research is its ability to eliminate bias. This research method leaves no room for personal comments or the biasing of results, as the findings are presented in numerical form. This objectivity makes the results fair and reliable in most cases, reducing the potential for researcher bias or subjectivity.

In summary, quantitative research involves collecting, analyzing, and presenting quantitative data using statistical analysis. It offers numerous advantages, including the collection of reliable and accurate data, quick data collection, a broader scope of data analysis, and the elimination of bias, making it a valuable approach in the field of research. When considering the benefits of quantitative research, it’s essential to recognize its strengths in contrast to qualitative methods and its role in collecting and analyzing numerical data for a more comprehensive understanding of research topics.

Best Practices to Conduct Quantitative Research

Here are some best practices for conducting quantitative research:

• Differentiate between quantitative and qualitative: Understand the difference between the two methodologies and apply the one that suits your needs best.
• Choose a suitable sample size: Ensure that you have a sample representative of your population and large enough to be statistically weighty.
• Keep your research goals clear and concise: Know your research goals before you begin data collection to ensure you collect the right amount and the right quantity of data.
• Keep the questions simple: Remember that you will be reaching out to a demographically wide audience. Pose simple questions for your respondents to understand easily.

Quantitative Research vs Qualitative Research

Quantitative research and qualitative research are two distinct approaches to conducting research, each with its own set of methods and objectives. Here’s a comparison of the two:

Quantitative Research

• Objective: The primary goal of quantitative research is to quantify and measure phenomena by collecting numerical data. It aims to test hypotheses, establish patterns, and generalize findings to a larger population.
• Data Collection: Quantitative research employs systematic and standardized approaches for data collection, including techniques like surveys, experiments, and observations that involve predefined variables. It is often collected from a large and representative sample.
• Data Analysis: Data is analyzed using statistical techniques, such as descriptive statistics, inferential statistics, and mathematical modeling. Researchers use statistical tests to draw conclusions and make generalizations based on numerical data.
• Sample Size: Quantitative research often involves larger sample sizes to ensure statistical significance and generalizability.
• Results: The results are typically presented in tables, charts, and statistical summaries, making them highly structured and objective.
• Generalizability: Researchers intentionally structure quantitative research to generate outcomes that can be helpful to a larger population, and they frequently seek to establish causative connections.
• Emphasis on Objectivity: Researchers aim to minimize bias and subjectivity, focusing on replicable and objective findings.

Qualitative Research

• Objective: Qualitative research seeks to gain a deeper understanding of the underlying motivations, behaviors, and experiences of individuals or groups. It explores the context and meaning of phenomena.
• Data Collection: Qualitative research employs adaptable and open-ended techniques for data collection, including methods like interviews, focus groups, observations, and content analysis. It allows participants to express their perspectives in their own words.
• Data Analysis: Data is analyzed through thematic analysis, content analysis, or grounded theory. Researchers focus on identifying patterns, themes, and insights in the data.
• Sample Size: Qualitative research typically involves smaller sample sizes due to the in-depth nature of data collection and analysis.
• Results: Findings are presented in narrative form, often in the participants’ own words. Results are subjective, context-dependent, and provide rich, detailed descriptions.
• Generalizability: Qualitative research does not aim for broad generalizability but focuses on in-depth exploration within a specific context. It provides a detailed understanding of a particular group or situation.
• Emphasis on Subjectivity: Researchers acknowledge the role of subjectivity and the researcher’s influence on the Research Process . Participant perspectives and experiences are central to the findings.

Researchers choose between quantitative and qualitative research methods based on their research objectives and the nature of the research question. Each approach has its advantages and drawbacks, and the decision between them hinges on the particular research objectives and the data needed to address research inquiries effectively.

Quantitative research is a structured way of collecting and analyzing data from various sources. Its purpose is to quantify the problem and understand its extent, seeking results that someone can project to a larger population.

Companies that use quantitative rather than qualitative research typically aim to measure magnitudes and seek objectively interpreted statistical results. So if you want to obtain quantitative data that helps you define the structured cause-and-effect relationship between the research problem and the factors, you should opt for this type of research.

At QuestionPro , we have various Best Data Collection Tools and features to conduct investigations of this type. You can create questionnaires and distribute them through our various methods. We also have sample services or various questions to guarantee the success of your study and the quality of the collected data.

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Quantitative research is a systematic and structured approach to studying phenomena that involves the collection of measurable data and the application of statistical, mathematical, or computational techniques for analysis.

Quantitative research is characterized by structured tools like surveys, substantial sample sizes, closed-ended questions, reliance on prior studies, data presented numerically, and the ability to generalize findings to the broader population.

The two main methods of quantitative research are Primary quantitative research methods, involving data collection directly from sources, and Secondary quantitative research methods, which utilize existing data for analysis.

1.Surveying to measure employee engagement with numerical rating scales. 2.Analyzing sales data to identify trends in product demand and market share. 4.Examining test scores to assess the impact of a new teaching method on student performance. 4.Using website analytics to track user behavior and conversion rates for an online store.

1.Differentiate between quantitative and qualitative approaches. 2.Choose a representative sample size. 3.Define clear research goals before data collection. 4.Use simple and easily understandable survey questions.

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Quantitative Data Analysis

9 Presenting the Results of Quantitative Analysis

Mikaila Mariel Lemonik Arthur

This chapter provides an overview of how to present the results of quantitative analysis, in particular how to create effective tables for displaying quantitative results and how to write quantitative research papers that effectively communicate the methods used and findings of quantitative analysis.

Writing the Quantitative Paper

Standard quantitative social science papers follow a specific format. They begin with a title page that includes a descriptive title, the author(s)’ name(s), and a 100 to 200 word abstract that summarizes the paper. Next is an introduction that makes clear the paper’s research question, details why this question is important, and previews what the paper will do. After that comes a literature review, which ends with a summary of the research question(s) and/or hypotheses. A methods section, which explains the source of data, sample, and variables and quantitative techniques used, follows. Many analysts will include a short discussion of their descriptive statistics in the methods section. A findings section details the findings of the analysis, supported by a variety of tables, and in some cases graphs, all of which are explained in the text. Some quantitative papers, especially those using more complex techniques, will include equations. Many papers follow the findings section with a discussion section, which provides an interpretation of the results in light of both the prior literature and theory presented in the literature review and the research questions/hypotheses. A conclusion ends the body of the paper. This conclusion should summarize the findings, answering the research questions and stating whether any hypotheses were supported, partially supported, or not supported. Limitations of the research are detailed. Papers typically include suggestions for future research, and where relevant, some papers include policy implications. After the body of the paper comes the works cited; some papers also have an Appendix that includes additional tables and figures that did not fit into the body of the paper or additional methodological details. While this basic format is similar for papers regardless of the type of data they utilize, there are specific concerns relating to quantitative research in terms of the methods and findings that will be discussed here.

In the methods section, researchers clearly describe the methods they used to obtain and analyze the data for their research. When relying on data collected specifically for a given paper, researchers will need to discuss the sample and data collection; in most cases, though, quantitative research relies on pre-existing datasets. In these cases, researchers need to provide information about the dataset, including the source of the data, the time it was collected, the population, and the sample size. Regardless of the source of the data, researchers need to be clear about which variables they are using in their research and any transformations or manipulations of those variables. They also need to explain the specific quantitative techniques that they are using in their analysis; if different techniques are used to test different hypotheses, this should be made clear. In some cases, publications will require that papers be submitted along with any code that was used to produce the analysis (in SPSS terms, the syntax files), which more advanced researchers will usually have on hand. In many cases, basic descriptive statistics are presented in tabular form and explained within the methods section.

The findings sections of quantitative papers are organized around explaining the results as shown in tables and figures. Not all results are depicted in tables and figures—some minor or null findings will simply be referenced—but tables and figures should be produced for all findings to be discussed at any length. If there are too many tables and figures, some can be moved to an appendix after the body of the text and referred to in the text (e.g. “See Table 12 in Appendix A”).

Discussions of the findings should not simply restate the contents of the table. Rather, they should explain and interpret it for readers, and they should do so in light of the hypothesis or hypotheses that are being tested. Conclusions—discussions of whether the hypothesis or hypotheses are supported or not supported—should wait for the conclusion of the paper.

Creating Effective Tables

When creating tables to display the results of quantitative analysis, the most important goals are to create tables that are clear and concise but that also meet standard conventions in the field. This means, first of all, paring down the volume of information produced in the statistical output to just include the information most necessary for interpreting the results, but doing so in keeping with standard table conventions. It also means making tables that are well-formatted and designed, so that readers can understand what the tables are saying without struggling to find information. For example, tables (as well as figures such as graphs) need clear captions; they are typically numbered and referred to by number in the text. Columns and rows should have clear headings. Depending on the content of the table, formatting tools may need to be used to set off header rows/columns and/or total rows/columns; cell-merging tools may be necessary; and shading may be important in tables with many rows or columns.

Here, you will find some instructions for creating tables of results from descriptive, crosstabulation, correlation, and regression analysis that are clear, concise, and meet normal standards for data display in social science. In addition, after the instructions for creating tables, you will find an example of how a paper incorporating each table might describe that table in the text.

Descriptive Statistics

When presenting the results of descriptive statistics, we create one table with columns for each type of descriptive statistic and rows for each variable. Note, of course, that depending on level of measurement only certain descriptive statistics are appropriate for a given variable, so there may be many cells in the table marked with an — to show that this statistic is not calculated for this variable. So, consider the set of descriptive statistics below, for occupational prestige, age, highest degree earned, and whether the respondent was born in this country.

To display these descriptive statistics in a paper, one might create a table like Table 2. Note that for discrete variables, we use the value label in the table, not the value.

If we were then to discuss our descriptive statistics in a quantitative paper, we might write something like this (note that we do not need to repeat every single detail from the table, as readers can peruse the table themselves):

This analysis relies on four variables from the 2021 General Social Survey: occupational prestige score, age, highest degree earned, and whether the respondent was born in the United States. Descriptive statistics for all four variables are shown in Table 2. The median occupational prestige score is 47, with a range from 16 to 80. 50% of respondents had occupational prestige scores scores between 35 and 59. The median age of respondents is 53, with a range from 18 to 89. 50% of respondents are between ages 37 and 66. Both variables have little skew. Highest degree earned ranges from less than high school to a graduate degree; the median respondent has earned an associate’s degree, while the modal response (given by 39.8% of the respondents) is a high school degree. 88.8% of respondents were born in the United States.

Crosstabulation

When presenting the results of a crosstabulation, we simplify the table so that it highlights the most important information—the column percentages—and include the significance and association below the table. Consider the SPSS output below.

Table 4 shows how a table suitable for include in a paper might look if created from the SPSS output in Table 3. Note that we use asterisks to indicate the significance level of the results: * means p < 0.05; ** means p < 0.01; *** means p < 0.001; and no stars mean p > 0.05 (and thus that the result is not significant). Also note than N is the abbreviation for the number of respondents.

If we were going to discuss the results of this crosstabulation in a quantitative research paper, the discussion might look like this:

A crosstabulation of respondent’s class identification and their highest degree earned, with class identification as the independent variable, is significant, with a Spearman correlation of 0.419, as shown in Table 4. Among lower class and working class respondents, more than 50% had earned a high school degree. Less than 20% of poor respondents and less than 40% of working-class respondents had earned more than a high school degree. In contrast, the majority of middle class and upper class respondents had earned at least a bachelor’s degree. In fact, 50% of upper class respondents had earned a graduate degree.

Correlation

When presenting a correlating matrix, one of the most important things to note is that we only present half the table so as not to include duplicated results. Think of the line through the table where empty cells exist to represent the correlation between a variable and itself, and include only the triangle of data either above or below that line of cells. Consider the output in Table 5.

Table 6 shows what the contents of Table 5 might look like when a table is constructed in a fashion suitable for publication.

If we were to discuss the results of this bivariate correlation analysis in a quantitative paper, the discussion might look like this:

Bivariate correlations were run among variables measuring age, occupational prestige, the highest year of school respondents completed, and family income in constant 1986 dollars, as shown in Table 6. Correlations between age and highest year of school completed and between age and family income are not significant. All other correlations are positive and significant at the p<0.001 level. The correlation between age and occupational prestige is weak; the correlations between income and occupational prestige and between income and educational attainment are moderate, and the correlation between education and occupational prestige is strong.

To present the results of a regression, we create one table that includes all of the key information from the multiple tables of SPSS output. This includes the R 2 and significance of the regression, either the B or the beta values (different analysts have different preferences here) for each variable, and the standard error and significance of each variable. Consider the SPSS output in Table 7.

The regression output in shown in Table 7 contains a lot of information. We do not include all of this information when making tables suitable for publication. As can be seen in Table 8, we include the Beta (or the B), the standard error, and the significance asterisk for each variable; the R 2 and significance for the overall regression; the degrees of freedom (which tells readers the sample size or N); and the constant; along with the key to p/significance values.

If we were to discuss the results of this regression in a quantitative paper, the results might look like this:

Table 8 shows the results of a regression in which age, occupational prestige, and highest year of school completed are the independent variables and family income is the dependent variable. The regression results are significant, and all of the independent variables taken together explain 15.6% of the variance in family income. Age is not a significant predictor of income, while occupational prestige and educational attainment are. Educational attainment has a larger effect on family income than does occupational prestige. For every year of additional education attained, family income goes up on average by $3,988.545; for every one-unit increase in occupational prestige score, family income goes up on average by $522.887. [1]

• Choose two discrete variables and three continuous variables from a dataset of your choice. Produce appropriate descriptive statistics on all five of the variables and create a table of the results suitable for inclusion in a paper.
• Using the two discrete variables you have chosen, produce an appropriate crosstabulation, with significance and measure of association. Create a table of the results suitable for inclusion in a paper.
• Using the three continuous variables you have chosen, produce a correlation matrix. Create a table of the results suitable for inclusion in a paper.
• Using the three continuous variables you have chosen, produce a multivariate linear regression. Create a table of the results suitable for inclusion in a paper.
• Write a methods section describing the dataset, analytical methods, and variables you utilized in questions 1, 2, 3, and 4 and explaining the results of your descriptive analysis.
• Write a findings section explaining the results of the analyses you performed in questions 2, 3, and 4.
• Note that the actual numberical increase comes from the B values, which are shown in the SPSS output in Table 7 but not in the reformatted Table 8. ↵

Social Data Analysis Copyright © 2021 by Mikaila Mariel Lemonik Arthur is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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• What Is Quantitative Research? | Definition & Methods

What Is Quantitative Research? | Definition & Methods

Published on 4 April 2022 by Pritha Bhandari . Revised on 10 October 2022.

Quantitative research is the process of collecting and analysing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalise results to wider populations.

Quantitative research is the opposite of qualitative research , which involves collecting and analysing non-numerical data (e.g. text, video, or audio).

Quantitative research is widely used in the natural and social sciences: biology, chemistry, psychology, economics, sociology, marketing, etc.

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Table of contents

Quantitative research methods, quantitative data analysis, advantages of quantitative research, disadvantages of quantitative research, frequently asked questions about quantitative research.

You can use quantitative research methods for descriptive, correlational or experimental research.

• In descriptive research , you simply seek an overall summary of your study variables.
• In correlational research , you investigate relationships between your study variables.
• In experimental research , you systematically examine whether there is a cause-and-effect relationship between variables.

Correlational and experimental research can both be used to formally test hypotheses , or predictions, using statistics. The results may be generalised to broader populations based on the sampling method used.

To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels).

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Once data is collected, you may need to process it before it can be analysed. For example, survey and test data may need to be transformed from words to numbers. Then, you can use statistical analysis to answer your research questions .

Descriptive statistics will give you a summary of your data and include measures of averages and variability. You can also use graphs, scatter plots and frequency tables to visualise your data and check for any trends or outliers.

Using inferential statistics , you can make predictions or generalisations based on your data. You can test your hypothesis or use your sample data to estimate the population parameter .

You can also assess the reliability and validity of your data collection methods to indicate how consistently and accurately your methods actually measured what you wanted them to.

Quantitative research is often used to standardise data collection and generalise findings . Strengths of this approach include:

• Replication

Repeating the study is possible because of standardised data collection protocols and tangible definitions of abstract concepts.

• Direct comparisons of results

The study can be reproduced in other cultural settings, times or with different groups of participants. Results can be compared statistically.

• Large samples

Data from large samples can be processed and analysed using reliable and consistent procedures through quantitative data analysis.

• Hypothesis testing

Using formalised and established hypothesis testing procedures means that you have to carefully consider and report your research variables, predictions, data collection and testing methods before coming to a conclusion.

Despite the benefits of quantitative research, it is sometimes inadequate in explaining complex research topics. Its limitations include:

• Superficiality

Using precise and restrictive operational definitions may inadequately represent complex concepts. For example, the concept of mood may be represented with just a number in quantitative research, but explained with elaboration in qualitative research.

• Narrow focus

Predetermined variables and measurement procedures can mean that you ignore other relevant observations.

• Structural bias

Despite standardised procedures, structural biases can still affect quantitative research. Missing data , imprecise measurements or inappropriate sampling methods are biases that can lead to the wrong conclusions.

• Lack of context

Quantitative research often uses unnatural settings like laboratories or fails to consider historical and cultural contexts that may affect data collection and results.

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

Quantitative methods allow you to test a hypothesis by systematically collecting and analysing data, while qualitative methods allow you to explore ideas and experiences in depth.

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

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organisations.

Operationalisation means turning abstract conceptual ideas into measurable observations.

For example, the concept of social anxiety isn’t directly observable, but it can be operationally defined in terms of self-rating scores, behavioural avoidance of crowded places, or physical anxiety symptoms in social situations.

Before collecting data , it’s important to consider how you will operationalise the variables that you want to measure.

Reliability and validity are both about how well a method measures something:

• Reliability refers to the  consistency of a measure (whether the results can be reproduced under the same conditions).
• Validity   refers to the  accuracy of a measure (whether the results really do represent what they are supposed to measure).

If you are doing experimental research , you also have to consider the internal and external validity of your experiment.

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.

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Your ultimate guide to quantitative research.

12 min read You may be already using quantitative research and want to check your understanding, or you may be starting from the beginning. Here’s an exploration of this research method and how you can best use it for maximum effect for your business.

You may be already using quantitative research and want to check your understanding, or you may be starting from the beginning. Here’s an exploration of this research method and how you can best use it for maximum effect for your business.

What is quantitative research?

Quantitative is the research method of collecting quantitative data – this is data that can be converted into numbers or numerical data, which can be easily quantified, compared, and analyzed.

Quantitative research deals with primary and secondary sources where data is represented in numerical form. This can include closed-question poll results, statistics, and census information or demographic data .

Quantitative data tends to be used when researchers are interested in understanding a particular moment in time and examining data sets over time to find trends and patterns.

To collect numerical data, surveys are often employed as one of the main research methods to source first-hand information in primary research . Quantitative research can also come from third-party research studies .

Quantitative research is widely used in the realms of social sciences, such as biology, chemistry, psychology, economics, sociology, and marketing .

Research teams collect data that is significant to proving or disproving a hypothesis research question – known as the research objective. When they collect quantitative data, researchers will aim to use a sample size that is representative of the total population of the target market they’re interested in.

Then the data collected will be manually or automatically stored and compared for insights.

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Quantitative vs qualitative research

While the quantitative research definition focuses on numerical data, qualitative research is defined as data that supplies non-numerical information.

Quantitative research focuses on the thoughts, feelings, and values of a participant , to understand why people act in the way they do . They result in data types like quotes, symbols, images, and written testimonials.

These data types tell researchers subjective information, which can help us assign people into categories, such as a participant’s religion, gender , social class, political alignment, likely favored products to buy, or their preferred training learning style.

For this reason, qualitative research is often used in social research, as this gives a window into the behavior and actions of people.

In general, if you’re interested in measuring something or testing a hypothesis, use quantitative methods. If you want to explore ideas, thoughts, and meanings, use qualitative methods.

However, quantitative and qualitative research methods are both recommended when you’re looking to understand a point in time, while also finding out the reason behind the facts.

Quantitative research data collection methods

Quantitative research methods can use structured research instruments like:

• Surveys : A survey is a simple-to-create and easy-to-distribute research method , which helps gather information from large groups of participants quickly. Traditionally, paper-based surveys can now be made online, so costs can stay quite low.

Quantitative questions tend to be closed questions that ask for a numerical result, based on a range of options, or a yes/no answer that can be tallied quickly.

• Face-to-face or phone interviews: Interviews are a great way to connect with participants , though they require time from the research team to set up and conduct.

Researchers may also have issues connecting with participants in different geographical regions . The researcher uses a set of predefined close-ended questions, which ask for yes/no or numerical values.

• Polls: Polls can be a shorter version of surveys , used to get a ‘flavor’ of what the current situation is with participants. Online polls can be shared easily, though polls are best used with simple questions that request a range or a yes/no answer.

Quantitative data is the opposite of qualitative research, another dominant framework for research in the social sciences, explored further below.

Quantitative data types

Quantitative research methods often deliver the following data types:

• Test Scores
• Percent of training course completed
• Performance score out of 100
• Number of support calls active
• Customer Net Promoter Score (NPS)

When gathering numerical data, the emphasis is on how specific the data is, and whether they can provide an indication of what ‘is’ at the time of collection. Pre-existing statistical data can tell us what ‘was’ for the date and time range that it represented

Quantitative research design methods (with examples)

Quantitative research has a number of quantitative research designs you can choose from:

Descriptive

This design type describes the state of a data type is telling researchers, in its native environment. There won’t normally be a clearly defined research question to start with. Instead, data analysis will suggest a conclusion , which can become the hypothesis to investigate further.

Examples of descriptive quantitative design include:

• A description of child’s Christmas gifts they received that year
• A description of what businesses sell the most of during Black Friday
• A description of a product issue being experienced by a customer

Correlational

This design type looks at two or more data types, the relationship between them, and the extent that they differ or align. This does not look at the causal links deeper – instead statistical analysis looks at the variables in a natural environment.

Examples of correlational quantitative design include:

• The relationship between a child’s Christmas gifts and their perceived happiness level
• The relationship between a business’ sales during Black Friday and the total revenue generated over the year
• The relationship between a customer’s product issue and the reputation of the product

Causal-Comparative/Quasi-Experimental

This design type looks at two or more data types and tries to explain any relationship and differences between them, using a cause-effect analysis. The research is carried out in a near-natural environment, where information is gathered from two groups – a naturally occurring group that matches the original natural environment, and one that is not naturally present.

This allows for causal links to be made, though they might not be correct, as other variables may have an impact on results.

Examples of causal-comparative/quasi-experimental quantitative design include:

• The effect of children’s Christmas gifts on happiness
• The effect of Black Friday sales figures on the productivity of company yearly sales
• The effect of product issues on the public perception of a product

Experimental Research

This design type looks to make a controlled environment in which two or more variables are observed to understand the exact cause and effect they have. This becomes a quantitative research study, where data types are manipulated to assess the effect they have. The participants are not naturally occurring groups, as the setting is no longer natural. A quantitative research study can help pinpoint the exact conditions in which variables impact one another.

Examples of experimental quantitative design include:

• The effect of children’s Christmas gifts on a child’s dopamine (happiness) levels
• The effect of Black Friday sales on the success of the company
• The effect of product issues on the perceived reliability of the product

Quantitative research methods need to be carefully considered, as your data collection of a data type can be used to different effects. For example, statistics can be descriptive or correlational (or inferential). Descriptive statistics help us to summarize our data, while inferential statistics help infer conclusions about significant differences.

Advantages of quantitative research

• Easy to do : Doing quantitative research is more straightforward, as the results come in numerical format, which can be more easily interpreted.
• Less interpretation : Due to the factual nature of the results, you will be able to accept or reject your hypothesis based on the numerical data collected.
• Less bias : There are higher levels of control that can be applied to the research, so bias can be reduced , making your data more reliable and precise.

Disadvantages of quantitative research

• Can’t understand reasons: Quantitative research doesn’t always tell you the full story, meaning you won’t understand the context – or the why, of the data you see, why do you see the results you have uncovered?
• Useful for simpler situations: Quantitative research on its own is not great when dealing with complex issues. In these cases, quantitative research may not be enough.

How to use quantitative research to your business’s advantage

Quantitative research methods may help in areas such as:

• Identifying which advert or landing page performs better
• Identifying how satisfied your customers are
• How many customers are likely to recommend you
• Tracking how your brand ranks in awareness and customer purchase intent
• Learn what consumers are likely to buy from your brand.

6 steps to conducting good quantitative research

Businesses can benefit from quantitative research by using it to evaluate the impact of data types. There are several steps to this:

• Define your problem or interest area : What do you observe is happening and is it frequent? Identify the data type/s you’re observing.
• Create a hypothesis : Ask yourself what could be the causes for the situation with those data types.
• Plan your quantitative research : Use structured research instruments like surveys or polls to ask questions that test your hypothesis.
• Data Collection : Collect quantitative data and understand what your data types are telling you. Using data collected on different types over long time periods can give you information on patterns.
• Data analysis : Does your information support your hypothesis? (You may need to redo the research with other variables to see if the results improve)
• Effectively present data : Communicate the results in a clear and concise way to help other people understand the findings.

How Qualtrics products can enhance & simplify the quantitative research process

The Qualtrics XM system gives you an all-in-one, integrated solution to help you all the way through conducting quantitative research. From survey creation and data collection to statistical analysis and data reporting, it can help all your internal teams gain insights from your numerical data.

Quantitative methods are catered to your business through templates or advanced survey designs. While you can manually collect data and conduct data analysis in a spreadsheet program, this solution helps you automate the process of quantitative research, saving you time and administration work.

Using computational techniques helps you to avoid human errors, and participant results come in are already incorporated into the analysis in real-time.

Our key tools, Stats IQ™ and Driver IQ™ make analyzing numerical data easy and simple. Choose to highlight key findings based on variables or highlight statistically insignificant findings. The choice is yours.

Some examples of your workspace in action, using drag and drop to create fast data visualizations quickly:

Related resources

Market intelligence 10 min read, marketing insights 11 min read, ethnographic research 11 min read, qualitative vs quantitative research 13 min read, qualitative research questions 11 min read, qualitative research design 12 min read, primary vs secondary research 14 min read, request demo.

Ready to learn more about Qualtrics?

What is Quantitative Data?

Data professionals work with two types of data: quantitative and qualitative. What is quantitative data? What is qualitative data? In simple terms, quantitative data is measurable while qualitative data is descriptive—think numbers versus words.

If you plan on working as a data analyst or a data scientist (or in any field that involves conducting research, like psychology), you’ll need to get to grips with both. In this post, we’ll focus on quantitative data. We’ll explain exactly what quantitative data is, including plenty of useful examples. We’ll also show you what methods you can use to collect and analyze quantitative data.

By the end of this post, you’ll have a clear understanding of quantitative data and how it’s used.

We’ll cover:

• What is quantitative data? (Definition)
• What are some examples of quantitative data?
• What’s the difference between quantitative and qualitative data?
• What are the different types of quantitative data?
• How is quantitative data collected?
• What methods are used to analyze quantitative data?
• What are the advantages and disadvantages of quantitative data?
• Should I use quantitative or qualitative data in my research?
• What are some common quantitative data analysis tools?
• What is quantitative data? FAQs
• Key takeaways

So: what is quantitative data? Let’s find out.

1. What is quantitative data? (Definition)

Quantitative data is, quite simply, information that can be quantified. It can be counted or measured, and given a numerical value—such as length in centimeters or revenue in dollars. Quantitative data tends to be structured in nature and is suitable for statistical analysis. If you have questions such as “How many?”, “How often?” or “How much?”, you’ll find the answers in quantitative data.

2. What are some examples of quantitative data?

Some examples of quantitative data include:

• Revenue in dollars
• Weight in kilograms
• Age in months or years
• Length in centimeters
• Distance in kilometers
• Height in feet or inches
• Number of weeks in a year

3. What is the difference between quantitative and qualitative data?

It’s hard to define quantitative data without comparing it to qualitative data—so what’s the difference between the two?

While quantitative data can be counted and measured, qualitative data is descriptive and, typically, unstructured. It usually takes the form of words and text—for example, a status posted on Facebook or an interview transcript are both forms of qualitative data. You can also think of qualitative data in terms of the “descriptors” you would use to describe certain attributes. For example, if you were to describe someone’s hair color as auburn, or an ice cream flavor as vanilla, these labels count as qualitative data.

Qualitative data cannot be used for statistical analysis; to make sense of such data, researchers and analysts will instead try to identify meaningful groups and themes.

You’ll find a detailed exploration of the differences between qualitative and quantitative data in this post . But, to summarize:

• Quantitative data is countable or measurable, relating to numbers; qualitative data is descriptive, relating to words.
• Quantitative data lends itself to statistical analysis; qualitative data is grouped and categorized according to themes.
• Examples of quantitative data include numerical values such as measurements, cost, and weight; examples of qualitative data include descriptions (or labels) of certain attributes, such as “brown eyes” or “vanilla flavored ice cream”.

Now we know the difference between the two, let’s get back to quantitative data.

4. What are the different types of quantitative data?

There are two main types of quantitative data: discrete and continuous .

Discrete data

Discrete data is quantitative data that can only take on certain numerical values. These values are fixed and cannot be broken down. When you count something, you get discrete data. For example, if a person has three children, this is an example of discrete data. The number of children is fixed—it’s not possible for them to have, say, 3.2 children.

Another example of discrete quantitative data could be the number of visits to your website; you could have 150 visits in one day, but not 150.6 visits. Discrete data is usually visualized using tally charts, bar charts, and pie charts.

Continuous data

Continuous data, on the other hand, can be infinitely broken down into smaller parts. This type of quantitative data can be placed on a measurement scale; for example, the length of a piece of string in centimeters, or the temperature in degrees Celsius. Essentially, continuous data can take any value; it’s not limited to fixed values. What’s more, continuous data can also fluctuate over time—the room temperature will vary throughout the day, for example. Continuous data is usually represented using a line graph.

Continuous data can be further classified depending on whether it’s interval data or ratio data . Let’s take a look at those now.

Interval vs. ratio data

Interval data can be measured along a continuum, where there is an equal distance between each point on the scale. For example: The difference between 30 and 31 degrees C is equal to the difference between 99 and 100 degrees. Another thing to bear in mind is that interval data has no true or meaningful zero value . Temperature is a good example; a temperature of zero degrees does not mean that there is “no temperature”—it just means that it’s extremely cold!

Ratio data is the same as interval data in terms of equally spaced points on a scale, but unlike interval data, ratio data does have a true zero . Weight in grams would be classified as ratio data; the difference between 20 grams and 21 grams is equal to the difference between 8 and 9 grams, and if something weighs zero grams, it truly weighs nothing.

Beyond the distinction between discrete and continuous data, quantitative data can also be broken down into several different types:

• Measurements: This type of data refers to the measurement of physical objects. For example, you might measure the length and width of your living room before ordering new sofas.
• Sensors: A sensor is a device or system which detects changes in the surrounding environment and sends this information to another electronic device, usually a computer. This information is then converted into numbers—that’s your quantitative data. For example, a smart temperature sensor will provide you with a stream of data about the temperature of the room throughout the day.
• Counts: As the name suggests, this is the quantitative data you get when you count things. You might count the number of people who attended an event, or the number of visits to your website in one week.
• Quantification of qualitative data: This is when qualitative data is converted into numbers. Take the example of customer satisfaction. If a customer said “I’m really happy with this product”, that would count as qualitative data. You could turn this into quantitative data by asking them to rate their satisfaction on a scale of 1-10.
• Calculations: This is any quantitative data that results from mathematical calculations, such as calculating your final profit at the end of the month.
• Projections: Analysts may estimate or predict quantities using algorithms, artificial intelligence, or “manual” analysis. For example, you might predict how many sales you expect to make in the next quarter. The figure you come up with is a projection of quantitative data.

Knowing what type of quantitative data you’re working with helps you to apply the correct type of statistical analysis. We’ll look at how quantitative data is analyzed in section five.

5. How is quantitative data collected?

Now we know what quantitative data is, we can start to think about how analysts actually work with it in the real world. Before the data can be analyzed, it first needs to be generated or collected. So how is this done?

Researchers (for example, psychologists or scientists) will often conduct experiments and studies in order to gather quantitative data and test certain hypotheses. A psychologist investigating the relationship between social media usage and self-esteem might devise a questionnaire with various scales—for example, asking participants to rate, on a scale of one to five, the extent to which they agree with certain statements.

If the survey reaches enough people, the psychologist ends up with a large sample of quantitative data (for example, an overall self-esteem score for each participant) which they can then analyze.

Data analysts and data scientists are less likely to conduct experiments, but they may send out questionnaires and surveys—it all depends on the sector they’re working in. Usually, data professionals will work with “naturally occurring” quantitative data, such as the number of sales per quarter, or how often a customer uses a particular service.

Some common methods of data collection include:

• Analytics tools, such as Google Analytics
• Probability sampling

Questionnaires and surveys

• Open-source datasets on the web

Analytics tools

Data analysts and data scientists rely on specialist tools to gather quantitative data from various sources. Google Analytics, for example, will gather data pertaining to your website; at a glance, you can see metrics such as how much traffic you got in one week, how many page views per minute, and average session length—all useful insights if you want to optimize the performance of your site.

Aside from Google Analytics, which tends to be used within the marketing sector, there are loads of tools out there which can be connected to multiple data sources at once. Tools like RapidMiner, Knime, Qlik, and Splunk can be integrated with internal databases, data lakes, cloud storage, business apps, social media, and IoT devices, allowing you to access data from multiple sources all in one place.

You can learn more about the top tools used by data analysts in this guide

Sampling is when, instead of analyzing an entire dataset, you select a sample or “section” of the data. Sampling may be used to save time and money, and in cases where it’s simply not possible to study an entire population. For example, if you wanted to analyze data pertaining to the residents of New York, it’s unlikely that you’d be able to get hold of data for every single person in the state. Instead, you’d analyze a representative sample.

There are two types of sampling: Random probability sampling, where each unit within the overall dataset has the same chance of being selected (i.e. included in the sample), and non-probability sampling, where the sample is actively selected by the researcher or analyst—not at random. Data analysts and scientists may use Python (the popular programming language) and various algorithms to extract samples from large datasets.

Another way to collect quantitative data is through questionnaires and surveys. Nowadays, it’s easy to create a survey and distribute it online—with tools like Typeform , SurveyMonkey , and Qualtrics , practically anyone can collect quantitative data. Surveys are a useful tool for gathering customer or user feedback, and generally finding out how people feel about certain products or services.

To make sure you gather quantitative data from your surveys, it’s important that you ask respondents to quantify their feelings—for example, asking them to rate their satisfaction on a scale of one to ten.

Open-source datasets online

In addition to analyzing data from internal databases, data analysts might also collect quantitative data from external sources. Again, it all depends on the field you’re working in and what kind of data you need. The internet is full of free and open datasets spanning a range of sectors, from government, business and finance, to science, transport, film, and entertainment—pretty much anything you can think of! We’ve put together a list of places where you can find free datasets here .

6. How is quantitative data analyzed?

A defining characteristic of quantitative data is that it’s suitable for statistical analysis. There are many different methods and techniques used for quantitative data analysis, and how you analyze your data depends on what you hope to find out.

Before we go into some specific methods of analysis, it’s important to distinguish between descriptive and inferential analysis .

What’s the difference between descriptive and inferential analysis of quantitative data?

Descriptive analysis does exactly what it says on the tin; it describes the data. This is useful as it allows you to see, at a glance, what the basic qualities of your data are and what you’re working with. Some commonly used descriptive statistics include the range (the difference between the highest and lowest scores), the minimum and maximum (the lowest and highest scores in a dataset), and frequency (how often a certain value appears in the dataset).

You might also calculate various measures of central tendency in order to gauge the general trend of your data. Measures of central tendency include the mean (the sum of all values divided by the number of values, otherwise known as the average), the median (the middle score when all scores are ordered numerically), and the mode (the most frequently occurring score). Another useful calculation is standard deviation . This tells you how representative of the entire dataset the mean value actually is.

While descriptive statistics give you an initial read on your quantitative data, they don’t allow you to draw definitive conclusions. That’s where inferential analysis comes in. With inferential statistics, you can make inferences and predictions. This allows you to test various hypotheses and to predict future outcomes based on probability theory.

Quantitative data analysis methods

When it comes to deriving insights from your quantitative data, there’s a whole host of techniques at your disposal. Some of the most common (and useful) methods of quantitative data analysis include:

• Regression analysis: This is used to estimate the relationship between a set of variables, and to see if there’s any kind of correlation between the two. Regression is especially useful for making predictions and forecasting future trends.
• Monte Carlo simulation : The Monte Carlo method is a computerized technique used to generate models of possible outcomes and their probability distributions based on your dataset. It essentially considers a range of possible outcomes and then calculates how likely it is that each particular outcome will occur. It’s used by data analysts to conduct advanced risk analysis, allowing them to accurately predict what might happen in the future.
• Cohort analysis: A cohort is a group of people who share a common attribute or behavior during a given time period—for example, a cohort of students who all started university in 2020, or a cohort of customers who purchased via your app in the month of February. Cohort analysis essentially divides your dataset into cohorts and analyzes how these cohorts behave over time. This is especially useful for identifying patterns in customer behavior and tailoring your products and services accordingly.
• Cluster analysis : This is an exploratory technique used to identify structures within a dataset. The aim of cluster analysis is to sort different data points into groups that are internally homogenous and externally heterogeneous—in other words, data points within a cluster are similar to each other, but dissimilar to data points in other clusters. Clustering is used to see how data is distributed in a given dataset, or as a preprocessing step for other algorithms.
• Time series analysis : This is used to identify trends and cycles over time. Time series data is a sequence of data points which measure the same variable at different points in time, such as weekly sales figures or monthly email sign-ups. By looking at time-related trends, analysts can forecast how the variable of interest may fluctuate in the future. Extremely handy when it comes to making business decisions!

Above is just a very brief introduction to how you might analyze your quantitative data. For a more in-depth look, check out this comprehensive guide to some of the most useful data analysis techniques .

7. What are the advantages and disadvantages of quantitative data?

As with anything, there are both advantages and disadvantages of using quantitative data. So what are they? Let’s take a look.

Advantages of quantitative data

The main advantages of working with quantitative data are as follows:

• Quantitative data is relatively quick and easy to collect , allowing you to gather a large sample size. And, the larger your sample size, the more accurate your conclusions are likely to be.
• Quantitative data is less susceptible to bias. The use of random sampling helps to ensure that a given dataset is as representative as possible, and protects the sample from bias. This is crucial for drawing reliable conclusions.
• Quantitative data is analyzed objectively. Because quantitative data is suitable for statistical analysis, it can be analyzed according to mathematical rules and principles. This greatly reduces the impact of analyst or researcher bias on how the results are interpreted.

Disadvantages of quantitative data

There are two main drawbacks to be aware of when working with quantitative data, especially within a research context:

• Quantitative data can lack context. In some cases, context is key; for example, if you’re conducting a questionnaire to find out how customers feel about a new product. The quantitative data may tell you that 60% of customers are unhappy with the product, but that figure alone will not tell you why. Sometimes, you’ll need to delve deeper to gain valuable insights beyond the numbers.
• There is a risk of bias when using surveys and questionnaires. Again, this point relates more to a research context, but it’s important to bear in mind when creating surveys and questionnaires. The way in which questions are worded can allow researcher bias to seep in, so it’s important to make sure that surveys are devised carefully. You can learn all about how to reduce survey bias in this post .

8. Should I use quantitative or qualitative data in my research?

Okay—so now we know what the difference between quantitative and qualitative data is, as well as other aspects of quantitative data. But when should you make use of quantitative or qualitative research? This answer to this question will depend on the type of project you’re working on—or client you’re working for—specifically. But use these simple criteria as a guide:

• When to use quantitative research: when you want to confirm or test something, like a theory or hypothesis. When the data can be shown clearly in numbers. Think of a city census that shows the whole number of people living there, as well as their ages, incomes, and other useful information that makes up a city’s demographic.
• When to use qualitative research: when you want to understand something—for example, a concept, experience, or opinions. Maybe you’re testing out a run of experiences for your company, and need to gather reviews for a specific time period. This would be an example of qualitative research.
• When to use both quantitative and qualitative research: when you’re taking on a research project that demands both numerical and non-numerical data.

9. What are some common quantitative analysis tools?

The tools used for quantitative data collection and analysis should come as no surprise to the budding data analyst. You may end up using one tool per project, or a combination of tools:

• Microsoft Power BI

10. What is quantitative data? FAQs

Who uses quantitative data.

Quantitative data is used in many fields—not just data analytics (though, you could argue that all of these fields are at least data-analytics-adjacent)! Those working in the fields of economics, epidemiology, psychology, sociology, and health—to name a few—would make great use of quantitative data in their work. You would be less likely to see quantitative data being used in fields such as anthropology and history.

Is quantitative data better than qualitative data?

It would be hard to make a solid argument of which form of data collection is “better”, as it really depends on the type of project you’re working on. However, quantitative research provides more “hard and fast” information that can be used to make informed, objective decisions.

Where is quantitative data used?

Quantitative data is used when a problem needs to be quantified. That is, to answer the questions that start with “how many…” or “how often…”, for example.

What is quantitative data in statistics?

As statistics is an umbrella term of a discipline concerning the collection, organization and analysis of data, it’s only natural that quantitative data falls under that umbrella—the practice of counting and measuring data sets according to a research question or set of research needs.

Can quantitative data be ordinal?

Ordinal data is a type of statistical data where the variables are sorted into ranges, and the distance between the ranges are not known. Think of the pain scale they sometimes use in the hospital, where you judge the level of pain you have on a scale of 1-10, with 1 being low and 10 being the highest. However, you can’t really quantify the difference between 1-10—it’s a matter of how you feel!

By that logic, ordinal data falls under qualitative data, not quantitative. You can learn more about the data levels of measurement in this post .

Is quantitative data objective?

Due to the nature of how quantitative data is produced—that is, using methods that are verifiable and replicable—it is objective.

11. Key takeaways and further reading

In this post, we answered the question: what is quantitative data? We looked at how it differs from qualitative data, and how it’s collected and analyzed. To recap what we’ve learned:

• Quantitative data is data that can be quantified. It can be counted or measured, and given a numerical value.
• Quantitative data lends itself to statistical analysis, while qualitative data is grouped according to themes.
• Quantitative data can be discrete or continuous. Discrete data takes on fixed values (e.g. a person has three children), while continuous data can be infinitely broken down into smaller parts.
• Quantitative data has several advantages: It is relatively quick and easy to collect, and it is analyzed subjectively.

Collecting and analyzing quantitative data is just one aspect of the data analyst’s work. To learn more about what it’s like to work as a data analyst, check out the following guides. And, if you’d like to dabble in some analytics yourself, why not try our free five-day introductory short course ?

• What is data analytics? A beginner’s guide
• A step-by-step guide to the data analysis process
• Where could a career in data analytics take you?

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7.1 Reading results in quantitative research

Learning objectives.

Learners will be able to…

• Describe how statistical significance and confidence intervals demonstrate which results are most important

Pre-awareness check (Knowledge)

What do you know about previously conducted research on your topic (e.g., statistical analyses, qualitative and quantitative results)?

If you recall, empirical journal articles are those that report the results of quantitative or qualitative data analyzed by the author. They follow a set structure—introduction, methods, results, discussion/conclusions. This chapter is about reading what is often the most challenging section: results.

Quantitative results

Quantitative articles often contain tables, and scanning them is a good way to begin reading the results. A table usually provides a quick, condensed summary of the report’s key findings. Tables are a concise way to report large amounts of data. Some tables present descriptive information about a researcher’s sample (often the first table in a results section). These tables will likely contain frequencies ( n ) and percentages (%). For example, if gender happened to be an important variable for the researcher’s analysis, a descriptive table would show how many and what percent of all study participants are of a particular gender. Frequencies or “how many” will probably be listed as n , while the percent symbol (%) might be used to indicate percentages. The symbol N is used for the entire sample size, and  n is used for the size of a portion of the entire sample.

In a table presenting a causal relationship, two sets of variables are represented. The independent variable , or cause, and the dependent variable , the effect. We’ll go into more detail on variables in Chapter 8. Independent variable attributes are typically presented in the table’s columns, while dependent variable attributes are presented in rows. This allows the reader to scan a table’s rows to see how values on the dependent variable change as the independent variable values change. Tables displaying results of quantitative analysis will also likely include some information about which relationships are significant or not. We will discuss the details of significance and p -values later in this section.

Let’s look at a specific example: Table 7.1 below.

Table 7.1 presents the association between gender and experiencing harassing behaviors at work. In this example, gender is the independent variable (the predictor) and the harassing behaviors listed are the dependent variables (the outcome). [1] Therefore, we place gender in the table’s columns and harassing behaviors in the table’s rows.

Reading across the table’s top row, we see that 2.9% of women in the sample reported experiencing subtle or obvious threats to their safety at work, while 4.7% of men in the sample reported the same. We can read across each of the rows of the table in this way. Reading across the bottom row, we see that 9.4% of women in the sample reported experiencing staring or invasion of their personal space at work while just 2.3% of men in the sample reported having the same experience. We’ll discuss  p- values later in this section.

While you can certainly scan tables for key results, they are often difficult to understand without reading the text of the article. The article and table were meant to complement each other, and the text should provide information on how the authors interpret their findings. The table is not redundant with the text of the results section. Additionally, the first table in most results sections is a summary of the study’s sample, which provides more background information on the study than information about hypotheses and findings. It is also a good idea to look back at the methods section of the article as the data analysis plan the authors outline should walk you through the steps they took to analyze their data which will inform how they report them in the results section.

Statistical significance

The statistics reported in Table 7.1 represent what the researchers found in their sample. The purpose of statistical analysis is usually to generalize from a the small number of people in a study’s sample to a larger population of people. Thus, the researchers intend to make causal arguments about harassing behaviors at workplaces beyond those covered in the sample.

Generalizing is key to understanding statistical significance . According to Cassidy et al. (2019), [2] 89% of research methods textbooks in psychology define statistical significance incorrectly. This includes an early draft of this textbook which defined statistical significance as “the likelihood that the relationships we observe could be caused by something other than chance.” If you have previously had a research methods class, this might sound familiar to you. It certainly did to me!

But statistical significance is less about “random chance” than more about the null hypothesis . Basically, at the beginning of a study a researcher develops a hypothesis about what they expect to find, usually that there is a statistical relationship between two or more variables . The null hypothesis is the opposite. It is the hypothesis that there is no relationship between the variables in a research study. Researchers then can hopefully reject the null hypothesis because they find a relationship between the variables.

For example, in Table 7.1 researchers were examining whether gender impacts harassment. Of course, researchers assumed that women were more likely to experience harassment than men. The null hypothesis, then, would be that gender has no impact on harassment. Once we conduct the study, our results will hopefully lead us to reject the null hypothesis because we find that gender impacts harassment. We would then generalize from our study’s sample to the larger population of people in the workplace.

Statistical significance is calculated using a p -value which is obtained by comparing the statistical results with a hypothetical set of results if the researchers re-ran their study a large number of times. Keeping with our example, imagine we re-ran our study with different men and women from different workplaces hundreds and hundred of times and we assume that the null hypothesis is true that gender has no impact on harassment. If results like ours come up pretty often when the null hypothesis is true, our results probably don’t mean much. “The smaller the p -value, the greater the statistical incompatibility with the null hypothesis” (Wasserstein & Lazar, 2016, p. 131). [3] Generally, researchers in the social sciences have set alpha at .05 for the value at which a result is significant ( p is less than or equal to .05) or not significant ( p is greater than .05). The p -value .05 refers to if less than 5% of those hypothetical results from re-running our study show the same or more extreme relationships when the null hypothesis is true. Researchers, however, may choose a stricter standard such as .01 in which 1% or less of those hypothetical results are more extreme or a more lenient standard like .1 in which 10% or less of those hypothetical results are more extreme than what was found in the study.

Let’s look back at Table 7.1. Which one of the relationships between gender and harassing behaviors is statistically significant? It’s the last one in the table, “staring or invasion of personal space,” whose p -value is .039 (under the p<.05 standard to establish statistical significance). Again, this indicates that if we re-ran our study over and over again and gender did not  impact staring/invasion of space (i.e., the null hypothesis was true), only 3.9% of the time would we find similar or more extreme differences between men and women than what we observed in our study. Thus, we conclude that for staring or invasion of space only , there is a statistically significant relationship.

For contrast, let’s look at “being pushed, hit, or grabbed” and run through the same analysis to see if it is statistically significant. If we re-ran our study over and over again and the null hypothesis was true, 48% of the time ( p =.48) we would find similar or more extreme differences between men and women. That means these results are not statistically significant.

This discussion should also highlight a point we discussed previously: that it is important to read the full results section, rather than simply relying on the summary in the abstract. If the abstract stated that most tests revealed no statistically significant relationships between gender and harassment, you would have missed the detail on which behaviors were and were not associated with gender. Read the full results section! And don’t be afraid to ask for help from a professor in understanding what you are reading, as results sections are often not written to be easily understood.

Statistical significance and p -values have been critiqued recently for a number of reasons, including that they are misused and misinterpreted (Wasserstein & Lazar, 2016) [4] , that researchers deliberately manipulate their analyses to have significant results (Head et al., 2015) [5] , and factor into the difficulty scientists have today in reproducing many of the results of previous social science studies (Peng, 2015). [6] For this reason, we share these principles, adapted from those put forth by the American Statistical Association, [7]  for understanding and using p -values in social science:

• p -values provide evidence against a null hypothesis.
• p -values do not indicate whether the results were produced by random chance alone or if the researcher’s hypothesis is true, though both are common misconceptions.
• Statistical significance can be detected in minuscule differences that have very little effect on the real world.
• Nuance is needed to interpret scientific findings, as a conclusion does not become true or false when the p -value passes from p =.051 to p =.049.
• Real-world decision-making must use more than reported p -values. It’s easy to run analyses of large datasets and only report the significant findings.
• Greater confidence can be placed in studies that pre-register their hypotheses and share their data and methods openly with the public.
• “By itself, a p -value does not provide a good measure of evidence regarding a model or hypothesis. For example, a p -value near .05 taken by itself offers only weak evidence against the null hypothesis. Likewise, a relatively large p -value does not imply evidence in favor of the null hypothesis; many other hypotheses may be equally or more consistent with the observed data” (Wasserstein & Lazar, 2016, p. 132).

Confidence intervals

Because of the limitations of p -values, scientists can use other methods to determine whether their models of the world are true. One common approach is to use a confidence interval , or a range of values in which the true value is likely to be found. Confidence intervals are helpful because, as principal #5 above points out, p -values do not measure the size of an effect (Greenland et al., 2016). [8] Remember, something that has very little impact on the world can be statistically significant, and the values in a confidence interval would be helpful. In our example from Table 7.1, imagine our analysis produced a confidence interval that women are 1.2-3.4 times more likely to experience “staring or invasion of personal space” than men. As with p -values, calculation for a confidence interval compares what was found in one study with a hypothetical set of results if we repeated the study over and over again. If we calculated 95% confidence intervals for all of the hypothetical set of hundreds and hundreds of studies, that would be our confidence interval. 

Confidence intervals are pretty intuitive. As of this writing, my wife and are expecting our second child. The doctor told us our due date was December 11th. But the doctor also told us that December 11th was only their best estimate. They were actually 95% sure our baby might be born any time in the 30-day period between November 27th and December 25th. Confidence intervals are often listed with a percentage, like 90% or 95%, and a range of values, such as between November 27th and December 25th. You can read that as: “we are 95% sure your baby will be born between November 27th and December 25th because we’ve studied hundreds of thousands of fetuses and mothers, and we’re 95% sure your baby will be within these two dates.”

Notice that we’re hedging our bets here by using words like “best estimate.” When testing hypotheses, social scientists generally phrase their findings in a tentative way, talking about what results “indicate” or “support,” rather than making bold statements about what their results “prove.” Social scientists have humility because they understand the limitations of their knowledge. In a literature review, using a single study or fact to “prove” an argument right or wrong is often a signal to the person reading your literature review (usually your professor) that you may not have appreciated the limitations of that study or its place in the broader literature on the topic. Strong arguments in a literature review include multiple facts and ideas that span across multiple studies.

You can learn more about creating tables, reading tables, and tests of statistical significance in a class focused exclusively on statistical analysis. We provide links to many free and openly licensed resources on statistics in Chapter 16. For now, we hope this brief introduction to reading tables will improve your confidence in reading and understanding the results sections in quantitative empirical articles.

Key Takeaways

• The results section of empirical articles are often the most difficult to understand.
• To understand a quantitative results section, look for results that were statistically significant and examine the confidence interval, if provided.

Post-awareness check (Emotional)

On a scale of 1-10 (10 being excellent), how would you rate your confidence level in your ability to understand a quantitative results section in empirical articles on your topic of interest?

TRACK 1 (IF YOU ARE CREATING A RESEARCH PROPOSAL FOR THIS CLASS)

Select a quantitative empirical article related to your topic.

• Write down the results the authors identify as statistically significant in the results section.
• How do the authors interpret their results in the discussion section?
• Do the authors provide enough information in the introduction for you to understand their results?

TRACK 2 (IF YOU  AREN’T CREATING A RESEARCH PROPOSAL FOR THIS CLASS)

You are interested in researching the effects of race-based stress and burnout among social workers.

Select a quantitative empirical article related to this topic.

• It wouldn’t make any sense to say that people’s workplace experiences predict their gender, so in this example, the question of which is the independent variable and which are the dependent variables has a pretty obvious answer. ↵
• Cassidy, S. A., Dimova, R., Giguère, B., Spence, J. R., & Stanley, D. J. (2019). Failing grade: 89% of introduction-to-psychology textbooks that define or explain statistical significance do so incorrectly. Advances in Methods and Practices in Psychological Science ,  2 (3), 233-239. ↵
• Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p -values: context, process, and purpose. The American Statistician, 70 , p. 129-133. ↵
• Head, M. L., Holman, L., Lanfear, R., Kahn, A. T., & Jennions, M. D. (2015). The extent and consequences of p-hacking in science. PLoS biology, 13 (3). ↵
• Peng, R. (2015), The reproducibility crisis in science: A statistical counterattack. Significance , 12 , 30–32. ↵
• Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations.  European journal of epidemiology ,  31 (4), 337-350. ↵

report the results of a quantitative or qualitative data analysis conducted by the author

a quick, condensed summary of the report’s key findings arranged by row and column

causes a change in the dependent variable

a variable that depends on changes in the independent variable

(as in generalization) to make claims about a large population based on a smaller sample of people or items

"Assuming that the null hypothesis is true and the study is repeated an infinite number times by drawing random samples from the same populations(s), less than 5% of these results will be more extreme than the current result" (Cassidy et al., 2019, p. 233).

the assumption that no relationship exists between the variables in question

“a logical grouping of attributes that can be observed and measured and is expected to vary from person to person in a population” (Gillespie & Wagner, 2018, p. 9)

summarizes the incompatibility between a particular set of data and a proposed model for the data, usually the null hypothesis. The lower the p-value, the more inconsistent the data are with the null hypothesis, indicating that the relationship is statistically significant.

a range of values in which the true value is likely to be, to provide a more accurate description of their data

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A Practical Guide to Writing Quantitative and Qualitative Research Questions and Hypotheses in Scholarly Articles

Edward barroga.

1 Department of General Education, Graduate School of Nursing Science, St. Luke’s International University, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

The development of research questions and the subsequent hypotheses are prerequisites to defining the main research purpose and specific objectives of a study. Consequently, these objectives determine the study design and research outcome. The development of research questions is a process based on knowledge of current trends, cutting-edge studies, and technological advances in the research field. Excellent research questions are focused and require a comprehensive literature search and in-depth understanding of the problem being investigated. Initially, research questions may be written as descriptive questions which could be developed into inferential questions. These questions must be specific and concise to provide a clear foundation for developing hypotheses. Hypotheses are more formal predictions about the research outcomes. These specify the possible results that may or may not be expected regarding the relationship between groups. Thus, research questions and hypotheses clarify the main purpose and specific objectives of the study, which in turn dictate the design of the study, its direction, and outcome. Studies developed from good research questions and hypotheses will have trustworthy outcomes with wide-ranging social and health implications.

INTRODUCTION

Scientific research is usually initiated by posing evidenced-based research questions which are then explicitly restated as hypotheses. 1 , 2 The hypotheses provide directions to guide the study, solutions, explanations, and expected results. 3 , 4 Both research questions and hypotheses are essentially formulated based on conventional theories and real-world processes, which allow the inception of novel studies and the ethical testing of ideas. 5 , 6

It is crucial to have knowledge of both quantitative and qualitative research 2 as both types of research involve writing research questions and hypotheses. 7 However, these crucial elements of research are sometimes overlooked; if not overlooked, then framed without the forethought and meticulous attention it needs. Planning and careful consideration are needed when developing quantitative or qualitative research, particularly when conceptualizing research questions and hypotheses. 4

There is a continuing need to support researchers in the creation of innovative research questions and hypotheses, as well as for journal articles that carefully review these elements. 1 When research questions and hypotheses are not carefully thought of, unethical studies and poor outcomes usually ensue. Carefully formulated research questions and hypotheses define well-founded objectives, which in turn determine the appropriate design, course, and outcome of the study. This article then aims to discuss in detail the various aspects of crafting research questions and hypotheses, with the goal of guiding researchers as they develop their own. Examples from the authors and peer-reviewed scientific articles in the healthcare field are provided to illustrate key points.

DEFINITIONS AND RELATIONSHIP OF RESEARCH QUESTIONS AND HYPOTHESES

A research question is what a study aims to answer after data analysis and interpretation. The answer is written in length in the discussion section of the paper. Thus, the research question gives a preview of the different parts and variables of the study meant to address the problem posed in the research question. 1 An excellent research question clarifies the research writing while facilitating understanding of the research topic, objective, scope, and limitations of the study. 5

On the other hand, a research hypothesis is an educated statement of an expected outcome. This statement is based on background research and current knowledge. 8 , 9 The research hypothesis makes a specific prediction about a new phenomenon 10 or a formal statement on the expected relationship between an independent variable and a dependent variable. 3 , 11 It provides a tentative answer to the research question to be tested or explored. 4

Hypotheses employ reasoning to predict a theory-based outcome. 10 These can also be developed from theories by focusing on components of theories that have not yet been observed. 10 The validity of hypotheses is often based on the testability of the prediction made in a reproducible experiment. 8

Conversely, hypotheses can also be rephrased as research questions. Several hypotheses based on existing theories and knowledge may be needed to answer a research question. Developing ethical research questions and hypotheses creates a research design that has logical relationships among variables. These relationships serve as a solid foundation for the conduct of the study. 4 , 11 Haphazardly constructed research questions can result in poorly formulated hypotheses and improper study designs, leading to unreliable results. Thus, the formulations of relevant research questions and verifiable hypotheses are crucial when beginning research. 12

CHARACTERISTICS OF GOOD RESEARCH QUESTIONS AND HYPOTHESES

Excellent research questions are specific and focused. These integrate collective data and observations to confirm or refute the subsequent hypotheses. Well-constructed hypotheses are based on previous reports and verify the research context. These are realistic, in-depth, sufficiently complex, and reproducible. More importantly, these hypotheses can be addressed and tested. 13

There are several characteristics of well-developed hypotheses. Good hypotheses are 1) empirically testable 7 , 10 , 11 , 13 ; 2) backed by preliminary evidence 9 ; 3) testable by ethical research 7 , 9 ; 4) based on original ideas 9 ; 5) have evidenced-based logical reasoning 10 ; and 6) can be predicted. 11 Good hypotheses can infer ethical and positive implications, indicating the presence of a relationship or effect relevant to the research theme. 7 , 11 These are initially developed from a general theory and branch into specific hypotheses by deductive reasoning. In the absence of a theory to base the hypotheses, inductive reasoning based on specific observations or findings form more general hypotheses. 10

TYPES OF RESEARCH QUESTIONS AND HYPOTHESES

Research questions and hypotheses are developed according to the type of research, which can be broadly classified into quantitative and qualitative research. We provide a summary of the types of research questions and hypotheses under quantitative and qualitative research categories in Table 1 .

Research questions in quantitative research

In quantitative research, research questions inquire about the relationships among variables being investigated and are usually framed at the start of the study. These are precise and typically linked to the subject population, dependent and independent variables, and research design. 1 Research questions may also attempt to describe the behavior of a population in relation to one or more variables, or describe the characteristics of variables to be measured ( descriptive research questions ). 1 , 5 , 14 These questions may also aim to discover differences between groups within the context of an outcome variable ( comparative research questions ), 1 , 5 , 14 or elucidate trends and interactions among variables ( relationship research questions ). 1 , 5 We provide examples of descriptive, comparative, and relationship research questions in quantitative research in Table 2 .

Hypotheses in quantitative research

In quantitative research, hypotheses predict the expected relationships among variables. 15 Relationships among variables that can be predicted include 1) between a single dependent variable and a single independent variable ( simple hypothesis ) or 2) between two or more independent and dependent variables ( complex hypothesis ). 4 , 11 Hypotheses may also specify the expected direction to be followed and imply an intellectual commitment to a particular outcome ( directional hypothesis ) 4 . On the other hand, hypotheses may not predict the exact direction and are used in the absence of a theory, or when findings contradict previous studies ( non-directional hypothesis ). 4 In addition, hypotheses can 1) define interdependency between variables ( associative hypothesis ), 4 2) propose an effect on the dependent variable from manipulation of the independent variable ( causal hypothesis ), 4 3) state a negative relationship between two variables ( null hypothesis ), 4 , 11 , 15 4) replace the working hypothesis if rejected ( alternative hypothesis ), 15 explain the relationship of phenomena to possibly generate a theory ( working hypothesis ), 11 5) involve quantifiable variables that can be tested statistically ( statistical hypothesis ), 11 6) or express a relationship whose interlinks can be verified logically ( logical hypothesis ). 11 We provide examples of simple, complex, directional, non-directional, associative, causal, null, alternative, working, statistical, and logical hypotheses in quantitative research, as well as the definition of quantitative hypothesis-testing research in Table 3 .

Research questions in qualitative research

Unlike research questions in quantitative research, research questions in qualitative research are usually continuously reviewed and reformulated. The central question and associated subquestions are stated more than the hypotheses. 15 The central question broadly explores a complex set of factors surrounding the central phenomenon, aiming to present the varied perspectives of participants. 15

There are varied goals for which qualitative research questions are developed. These questions can function in several ways, such as to 1) identify and describe existing conditions ( contextual research question s); 2) describe a phenomenon ( descriptive research questions ); 3) assess the effectiveness of existing methods, protocols, theories, or procedures ( evaluation research questions ); 4) examine a phenomenon or analyze the reasons or relationships between subjects or phenomena ( explanatory research questions ); or 5) focus on unknown aspects of a particular topic ( exploratory research questions ). 5 In addition, some qualitative research questions provide new ideas for the development of theories and actions ( generative research questions ) or advance specific ideologies of a position ( ideological research questions ). 1 Other qualitative research questions may build on a body of existing literature and become working guidelines ( ethnographic research questions ). Research questions may also be broadly stated without specific reference to the existing literature or a typology of questions ( phenomenological research questions ), may be directed towards generating a theory of some process ( grounded theory questions ), or may address a description of the case and the emerging themes ( qualitative case study questions ). 15 We provide examples of contextual, descriptive, evaluation, explanatory, exploratory, generative, ideological, ethnographic, phenomenological, grounded theory, and qualitative case study research questions in qualitative research in Table 4 , and the definition of qualitative hypothesis-generating research in Table 5 .

Qualitative studies usually pose at least one central research question and several subquestions starting with How or What . These research questions use exploratory verbs such as explore or describe . These also focus on one central phenomenon of interest, and may mention the participants and research site. 15

Hypotheses in qualitative research

Hypotheses in qualitative research are stated in the form of a clear statement concerning the problem to be investigated. Unlike in quantitative research where hypotheses are usually developed to be tested, qualitative research can lead to both hypothesis-testing and hypothesis-generating outcomes. 2 When studies require both quantitative and qualitative research questions, this suggests an integrative process between both research methods wherein a single mixed-methods research question can be developed. 1

FRAMEWORKS FOR DEVELOPING RESEARCH QUESTIONS AND HYPOTHESES

Research questions followed by hypotheses should be developed before the start of the study. 1 , 12 , 14 It is crucial to develop feasible research questions on a topic that is interesting to both the researcher and the scientific community. This can be achieved by a meticulous review of previous and current studies to establish a novel topic. Specific areas are subsequently focused on to generate ethical research questions. The relevance of the research questions is evaluated in terms of clarity of the resulting data, specificity of the methodology, objectivity of the outcome, depth of the research, and impact of the study. 1 , 5 These aspects constitute the FINER criteria (i.e., Feasible, Interesting, Novel, Ethical, and Relevant). 1 Clarity and effectiveness are achieved if research questions meet the FINER criteria. In addition to the FINER criteria, Ratan et al. described focus, complexity, novelty, feasibility, and measurability for evaluating the effectiveness of research questions. 14

The PICOT and PEO frameworks are also used when developing research questions. 1 The following elements are addressed in these frameworks, PICOT: P-population/patients/problem, I-intervention or indicator being studied, C-comparison group, O-outcome of interest, and T-timeframe of the study; PEO: P-population being studied, E-exposure to preexisting conditions, and O-outcome of interest. 1 Research questions are also considered good if these meet the “FINERMAPS” framework: Feasible, Interesting, Novel, Ethical, Relevant, Manageable, Appropriate, Potential value/publishable, and Systematic. 14

As we indicated earlier, research questions and hypotheses that are not carefully formulated result in unethical studies or poor outcomes. To illustrate this, we provide some examples of ambiguous research question and hypotheses that result in unclear and weak research objectives in quantitative research ( Table 6 ) 16 and qualitative research ( Table 7 ) 17 , and how to transform these ambiguous research question(s) and hypothesis(es) into clear and good statements.

a These statements were composed for comparison and illustrative purposes only.

b These statements are direct quotes from Higashihara and Horiuchi. 16

a This statement is a direct quote from Shimoda et al. 17

The other statements were composed for comparison and illustrative purposes only.

CONSTRUCTING RESEARCH QUESTIONS AND HYPOTHESES

To construct effective research questions and hypotheses, it is very important to 1) clarify the background and 2) identify the research problem at the outset of the research, within a specific timeframe. 9 Then, 3) review or conduct preliminary research to collect all available knowledge about the possible research questions by studying theories and previous studies. 18 Afterwards, 4) construct research questions to investigate the research problem. Identify variables to be accessed from the research questions 4 and make operational definitions of constructs from the research problem and questions. Thereafter, 5) construct specific deductive or inductive predictions in the form of hypotheses. 4 Finally, 6) state the study aims . This general flow for constructing effective research questions and hypotheses prior to conducting research is shown in Fig. 1 .

Research questions are used more frequently in qualitative research than objectives or hypotheses. 3 These questions seek to discover, understand, explore or describe experiences by asking “What” or “How.” The questions are open-ended to elicit a description rather than to relate variables or compare groups. The questions are continually reviewed, reformulated, and changed during the qualitative study. 3 Research questions are also used more frequently in survey projects than hypotheses in experiments in quantitative research to compare variables and their relationships.

Hypotheses are constructed based on the variables identified and as an if-then statement, following the template, ‘If a specific action is taken, then a certain outcome is expected.’ At this stage, some ideas regarding expectations from the research to be conducted must be drawn. 18 Then, the variables to be manipulated (independent) and influenced (dependent) are defined. 4 Thereafter, the hypothesis is stated and refined, and reproducible data tailored to the hypothesis are identified, collected, and analyzed. 4 The hypotheses must be testable and specific, 18 and should describe the variables and their relationships, the specific group being studied, and the predicted research outcome. 18 Hypotheses construction involves a testable proposition to be deduced from theory, and independent and dependent variables to be separated and measured separately. 3 Therefore, good hypotheses must be based on good research questions constructed at the start of a study or trial. 12

In summary, research questions are constructed after establishing the background of the study. Hypotheses are then developed based on the research questions. Thus, it is crucial to have excellent research questions to generate superior hypotheses. In turn, these would determine the research objectives and the design of the study, and ultimately, the outcome of the research. 12 Algorithms for building research questions and hypotheses are shown in Fig. 2 for quantitative research and in Fig. 3 for qualitative research.

EXAMPLES OF RESEARCH QUESTIONS FROM PUBLISHED ARTICLES

• EXAMPLE 1. Descriptive research question (quantitative research)
• - Presents research variables to be assessed (distinct phenotypes and subphenotypes)
• “BACKGROUND: Since COVID-19 was identified, its clinical and biological heterogeneity has been recognized. Identifying COVID-19 phenotypes might help guide basic, clinical, and translational research efforts.
• RESEARCH QUESTION: Does the clinical spectrum of patients with COVID-19 contain distinct phenotypes and subphenotypes? ” 19
• EXAMPLE 2. Relationship research question (quantitative research)
• - Shows interactions between dependent variable (static postural control) and independent variable (peripheral visual field loss)
• “Background: Integration of visual, vestibular, and proprioceptive sensations contributes to postural control. People with peripheral visual field loss have serious postural instability. However, the directional specificity of postural stability and sensory reweighting caused by gradual peripheral visual field loss remain unclear.
• Research question: What are the effects of peripheral visual field loss on static postural control ?” 20
• EXAMPLE 3. Comparative research question (quantitative research)
• - Clarifies the difference among groups with an outcome variable (patients enrolled in COMPERA with moderate PH or severe PH in COPD) and another group without the outcome variable (patients with idiopathic pulmonary arterial hypertension (IPAH))
• “BACKGROUND: Pulmonary hypertension (PH) in COPD is a poorly investigated clinical condition.
• RESEARCH QUESTION: Which factors determine the outcome of PH in COPD?
• STUDY DESIGN AND METHODS: We analyzed the characteristics and outcome of patients enrolled in the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension (COMPERA) with moderate or severe PH in COPD as defined during the 6th PH World Symposium who received medical therapy for PH and compared them with patients with idiopathic pulmonary arterial hypertension (IPAH) .” 21
• EXAMPLE 4. Exploratory research question (qualitative research)
• - Explores areas that have not been fully investigated (perspectives of families and children who receive care in clinic-based child obesity treatment) to have a deeper understanding of the research problem
• “Problem: Interventions for children with obesity lead to only modest improvements in BMI and long-term outcomes, and data are limited on the perspectives of families of children with obesity in clinic-based treatment. This scoping review seeks to answer the question: What is known about the perspectives of families and children who receive care in clinic-based child obesity treatment? This review aims to explore the scope of perspectives reported by families of children with obesity who have received individualized outpatient clinic-based obesity treatment.” 22
• EXAMPLE 5. Relationship research question (quantitative research)
• - Defines interactions between dependent variable (use of ankle strategies) and independent variable (changes in muscle tone)
• “Background: To maintain an upright standing posture against external disturbances, the human body mainly employs two types of postural control strategies: “ankle strategy” and “hip strategy.” While it has been reported that the magnitude of the disturbance alters the use of postural control strategies, it has not been elucidated how the level of muscle tone, one of the crucial parameters of bodily function, determines the use of each strategy. We have previously confirmed using forward dynamics simulations of human musculoskeletal models that an increased muscle tone promotes the use of ankle strategies. The objective of the present study was to experimentally evaluate a hypothesis: an increased muscle tone promotes the use of ankle strategies. Research question: Do changes in the muscle tone affect the use of ankle strategies ?” 23

EXAMPLES OF HYPOTHESES IN PUBLISHED ARTICLES

• EXAMPLE 1. Working hypothesis (quantitative research)
• - A hypothesis that is initially accepted for further research to produce a feasible theory
• “As fever may have benefit in shortening the duration of viral illness, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response when taken during the early stages of COVID-19 illness .” 24
• “In conclusion, it is plausible to hypothesize that the antipyretic efficacy of ibuprofen may be hindering the benefits of a fever response . The difference in perceived safety of these agents in COVID-19 illness could be related to the more potent efficacy to reduce fever with ibuprofen compared to acetaminophen. Compelling data on the benefit of fever warrant further research and review to determine when to treat or withhold ibuprofen for early stage fever for COVID-19 and other related viral illnesses .” 24
• EXAMPLE 2. Exploratory hypothesis (qualitative research)
• - Explores particular areas deeper to clarify subjective experience and develop a formal hypothesis potentially testable in a future quantitative approach
• “We hypothesized that when thinking about a past experience of help-seeking, a self distancing prompt would cause increased help-seeking intentions and more favorable help-seeking outcome expectations .” 25
• “Conclusion
• Although a priori hypotheses were not supported, further research is warranted as results indicate the potential for using self-distancing approaches to increasing help-seeking among some people with depressive symptomatology.” 25
• EXAMPLE 3. Hypothesis-generating research to establish a framework for hypothesis testing (qualitative research)
• “We hypothesize that compassionate care is beneficial for patients (better outcomes), healthcare systems and payers (lower costs), and healthcare providers (lower burnout). ” 26
• Compassionomics is the branch of knowledge and scientific study of the effects of compassionate healthcare. Our main hypotheses are that compassionate healthcare is beneficial for (1) patients, by improving clinical outcomes, (2) healthcare systems and payers, by supporting financial sustainability, and (3) HCPs, by lowering burnout and promoting resilience and well-being. The purpose of this paper is to establish a scientific framework for testing the hypotheses above . If these hypotheses are confirmed through rigorous research, compassionomics will belong in the science of evidence-based medicine, with major implications for all healthcare domains.” 26
• EXAMPLE 4. Statistical hypothesis (quantitative research)
• - An assumption is made about the relationship among several population characteristics ( gender differences in sociodemographic and clinical characteristics of adults with ADHD ). Validity is tested by statistical experiment or analysis ( chi-square test, Students t-test, and logistic regression analysis)
• “Our research investigated gender differences in sociodemographic and clinical characteristics of adults with ADHD in a Japanese clinical sample. Due to unique Japanese cultural ideals and expectations of women's behavior that are in opposition to ADHD symptoms, we hypothesized that women with ADHD experience more difficulties and present more dysfunctions than men . We tested the following hypotheses: first, women with ADHD have more comorbidities than men with ADHD; second, women with ADHD experience more social hardships than men, such as having less full-time employment and being more likely to be divorced.” 27
• “Statistical Analysis
• ( text omitted ) Between-gender comparisons were made using the chi-squared test for categorical variables and Students t-test for continuous variables…( text omitted ). A logistic regression analysis was performed for employment status, marital status, and comorbidity to evaluate the independent effects of gender on these dependent variables.” 27

EXAMPLES OF HYPOTHESIS AS WRITTEN IN PUBLISHED ARTICLES IN RELATION TO OTHER PARTS

• EXAMPLE 1. Background, hypotheses, and aims are provided
• “Pregnant women need skilled care during pregnancy and childbirth, but that skilled care is often delayed in some countries …( text omitted ). The focused antenatal care (FANC) model of WHO recommends that nurses provide information or counseling to all pregnant women …( text omitted ). Job aids are visual support materials that provide the right kind of information using graphics and words in a simple and yet effective manner. When nurses are not highly trained or have many work details to attend to, these job aids can serve as a content reminder for the nurses and can be used for educating their patients (Jennings, Yebadokpo, Affo, & Agbogbe, 2010) ( text omitted ). Importantly, additional evidence is needed to confirm how job aids can further improve the quality of ANC counseling by health workers in maternal care …( text omitted )” 28
• “ This has led us to hypothesize that the quality of ANC counseling would be better if supported by job aids. Consequently, a better quality of ANC counseling is expected to produce higher levels of awareness concerning the danger signs of pregnancy and a more favorable impression of the caring behavior of nurses .” 28
• “This study aimed to examine the differences in the responses of pregnant women to a job aid-supported intervention during ANC visit in terms of 1) their understanding of the danger signs of pregnancy and 2) their impression of the caring behaviors of nurses to pregnant women in rural Tanzania.” 28
• EXAMPLE 2. Background, hypotheses, and aims are provided
• “We conducted a two-arm randomized controlled trial (RCT) to evaluate and compare changes in salivary cortisol and oxytocin levels of first-time pregnant women between experimental and control groups. The women in the experimental group touched and held an infant for 30 min (experimental intervention protocol), whereas those in the control group watched a DVD movie of an infant (control intervention protocol). The primary outcome was salivary cortisol level and the secondary outcome was salivary oxytocin level.” 29
• “ We hypothesize that at 30 min after touching and holding an infant, the salivary cortisol level will significantly decrease and the salivary oxytocin level will increase in the experimental group compared with the control group .” 29
• EXAMPLE 3. Background, aim, and hypothesis are provided
• “In countries where the maternal mortality ratio remains high, antenatal education to increase Birth Preparedness and Complication Readiness (BPCR) is considered one of the top priorities [1]. BPCR includes birth plans during the antenatal period, such as the birthplace, birth attendant, transportation, health facility for complications, expenses, and birth materials, as well as family coordination to achieve such birth plans. In Tanzania, although increasing, only about half of all pregnant women attend an antenatal clinic more than four times [4]. Moreover, the information provided during antenatal care (ANC) is insufficient. In the resource-poor settings, antenatal group education is a potential approach because of the limited time for individual counseling at antenatal clinics.” 30
• “This study aimed to evaluate an antenatal group education program among pregnant women and their families with respect to birth-preparedness and maternal and infant outcomes in rural villages of Tanzania.” 30
• “ The study hypothesis was if Tanzanian pregnant women and their families received a family-oriented antenatal group education, they would (1) have a higher level of BPCR, (2) attend antenatal clinic four or more times, (3) give birth in a health facility, (4) have less complications of women at birth, and (5) have less complications and deaths of infants than those who did not receive the education .” 30

Research questions and hypotheses are crucial components to any type of research, whether quantitative or qualitative. These questions should be developed at the very beginning of the study. Excellent research questions lead to superior hypotheses, which, like a compass, set the direction of research, and can often determine the successful conduct of the study. Many research studies have floundered because the development of research questions and subsequent hypotheses was not given the thought and meticulous attention needed. The development of research questions and hypotheses is an iterative process based on extensive knowledge of the literature and insightful grasp of the knowledge gap. Focused, concise, and specific research questions provide a strong foundation for constructing hypotheses which serve as formal predictions about the research outcomes. Research questions and hypotheses are crucial elements of research that should not be overlooked. They should be carefully thought of and constructed when planning research. This avoids unethical studies and poor outcomes by defining well-founded objectives that determine the design, course, and outcome of the study.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Barroga E, Matanguihan GJ.
• Methodology: Barroga E, Matanguihan GJ.
• Writing - original draft: Barroga E, Matanguihan GJ.
• Writing - review & editing: Barroga E, Matanguihan GJ.

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A Comprehensive Guide to Quantitative Research: Types, Characteristics, Methods & Examples

Step into the fascinating world of quantitative research, where numbers reveal extraordinary insights!

By gathering and studying data in a systematic way, quantitative research empowers us to understand our ever-changing world better. It helps understand a problem or an already-formed hypothesis by generating numerical data. The results don’t end here, as you can process these numbers to get actionable insights that aid decision-making.

You can use quantitative research to quantify opinions, behaviors, attitudes, and other definitive variables related to the market, customers, competitors, etc. The research is conducted on a larger sample population to draw predictive, average, and pattern-based insights.

Here, we delve into the intricacies of this research methodology, exploring various quantitative methods, their advantages, and real-life examples that showcase their impact and relevance.

Ready to embark on a journey of discovery and knowledge? Let’s go!

What Is Quantitative Research?

Quantitative research is a method that uses numbers and statistics to test theories about customer attitudes and behaviors. It helps researchers gather and analyze data systematically to gain valuable insights and draw evidence-based conclusions about customer preferences and trends.

Researchers use online surveys , questionnaires , polls , and quizzes to question a large number of people to obtain measurable and bias-free data.

In technical terms, quantitative research is mainly concerned with discovering facts about social phenomena while assuming a fixed and measurable reality.

Offering numbers and stats-based insights, this research methodology is a crucial part of primary research and helps understand how well an organizational decision is going to work out.

Let’s consider an example.

Suppose your qualitative analysis shows that your customers are looking for social media-based customer support . In that case, quantitative analysis will help you see how many of your customers are looking for this support.

If 10% of your customers are looking for such a service, you might or might not consider offering this feature. But, if 40% of your regular customers are seeking support via social media, then it is something you just cannot overlook.

Characteristics of Quantitative Research

Quantitative research clarifies the fuzziness of research data from qualitative research analysis. With numerical insights, you can formulate a better and more profitable business decision.

Hence, quantitative research is more readily contestable, sharpens intelligent discussion, helps you see the rival hypotheses, and dynamically contributes to the research process.

Let us have a quick look at some of its characteristics.

• Measurable Variables

The data collection methods in quantitative research are structured and contain items requiring measurable variables, such as age, number of family members, salary range, highest education, etc.

These structured data collection methods comprise polls, surveys, questionnaires, etc., and may have questions like the ones shown in the following image:

As you can see, all the variables are measurable. This ensures that the research is in-depth and provides less erroneous data for reliable, actionable insights.

• Sample Size

No matter what data analysis methods for quantitative research are being used, the sample size is kept such that it represents the target market.

As the main aim of the research methodology is to get numerical insights, the sample size should be fairly large. Depending on the survey objective and scope, it might span hundreds of thousands of people.

• Normal Population Distribution

To maintain the reliability of a quantitative research methodology, we assume that the population distribution curve is normal.

This type of population distribution curve is preferred over a non-normal distribution as the sample size is large, and the characteristics of the sample vary with its size.

This requires adhering to the random sampling principle to avoid the researcher’s bias in result interpretation. Any bias can ruin the fairness of the entire process and defeats the purpose of research.

• Well-Structured Data Representation

Data analysis in quantitative research produces highly structured results and can form well-defined graphical representations. Some common examples include tables, figures, graphs, etc., that combine large blocks of data.

This way, you can discover hidden data trends, relationships, and differences among various measurable variables. This can help researchers understand the survey data and formulate actionable insights for decision-making.

• Predictive Outcomes

Quantitative analysis of data can also be used for estimations and prediction outcomes. You can construct if-then scenarios and analyze the data for the identification of any upcoming trends or events.

However, this requires advanced analytics and involves complex mathematical computations. So, it is mostly done via quantitative research tools that come with advanced analytics capabilities.

8 Best Practices to Conduct Quantitative Research

Here are some best practices to keep in mind while conducting quantitative research:

1. Define Research Objectives

There can be many ways to collect data via quantitative research methods that are chosen as per the research objective and scope. These methods allow you to build your own observations regarding any hypotheses – unknown, entirely new, or unexplained. 

You can hypothesize a proof and build a prediction of outcomes supporting the same. You can also create a detailed stepwise plan for data collection, analysis, and testing. 

Below, we explore quantitative research methods and discuss some examples to enhance your understanding of them.

2. Keep Your Questions Simple

The surveys are meant to reach people en-masse, and that includes a wide demographic range with recipients from all walks of life. Asking simple questions will ensure that they grasp what’s being asked easily.

Read More: Proven Tips to Avoid Leading and Loaded Questions in Your Survey

3. Develop a Solid Research Design

Choose an appropriate research design that aligns with your objectives, whether it’s experimental, quasi-experimental, or correlational. You also need to pay attention to the sample size and sampling technique such that it represents the target population accurately.

4. Use Reliable & Valid Instruments

It’s crucial to select or develop measurement instruments such as questionnaires, scales, or tests that have been validated and are reliable. Before proceeding with the main study, pilot-test these instruments on a small sample to assess their effectiveness and make any necessary improvements.

5. Ensure Data Quality

Implement data collection protocols to minimize errors and bias during data gathering. Double-check data entries and cleaning procedures to eliminate any inconsistencies or missing values that may affect the accuracy of your results. For instance, you might regularly cross-verify data entries to identify and correct any discrepancies.

6. Employ Appropriate Data Analysis Techniques

Select statistical methods that match the nature of your data and research questions. Whether it’s regression analysis, t-tests, ANOVA, or other techniques, using the right approach is important for drawing meaningful conclusions. Utilize software tools like SPSS or R for data analysis to ensure the accuracy and reproducibility of your findings.

7. Interpret Results Objectively

Present your findings in a clear and unbiased manner. Avoid making unwarranted causal claims, especially in correlational studies. Instead, focus on describing the relationships and patterns observed in your data.

8. Address Ethical Considerations

Prioritize ethical considerations throughout your research process. Obtain informed consent from participants, ensuring their voluntary participation and confidentiality of data. Comply with ethical guidelines and gain approval from a governing body if necessary.

Read More: How to Find Survey Participants & Respondents

Types of Quantitative Research Methods

Quantitative research is usually conducted using two methods. They are-

• Primary quantitative research methods
• Secondary quantitative research methods

1. Primary Methods

Primary quantitative research is the most popular way of conducting market research. The differentiating factor of this method is that the researcher relies on collecting data firsthand instead of relying on data collected from previous research.

There are multiple types of primary quantitative research. They can be distinguished based on three distinctive aspects, which are:

A. Techniques & Types of Studies:

• Survey Research

Surveys are the easiest, most common, and one of the most sought-after quantitative research techniques. The main aim of a survey is to widely gather and describe the characteristics of a target population or customers. Surveys are the foremost quantitative method preferred by both small and large organizations.

They help them understand their customers, products, and other brand offerings in a proper manner.

Surveys can be conducted using various methods, such as online polls, web-based surveys, paper questionnaires, phone calls, or face-to-face interviews. Survey research allows organizations to understand customer opinions, preferences, and behavior, making it crucial for market research and decision-making.

You can watch this quick video to learn more about creating surveys.

Surveys are of two types:

• Cross-Sectional Surveys Cross-sectional surveys are used to collect data from a sample of the target population at a specific point in time. Researchers evaluate various variables simultaneously to understand the relationships and patterns within the data.
• Cross-sectional surveys are popular in retail, small and medium-sized enterprises (SMEs), and healthcare industries, where they assess customer satisfaction, market trends, and product feedback.
• Longitudinal Surveys Longitudinal surveys are conducted over an extended period, observing changes in respondent behavior and thought processes.
• Researchers gather data from the same sample multiple times, enabling them to study trends and developments over time. These surveys are valuable in fields such as medicine, applied sciences, and market trend analysis.

Surveys can be distributed via various channels. Some of the most popular ones are listed below:

• Email: Sending surveys via email is a popular and effective method. People recognize your brand, leading to a higher response rate. With ProProfs Survey Maker’s in-mail survey-filling feature, you can easily send out and collect survey responses.
• Embed on a website: Boost your response rate by embedding the survey on your website. When visitors are already engaged with your brand, they are more likely to take the survey.
• Social media: Take advantage of social media platforms to distribute your survey. People familiar with your brand are likely to respond, increasing your response numbers.
• QR codes: QR codes store your survey’s URL, and you can print or publish these codes in magazines, signs, business cards, or any object to make it easy for people to access your survey.
• SMS survey: Collect a high number of responses quickly with SMS surveys. It’s a time-effective way to reach your target audience.

Read More: 24 Different Types of Survey Methods With Examples

2. Correlational Research:

Correlational research aims to establish relationships between two or more variables.

Researchers use statistical analysis to identify patterns and trends in the data, but it does not determine causality between the variables. This method helps understand how changes in one variable may impact another.

Examples of correlational research questions include studying the relationship between stress and depression, fame and money, or classroom activities and student performance.

3. Causal-Comparative Research:

Causal-comparative research, also known as quasi-experimental research, seeks to determine cause-and-effect relationships between variables.

Researchers analyze how an independent variable influences a dependent variable, but they do not manipulate the independent variable. Instead, they observe and compare different groups to draw conclusions.

Causal-comparative research is useful in situations where it’s not ethical or feasible to conduct true experiments.

Examples of questions for this type of research include analyzing the effect of training programs on employee performance, studying the influence of customer support on client retention, investigating the impact of supply chain efficiency on cost reduction, etc.

4. Experimental Research:

Experimental research is based on testing theories to validate or disprove them. Researchers conduct experiments and manipulate variables to observe their impact on the outcomes.

This type of research is prevalent in natural and social sciences, and it is a powerful method to establish cause-and-effect relationships. By randomly assigning participants to experimental and control groups, researchers can draw more confident conclusions.

Examples of experimental research include studying the effectiveness of a new drug, the impact of teaching methods on student performance, or the outcomes of a marketing campaign.

B. Data collection methodologies

After defining research objectives, the next significant step in primary quantitative research is data collection. This involves using two main methods: sampling and conducting surveys or polls.

Sampling methods:

In quantitative research, there are two primary sampling methods: Probability and Non-probability sampling.

Probability Sampling

In probability sampling, researchers use the concept of probability to create samples from a population. This method ensures that every individual in the target audience has an equal chance of being selected for the sample.

There are four main types of probability sampling:

• Simple random sampling: Here, the elements or participants of a sample are selected randomly, and this technique is used in studies that are conducted over considerably large audiences. It works well for large target populations.
• Stratified random sampling: In this method, the entire population is divided into strata or groups, and the sample members get chosen randomly from these strata only. It is always ensured that different segregated strata do not overlap with each other.
• Cluster sampling: Here, researchers divide the population into clusters, often based on geography or demographics. Then, random clusters are selected for the sample.
• Systematic sampling: In this method, only the starting point of the sample is randomly chosen. All the other participants are chosen using a fixed interval. Researchers calculate this interval by dividing the size of the study population by the target sample size.

Non-probability Sampling

Non-probability sampling is a method where the researcher’s knowledge and experience guide the selection of samples. This approach doesn’t give all members of the target population an equal chance of being included in the sample.

There are five non-probability sampling models:

• Convenience sampling: The elements or participants are chosen on the basis of their nearness to the researcher. The people in close proximity can be studied and analyzed easily and quickly, as there is no other selection criterion involved. Researchers simply choose samples based on what is most convenient for them.
• Consecutive sampling: Similar to convenience sampling, researchers select samples one after another over a significant period. They can opt for a single participant or a group of samples to conduct quantitative research in a consecutive manner for a significant period of time. Once this is over, they can conduct the research from the start.
• Quota sampling: With quota sampling, researchers use their understanding of target traits and personalities to form groups (strata). They then choose samples from each stratum based on their own judgment.
• Snowball sampling: This method is used where the target audiences are difficult to contact and interviewed for data collection. Researchers start with a few participants and then ask them to refer others, creating a snowball effect.
• Judgmental sampling: In judgmental sampling, researchers rely solely on their experience and research skills to handpick samples that they believe will be most relevant to the study.

Read More: Data Collection Methods: Definition, Types & Examples

C. Data analysis techniques

To analyze the quantitative data accurately, you’ll need to use specific statistical methods such as:

• SWOT Analysis: This stands for Strengths, Weaknesses, Opportunities, and Threats analysis. Organizations use SWOT analysis to evaluate their performance internally and externally. It helps develop effective improvement strategies.
• Conjoint Analysis: This market research method uncovers how individuals make complex purchasing decisions. It involves considering trade-offs in their daily activities when choosing from a list of product/service options.
• Cross-tabulation: A preliminary statistical market analysis method that reveals relationships, patterns, and trends within various research study parameters.
• TURF Analysis: Short for Totally Unduplicated Reach and Frequency Analysis, this method helps analyze the reach and frequency of favorable communication sources. It provides insights into the potential of a target market.
• By using these statistical techniques and inferential statistics methods like confidence intervals and margin of error, you can draw meaningful insights from your primary quantitative research that you can use in making informed decisions.

II. Secondary Quantitative Research Methods

• Secondary quantitative research, also known as desk research, is a valuable method that uses existing data, called secondary data.
• Instead of collecting new data, researchers analyze and combine already available information to enhance their research. This approach involves gathering quantitative data from various sources such as the internet, government databases, libraries, and research reports.
• Secondary quantitative research plays a crucial role in validating data collected through primary quantitative research. It helps reinforce or challenge existing findings.

Here are five commonly used secondary quantitative research methods:

A. Data Available on the Internet:

The Internet has become a vast repository of data, making it easier for researchers to access a wealth of information. Online databases, websites, and research repositories provide valuable quantitative data for researchers to analyze and validate their primary research findings.

B. Government and Non-Government Sources:

Government agencies and non-government organizations often conduct extensive research and publish reports. These reports cover a wide range of topics, providing researchers with reliable and comprehensive data for quantitative analysis.

C. Public Libraries:

While less commonly used in the digital age, public libraries still hold valuable research reports, historical data, and publications that can contribute to quantitative research.

D. Educational Institutions:

Educational institutions frequently conduct research on various subjects. Their research reports and publications can serve as valuable sources of information for researchers, validating and supporting primary quantitative research outcomes.

E. Commercial Information Sources:

Commercial sources such as local newspapers, journals, magazines, and media outlets often publish relevant data on economic trends, market research, and demographic analyses. Researchers can access this data to supplement their own findings and draw better conclusions.

Advantages of Quantitative Research Methods

Quantitative research data is often standardized and can be easily used to generalize findings for making crucial business decisions and uncover insights to supplement the qualitative research findings.

Here are some core benefits this research methodology offers.

Direct Result Comparison

As the studies can be replicated for different cultural settings and different times, even with different groups of participants, they tend to be extremely useful. Researchers can compare the results of different studies in a statistical manner and arrive at comprehensive conclusions for a broader understanding.

Replication

Researchers can repeat the study by using standardized data collection protocols over well-structured data sets. They can also apply tangible definitions of abstract concepts to arrive at different conclusions for similar research objectives with minor variations.

Large Samples

As the research data comes from large samples, the researchers can process and analyze the data via highly reliable and consistent analysis procedures. They can arrive at well-defined conclusions that can be used to make the primary research more thorough and reliable.

Hypothesis Testing

This research methodology follows standardized and established hypothesis testing procedures. So, you have to be careful while reporting and analyzing your research data , and the overall quality of results gets improved.

Proven Examples of Quantitative Research Methods

Below, we discuss two excellent examples of quantitative research methods that were used by highly distinguished business and consulting organizations. Both examples show how different types of analysis can be performed with qualitative approaches and how the analysis is done once the data is collected.

1. STEP Project Global Consortium / KPMG 2019 Global Family Business survey

This research utilized quantitative methods to identify ways that kept the family businesses sustainably profitable with time.

The study also identified the ways in which the family business behavior changed with demographic changes and had “why” and “how” questions. Their qualitative research methods allowed the KPMG team to dig deeper into the mindsets and perspectives of the business owners and uncover unexpected research avenues as well.

It was a joint effort in which STEP Project Global Consortium collected 26 cases, and KPMG collected 11 cases.

The research reached the stage of data analysis in 2020, and the analysis process spanned over 4 stages.

The results, which were also the reasons why family businesses tend to lose their strength with time, were found to be:

• Family governance
• Family business legacy

2. EY Seren Teams Research 2020

This is yet another commendable example of qualitative research where the EY Seren Team digs into the unexplored depths of human behavior and how it affected their brand or service expectations.

The research was done across 200+ sources and involved in-depth virtual interviews with people in their homes, exploring their current needs and wishes. It also involved diary studies across the entire UK customer base to analyze human behavior changes and patterns.

The study also included interviews with professionals and design leaders from a wide range of industries to explore how COVID-19 transformed their industries. Finally, quantitative surveys were conducted to gain insights into the EY community after every 15 days.

The insights and results were:

• A culture of fear, daily resilience, and hopes for a better world and a better life – these were the macro trends.
• People felt massive digitization to be a resourceful yet demanding aspect as they have to adapt every day.
• Some people wished to have a new world with lots of possibilities, and some were looking for a new purpose.

Enhance Your Quantitative Research With Cutting-Edge Software

While no single research methodology can produce 100% reliable results, you can always opt for a hybrid research method by opting for the methods that are most relevant to your objective.

This understanding comes gradually as you learn how to implement the correct combination of qualitative and quantitative research methods for your research projects. For the best results, we recommend investing in smart, efficient, and scalable research tools that come with delightful reporting and advanced analytics to make every research initiative a success.

These software tools, such as ProProfs Survey Maker, come with pre-built survey templates and question libraries and allow you to create a high-converting survey in just a few minutes.

So, choose the best research partner, create the right research plan, and gather insights that drive sustainable growth for your business.

About the author

Emma David is a seasoned market research professional with 8+ years of experience. Having kick-started her journey in research, she has developed rich expertise in employee engagement, survey creation and administration, and data management. Emma believes in the power of data to shape business performance positively. She continues to help brands and businesses make strategic decisions and improve their market standing through her understanding of research methodologies.

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20 16. Reporting quantitative results

Chapter outline.

• Reporting quantitative results (8 minute read time)

Content warning: Brief discussion of violence against women.

16.1 Reporting quantitative results

Learning objectives.

Learners will be able to…

• Execute a quantitative research report using key elements for accuracy and openness

So you’ve completed your quantitative analyses and are ready to report your results. We’re going to spend some time talking about what matters in quantitative research reports, but the very first thing to understand is this: openness with your data and analyses is key. You should never hide what you did to get to a particular conclusion and, if someone wanted to and could ethically access your data, they should be able to replicate more or less exactly what you did. While your quantitative report won’t have every single step you took to get to your conclusion, it should have plenty of detail so someone can get the picture.

Below, I’m going to take you through the key elements of a quantitative research report. This overview is pretty general and conceptual, and it will be helpful for you to look at existing scholarly articles that deal with quantitative research (like ones in your literature review) to see the structure applied. Also keep in mind that your instructor may want the sections broken out slightly differently; nonetheless, the content I outline below should be in your research report.

Introduction and literature review

These are what you’re working on building with your research proposal this semester. They should be included as part of your research report so that readers have enough information to evaluate your research for themselves. What’s here should be very similar to the introduction and literature review from your research proposal, where you described the literature relevant to the study you wanted to do. With your results in hand, though, you may find that you have to add information to the literature you wrote previously to help orient the reader of the report to important topics needed to understand the results of your study.

In this section, you should explicitly lay out your study design – for instance, if it was experimental, be specific about the type of experimental design. Discuss the type of sampling that you used, if that’s applicable to your project. You should also go into a general description of your data, including the time period, any exclusions you made from the original data set and the source – i.e., did you collect it yourself or was it secondary data?  Next, talk about the specific statistical methods you used, like t- tests, Chi-square tests, or regression analyses. For descriptive statistics, you can be relatively general – you don’t need to say “I looked at means and medians,” for instance. You need to provide enough information here that someone could replicate what you did.

In this section, you should also discuss how you operationalized your variables. What did you mean when you asked about educational attainment – did you ask for a grade number, or did you ask them to pick a range that you turned into a category? This is key information for readers to understand your research. Remember when you were looking for ways to operationalize your variables? Be the kind of author who provides enough information on operationalization so people can actually understand what they did.

You’re going to run lots of different analyses to settle on what finally makes sense to get a result – positive or negative – for your study. For this section, you’re going to provide tables with descriptions of your sample, including, but not limited to, sample size, frequencies of sample characteristics like race and gender, levels of measurement, appropriate measures of central tendency, standard deviations and variances. Here you will also want to focus on the analyses you used to actually draw whatever conclusion you settled on, both descriptive and inferential (i.e., bivariate or multivariate).

The actual statistics you report depend entirely on the kind of statistical analysis you do. For instance, if you’re reporting on a logistic regression, it’s going to look a little different than reporting on an ANOVA. In the previous chapter, we provided links to open textbooks that detail how to conduct quantitative data analysis. You should look at these resources and consult with your research professor to help you determine what is expected in a report about the particular statistical method you used.

The important thing to remember here – as we mentioned above – is that you need to be totally transparent about your results, even and especially if they don’t support your hypothesis. There is value in a disproved hypothesis, too – you now know something about how the state of the world is not .

In this section, you’re going to connect your statistical results back to your hypothesis and discuss whether your results support your hypothesis or not. You are also going to talk about what the results mean for the larger field of study of which your research is a part, the implications of your findings if you’re evaluating some kind of intervention, and how your research relates to what is already out there in this field. When your research doesn’t pan out the way you expect, if you’re able to make some educated guesses as to why this might be (supported by literature if possible, but practice wisdom works too), share those as well.

Let’s take a minute to talk about what happens when your findings disprove your hypothesis or actually indicate something negative about the group you are studying. The discussion section is where you can contextualize “negative” findings. For example, say you conducted a study that indicated that a certain group is more likely to commit violent crime. Here, you have an opportunity to talk about why this might be the case outside of their membership in that group, and how membership in that group does not automatically mean someone will commit a violent crime. You can present mitigating factors, like a history of personal and community trauma. It’s extremely important to provide this relevant context so that your results are more difficult to use against a group you are studying in a way that doesn’t reflect your actual findings.

Limitations

In this section, you’re going to critique your own study. What are the advantages, disadvantages, and trade-offs of what you did to define and analyze your variables? Some questions you might consider include:  What limits the study’s applicability to the population at large? Were there trade-offs you had to make between rigor and available data? Did the statistical analyses you used mean that you could only get certain types of results? What would have made the study more widely applicable or more useful for a certain group? You should be thinking about this throughout the analysis process so you can properly contextualize your results.

In this section, you may also consider discussing any threats to internal validity that you identified and whether you think you can generalize your research. Finally, if you used any measurement tools that haven’t been validated yet, discuss how this could have affected your results.

Significance and conclusions

Finally, you want to use the conclusions section to bring it full circle for your reader – why did this research matter? Talk about how it contributed to knowledge around the topic and how might it be used to further practice. Identify and discuss ethical implications of your findings for social workers and social work research. Finally, make sure to talk about the next steps for you, other researchers, or policy-makers based on your research findings.

Key Takeaways

• Your quantitative research report should provide the reader with transparent, replicable methods and put your research into the context of existing literature, real-world practice and social work ethics.
• Think about the research project you are building now. What could a negative finding be, and how might you provide your reader with context to ensure that you are not harming your study population?

The process of determining how to measure a construct that cannot be directly observed

Ability to say that one variable "causes" something to happen to another variable. Very important to assess when thinking about studies that examine causation such as experimental or quasi-experimental designs.

Graduate research methods in social work Copyright © 2020 by Matthew DeCarlo, Cory Cummings, Kate Agnelli is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Quantitative Data Analysis: Types, Analysis & Examples

By Varun Saharawat | January 20, 2024

Analysis of Quantitative data enables you to transform raw data points, typically organised in spreadsheets, into actionable insights. Refer to the article to know more!

Analysis of Quantitative Data : Data, data everywhere — it’s impossible to escape it in today’s digitally connected world. With business and personal activities leaving digital footprints, vast amounts of quantitative data are being generated every second of every day. While data on its own may seem impersonal and cold, in the right hands it can be transformed into valuable insights that drive meaningful decision-making. In this article, we will discuss analysis of quantitative data types and examples!

If you are looking to acquire hands-on experience in quantitative data analysis, look no further than Physics Wallah’s Data Analytics Course . And as a token of appreciation for reading this blog post until the end, use our exclusive coupon code “READER” to get a discount on the course fee.

Table of Contents

What is the Quantitative Analysis Method?

Quantitative Analysis refers to a mathematical approach that gathers and evaluates measurable and verifiable data. This method is utilized to assess performance and various aspects of a business or research. It involves the use of mathematical and statistical techniques to analyze data. Quantitative methods emphasize objective measurements, focusing on statistical, analytical, or numerical analysis of data. It collects data and studies it to derive insights or conclusions.

In a business context, it helps in evaluating the performance and efficiency of operations. Quantitative analysis can be applied across various domains, including finance, research, and chemistry, where data can be converted into numbers for analysis.

Also Read: Analysis vs. Analytics: How Are They Different?

What is the Best Analysis for Quantitative Data?

The “best” analysis for quantitative data largely depends on the specific research objectives, the nature of the data collected, the research questions posed, and the context in which the analysis is conducted. Quantitative data analysis encompasses a wide range of techniques, each suited for different purposes. Here are some commonly employed methods, along with scenarios where they might be considered most appropriate:

1) Descriptive Statistics:

• When to Use: To summarize and describe the basic features of the dataset, providing simple summaries about the sample and measures of central tendency and variability.
• Example: Calculating means, medians, standard deviations, and ranges to describe a dataset.

2) Inferential Statistics:

• When to Use: When you want to make predictions or inferences about a population based on a sample, testing hypotheses, or determining relationships between variables.
• Example: Conducting t-tests to compare means between two groups or performing regression analysis to understand the relationship between an independent variable and a dependent variable.

3) Correlation and Regression Analysis:

• When to Use: To examine relationships between variables, determining the strength and direction of associations, or predicting one variable based on another.
• Example: Assessing the correlation between customer satisfaction scores and sales revenue or predicting house prices based on variables like location, size, and amenities.

4) Factor Analysis:

• When to Use: When dealing with a large set of variables and aiming to identify underlying relationships or latent factors that explain patterns of correlations within the data.
• Example: Exploring underlying constructs influencing employee engagement using survey responses across multiple indicators.

5) Time Series Analysis:

• When to Use: When analyzing data points collected or recorded at successive time intervals to identify patterns, trends, seasonality, or forecast future values.
• Example: Analyzing monthly sales data over several years to detect seasonal trends or forecasting stock prices based on historical data patterns.

6) Cluster Analysis:

• When to Use: To segment a dataset into distinct groups or clusters based on similarities, enabling pattern recognition, customer segmentation, or data reduction.
• Example: Segmenting customers into distinct groups based on purchasing behavior, demographic factors, or preferences.

The “best” analysis for quantitative data is not one-size-fits-all but rather depends on the research objectives, hypotheses, data characteristics, and contextual factors. Often, a combination of analytical techniques may be employed to derive comprehensive insights and address multifaceted research questions effectively. Therefore, selecting the appropriate analysis requires careful consideration of the research goals, methodological rigor, and interpretative relevance to ensure valid, reliable, and actionable outcomes.

Analysis of Quantitative Data in Quantitative Research

Analyzing quantitative data in quantitative research involves a systematic process of examining numerical information to uncover patterns, relationships, and insights that address specific research questions or objectives. Here’s a structured overview of the analysis process:

1) Data Preparation:

• Data Cleaning: Identify and address errors, inconsistencies, missing values, and outliers in the dataset to ensure its integrity and reliability.
• Variable Transformation: Convert variables into appropriate formats or scales, if necessary, for analysis (e.g., normalization, standardization).

2) Descriptive Statistics:

• Central Tendency: Calculate measures like mean, median, and mode to describe the central position of the data.
• Variability: Assess the spread or dispersion of data using measures such as range, variance, standard deviation, and interquartile range.
• Frequency Distribution: Create tables, histograms, or bar charts to display the distribution of values for categorical or discrete variables.

3) Exploratory Data Analysis (EDA):

• Data Visualization: Generate graphical representations like scatter plots, box plots, histograms, or heatmaps to visualize relationships, distributions, and patterns in the data.
• Correlation Analysis: Examine the strength and direction of relationships between variables using correlation coefficients.

4) Inferential Statistics:

• Hypothesis Testing: Formulate null and alternative hypotheses based on research questions, selecting appropriate statistical tests (e.g., t-tests, ANOVA, chi-square tests) to assess differences, associations, or effects.
• Confidence Intervals: Estimate population parameters using sample statistics and determine the range within which the true parameter is likely to fall.

5) Regression Analysis:

• Linear Regression: Identify and quantify relationships between an outcome variable and one or more predictor variables, assessing the strength, direction, and significance of associations.
• Multiple Regression: Evaluate the combined effect of multiple independent variables on a dependent variable, controlling for confounding factors.

6) Factor Analysis and Structural Equation Modeling:

• Factor Analysis: Identify underlying dimensions or constructs that explain patterns of correlations among observed variables, reducing data complexity.
• Structural Equation Modeling (SEM): Examine complex relationships between observed and latent variables, assessing direct and indirect effects within a hypothesized model.

7) Time Series Analysis and Forecasting:

• Trend Analysis: Analyze patterns, trends, and seasonality in time-ordered data to understand historical patterns and predict future values.
• Forecasting Models: Develop predictive models (e.g., ARIMA, exponential smoothing) to anticipate future trends, demand, or outcomes based on historical data patterns.

8) Interpretation and Reporting:

• Interpret Results: Translate statistical findings into meaningful insights, discussing implications, limitations, and conclusions in the context of the research objectives.
• Documentation: Document the analysis process, methodologies, assumptions, and findings systematically for transparency, reproducibility, and peer review.

Also Read: Learning Path to Become a Data Analyst in 2024

Analysis of Quantitative Data Examples

Analyzing quantitative data involves various statistical methods and techniques to derive meaningful insights from numerical data. Here are some examples illustrating the analysis of quantitative data across different contexts:

How to Write Data Analysis in Quantitative Research Proposal?

Writing the data analysis section in a quantitative research proposal requires careful planning and organization to convey a clear, concise, and methodologically sound approach to analyzing the collected data. Here’s a step-by-step guide on how to write the data analysis section effectively:

Step 1: Begin with an Introduction

• Contextualize : Briefly reintroduce the research objectives, questions, and the significance of the study.
• Purpose Statement : Clearly state the purpose of the data analysis section, outlining what readers can expect in this part of the proposal.

Step 2: Describe Data Collection Methods

• Detail Collection Techniques : Provide a concise overview of the methods used for data collection (e.g., surveys, experiments, observations).
• Instrumentation : Mention any tools, instruments, or software employed for data gathering and its relevance.

Step 3 : Discuss Data Cleaning Procedures

• Data Cleaning : Describe the procedures for cleaning and pre-processing the data.
• Handling Outliers & Missing Data : Explain how outliers, missing values, and other inconsistencies will be managed to ensure data quality.

Step 4 : Present Analytical Techniques

• Descriptive Statistics : Outline the descriptive statistics that will be calculated to summarize the data (e.g., mean, median, mode, standard deviation).
• Inferential Statistics : Specify the inferential statistical tests or models planned for deeper analysis (e.g., t-tests, ANOVA, regression).

Step 5: State Hypotheses & Testing Procedures

• Hypothesis Formulation : Clearly state the null and alternative hypotheses based on the research questions or objectives.
• Testing Strategy : Detail the procedures for hypothesis testing, including the chosen significance level (e.g., α = 0.05) and statistical criteria.

Step 6 : Provide a Sample Analysis Plan

• Step-by-Step Plan : Offer a sample plan detailing the sequence of steps involved in the data analysis process.
• Software & Tools : Mention any specific statistical software or tools that will be utilized for analysis.

Step 7 : Address Validity & Reliability

• Validity : Discuss how you will ensure the validity of the data analysis methods and results.
• Reliability : Explain measures taken to enhance the reliability and replicability of the study findings.

Step 8 : Discuss Ethical Considerations

• Ethical Compliance : Address ethical considerations related to data privacy, confidentiality, and informed consent.
• Compliance with Guidelines : Ensure that your data analysis methods align with ethical guidelines and institutional policies.

Step 9 : Acknowledge Limitations

• Limitations : Acknowledge potential limitations in the data analysis methods or data set.
• Mitigation Strategies : Offer strategies or alternative approaches to mitigate identified limitations.

Step 10 : Conclude the Section

• Summary : Summarize the key points discussed in the data analysis section.
• Transition : Provide a smooth transition to subsequent sections of the research proposal, such as the conclusion or references.

Step 11 : Proofread & Revise

• Review : Carefully review the data analysis section for clarity, coherence, and consistency.
• Feedback : Seek feedback from peers, advisors, or mentors to refine your approach and ensure methodological rigor.

What are the 4 Types of Quantitative Analysis?

Quantitative analysis encompasses various methods to evaluate and interpret numerical data. While the specific categorization can vary based on context, here are four broad types of quantitative analysis commonly recognized:

• Descriptive Analysis: This involves summarizing and presenting data to describe its main features, such as mean, median, mode, standard deviation, and range. Descriptive statistics provide a straightforward overview of the dataset’s characteristics.
• Inferential Analysis: This type of analysis uses sample data to make predictions or inferences about a larger population. Techniques like hypothesis testing, regression analysis, and confidence intervals fall under this category. The goal is to draw conclusions that extend beyond the immediate data collected.
• Time-Series Analysis: In this method, data points are collected, recorded, and analyzed over successive time intervals. Time-series analysis helps identify patterns, trends, and seasonal variations within the data. It’s particularly useful in forecasting future values based on historical trends.
• Causal or Experimental Research: This involves establishing a cause-and-effect relationship between variables. Through experimental designs, researchers manipulate one variable to observe the effect on another variable while controlling for external factors. Randomized controlled trials are a common method within this type of quantitative analysis.

Each type of quantitative analysis serves specific purposes and is applied based on the nature of the data and the research objectives.

Also Read: AI and Predictive Analytics: Examples, Tools, Uses, Ai Vs Predictive Analytics

Steps to Effective Quantitative Data Analysis 

Quantitative data analysis need not be daunting; it’s a systematic process that anyone can master. To harness actionable insights from your company’s data, follow these structured steps:

Step 1 : Gather Data Strategically

Initiating the analysis journey requires a foundation of relevant data. Employ quantitative research methods to accumulate numerical insights from diverse channels such as:

• Interviews or Focus Groups: Engage directly with stakeholders or customers to gather specific numerical feedback.
• Digital Analytics: Utilize tools like Google Analytics to extract metrics related to website traffic, user behavior, and conversions.
• Observational Tools: Leverage heatmaps, click-through rates, or session recordings to capture user interactions and preferences.
• Structured Questionnaires: Deploy surveys or feedback mechanisms that employ close-ended questions for precise responses.

Ensure that your data collection methods align with your research objectives, focusing on granularity and accuracy.

Step 2 : Refine and Cleanse Your Data

Raw data often comes with imperfections. Scrutinize your dataset to identify and rectify:

• Errors and Inconsistencies: Address any inaccuracies or discrepancies that could mislead your analysis.
• Duplicates: Eliminate repeated data points that can skew results.
• Outliers: Identify and assess outliers, determining whether they should be adjusted or excluded based on contextual relevance.

Cleaning your dataset ensures that subsequent analyses are based on reliable and consistent information, enhancing the credibility of your findings.

Step 3 : Delve into Analysis with Precision

With a refined dataset at your disposal, transition into the analytical phase. Employ both descriptive and inferential analysis techniques:

• Descriptive Analysis: Summarize key attributes of your dataset, computing metrics like averages, distributions, and frequencies.
• Inferential Analysis: Leverage statistical methodologies to derive insights, explore relationships between variables, or formulate predictions.

The objective is not just number crunching but deriving actionable insights. Interpret your findings to discern underlying patterns, correlations, or trends that inform strategic decision-making. For instance, if data indicates a notable relationship between user engagement metrics and specific website features, consider optimizing those features for enhanced user experience.

Step 4 : Visual Representation and Communication

Transforming your analytical outcomes into comprehensible narratives is crucial for organizational alignment and decision-making. Leverage visualization tools and techniques to:

• Craft Engaging Visuals: Develop charts, graphs, or dashboards that encapsulate key findings and insights.
• Highlight Insights: Use visual elements to emphasize critical data points, trends, or comparative metrics effectively.
• Facilitate Stakeholder Engagement: Share your visual representations with relevant stakeholders, ensuring clarity and fostering informed discussions.

Tools like Tableau, Power BI, or specialized platforms like Hotjar can simplify the visualization process, enabling seamless representation and dissemination of your quantitative insights.

Also Read: Top 10 Must Use AI Tools for Data Analysis [2024 Edition]

Statistical Analysis in Quantitative Research

Statistical analysis is a cornerstone of quantitative research, providing the tools and techniques to interpret numerical data systematically. By applying statistical methods, researchers can identify patterns, relationships, and trends within datasets, enabling evidence-based conclusions and informed decision-making. Here’s an overview of the key aspects and methodologies involved in statistical analysis within quantitative research:

• Mean, Median, Mode: Measures of central tendency that summarize the average, middle, and most frequent values in a dataset, respectively.
• Standard Deviation, Variance: Indicators of data dispersion or variability around the mean.
• Frequency Distributions: Tabular or graphical representations that display the distribution of data values or categories.
• Hypothesis Testing: Formal methodologies to test hypotheses or assumptions about population parameters using sample data. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis.
• Confidence Intervals: Estimation techniques that provide a range of values within which a population parameter is likely to lie, based on sample data.
• Correlation and Regression Analysis: Techniques to explore relationships between variables, determining the strength and direction of associations. Regression analysis further enables prediction and modeling based on observed data patterns.

3) Probability Distributions:

• Normal Distribution: A bell-shaped distribution often observed in naturally occurring phenomena, forming the basis for many statistical tests.
• Binomial, Poisson, and Exponential Distributions: Specific probability distributions applicable to discrete or continuous random variables, depending on the nature of the research data.

4) Multivariate Analysis:

• Factor Analysis: A technique to identify underlying relationships between observed variables, often used in survey research or data reduction scenarios.
• Cluster Analysis: Methodologies that group similar objects or individuals based on predefined criteria, enabling segmentation or pattern recognition within datasets.
• Multivariate Regression: Extending regression analysis to multiple independent variables, assessing their collective impact on a dependent variable.

5) Data Modeling and Forecasting:

• Time Series Analysis: Analyzing data points collected or recorded at specific time intervals to identify patterns, trends, or seasonality.
• Predictive Analytics: Leveraging statistical models and machine learning algorithms to forecast future trends, outcomes, or behaviors based on historical data.

If this blog post has piqued your interest in the field of data analytics, then we highly recommend checking out Physics Wallah’s Data Analytics Course . This course covers all the fundamental concepts of quantitative data analysis and provides hands-on training for various tools and software used in the industry.

With a team of experienced instructors from different backgrounds and industries, you will gain a comprehensive understanding of a wide range of topics related to data analytics. And as an added bonus for being one of our dedicated readers, use the coupon code “ READER ” to get an exclusive discount on this course!

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Analysis of Quantitative Data FAQs

What is quantitative data analysis.

Quantitative data analysis involves the systematic process of collecting, cleaning, interpreting, and presenting numerical data to identify patterns, trends, and relationships through statistical methods and mathematical calculations.

What are the main steps involved in quantitative data analysis?

The primary steps include data collection, data cleaning, statistical analysis (descriptive and inferential), interpretation of results, and visualization of findings using graphs or charts.

What is the difference between descriptive and inferential analysis?

Descriptive analysis summarizes and describes the main aspects of the dataset (e.g., mean, median, mode), while inferential analysis draws conclusions or predictions about a population based on a sample, using statistical tests and models.

How do I handle outliers in my quantitative data?

Outliers can be managed by identifying them through statistical methods, understanding their nature (error or valid data), and deciding whether to remove them, transform them, or conduct separate analyses to understand their impact.

Which statistical tests should I use for my quantitative research?

The choice of statistical tests depends on your research design, data type, and research questions. Common tests include t-tests, ANOVA, regression analysis, chi-square tests, and correlation analysis, among others.

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

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

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 organize and summarize 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 generalize 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: summarize your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, other interesting articles.

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 operationalize 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.

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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 generalizable findings, you should use a probability sampling method. Random selection reduces several types of research bias , like 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 at risk for biases like self-selection bias , 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 generalizing your findings to.
• your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalize your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialized, 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 generalized 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 standardized 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 summarize them.

Inspect your data

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

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

By visualizing 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

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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 minimize 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 emphasizes 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.

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

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval

Methodology

• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hostile attribution bias
• Affect heuristic

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Quantitative Research

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Quantitative research methods are concerned with the planning, design, and implementation of strategies to collect and analyze data. Descartes, the seventeenth-century philosopher, suggested that how the results are achieved is often more important than the results themselves, as the journey taken along the research path is a journey of discovery. High-quality quantitative research is characterized by the attention given to the methods and the reliability of the tools used to collect the data. The ability to critique research in a systematic way is an essential component of a health professional’s role in order to deliver high quality, evidence-based healthcare. This chapter is intended to provide a simple overview of the way new researchers and health practitioners can understand and employ quantitative methods. The chapter offers practical, realistic guidance in a learner-friendly way and uses a logical sequence to understand the process of hypothesis development, study design, data collection and handling, and finally data analysis and interpretation.

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Babbie ER. The practice of social research. 14th ed. Belmont: Wadsworth Cengage; 2016.

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School of Science and Health, Western Sydney University, Penrith, NSW, Australia

Leigh A. Wilson

Faculty of Health Science, Discipline of Behavioural and Social Sciences in Health, University of Sydney, Lidcombe, NSW, Australia

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Wilson, L.A. (2019). Quantitative Research. In: Liamputtong, P. (eds) Handbook of Research Methods in Health Social Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-5251-4_54

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DOI : https://doi.org/10.1007/978-981-10-5251-4_54

Published : 13 January 2019

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Improved limit of detection for zoonotic Plasmodium knowlesi and P. cynomolgi surveillance using reverse transcription for total nucleic acid preserved samples or dried blood spots

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Background: Zoonotic P. knowlesi and P. cynomolgi symptomatic and asymptomatic infections occur across endemic areas of Southeast Asia. Most infections are low-parasitemia, with an unknown proportion below routine microscopy detection thresholds. Molecular surveillance tools optimizing the limit of detection (LOD) would allow more accurate estimates of zoonotic malaria prevalence. Methods: An established ultra-sensitive Plasmodium genus quantitative-PCR (qPCR) assay targeting the 18S rRNA gene underwent LOD evaluation with and without reverse transcription (RT) for P. knowlesi, P. cynomolgi and P. vivax using total nucleic acid preserved (DNA/RNA ShieldTM) isolates and archived dried blood spots (DBS). LODs for selected P. knowlesi -specific assays, and reference P. vivax - and P. cynomolgi -specific assays were determined with RT. Assay specificities were assessed using clinical malaria samples and malaria-negative controls. Results: The use of reverse transcription improved Plasmodium species detection by up to 10,000-fold ( Plasmodium genus), 2759-fold ( P. knowlesi ), 1000-fold ( P. vivax ) and 10-fold ( P. cynomolgi ). The median LOD with RT for the Kamau et al. Plasmodium genus RT-qPCR assay was ≤0.0002 parasites/µL for P. knowlesi and 0.002 parasites/µL for both P. cynomolgi and P. vivax . The LODs with RT for P. knowlesi -specific PCRs were: Imwong et al. 18S rRNA (0.0007 parasites/µL); Divis et al. real-time 18S rRNA (0.0002 parasites/µL); Lubis et al. hemi-nested SICAvar (1.1 parasites/µL) and Lee et al. nested 18S rRNA (11 parasites/µL). The LOD for P. vivax - and P. cynomolgi -specific assays with RT were 0.02 and 0.20 parasites/µL respectively. For DBS P. knowlesi samples the median LOD for the Plasmodium genus qPCR with RT was 0.08, and without RT was 19.89 parasites/uL (249-fold change); no LOD improvement was demonstrated in DBS archived beyond 6 years. The Plasmodium genus and P. knowlesi -assays were 100% specific for Plasmodium species and P. knowlesi detection, respectively, from 190 clinical infections and 48 healthy controls. Reference P. vivax -specific primers demonstrated known cross-reactivity with P. cynomolgi . Conclusion: Our findings support the use of an 18S rRNA Plasmodium genus qPCR and species-specific nested PCR protocol with RT for highly-sensitive surveillance of zoonotic and human Plasmodium species infections.

Competing Interest Statement

The authors have declared no competing interest.

Funding Statement

This work was supported by the ZOOMAL project, funded through the Australian Centre for International Agricultural Research and Indo-Pacific Centre for Health Security, DFAT, Australian Government (#LS-2019-116), the National Institutes of Health, USA (#R01AI160457-01), and DOD-DHA-Global Emerging Infections Surveillance program project P0097_22_N2.). Funding support was also through the National Health and Medical Research Council, Australia (Grant Numbers #1037304 and #1045156, fellowship to NMA [#1042072], Emerging Leadership 2 Investigator Grants to MJG [#2017436] and BEB [#2016792]), and the Ministry of Health, Malaysia (#BP00500/117/1002) awarded to GSR.

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I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

Sample collection and diagnostic evaluation were approved as part of prospective malaria studies by the Medical Research and Ethics Committee (MREC), Ministry of Health Malaysia (NMRR-10-754-6684, NMRR-19-4109-52172 and NMRR-19-3229-49967), Universitas Sumatera Utara, Indonesia (#723/KEP/USU/2021) and by the Menzies School of Health Research, Australia (HREC-2010-1431 and HREC-2022-4417) in accordance with all applicable Federal and other regulations governing the protection of human subject research.

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

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All data produced in the present work are contained in the manuscript

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