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What is a Research Hypothesis: How to Write it, Types, and Examples

Any research begins with a research question and a research hypothesis . A research question alone may not suffice to design the experiment(s) needed to answer it. A hypothesis is central to the scientific method. But what is a hypothesis ? A hypothesis is a testable statement that proposes a possible explanation to a phenomenon, and it may include a prediction. Next, you may ask what is a research hypothesis ? Simply put, a research hypothesis is a prediction or educated guess about the relationship between the variables that you want to investigate.  

It is important to be thorough when developing your research hypothesis. Shortcomings in the framing of a hypothesis can affect the study design and the results. A better understanding of the research hypothesis definition and characteristics of a good hypothesis will make it easier for you to develop your own hypothesis for your research. Let’s dive in to know more about the types of research hypothesis , how to write a research hypothesis , and some research hypothesis examples .  

Table of Contents

What is a hypothesis ?  

A hypothesis is based on the existing body of knowledge in a study area. Framed before the data are collected, a hypothesis states the tentative relationship between independent and dependent variables, along with a prediction of the outcome.  

What is a research hypothesis ?  

Young researchers starting out their journey are usually brimming with questions like “ What is a hypothesis ?” “ What is a research hypothesis ?” “How can I write a good research hypothesis ?”   

A research hypothesis is a statement that proposes a possible explanation for an observable phenomenon or pattern. It guides the direction of a study and predicts the outcome of the investigation. A research hypothesis is testable, i.e., it can be supported or disproven through experimentation or observation.     

Characteristics of a good hypothesis  

Here are the characteristics of a good hypothesis :  

• Clearly formulated and free of language errors and ambiguity  
• Concise and not unnecessarily verbose  
• Has clearly defined variables  
• Testable and stated in a way that allows for it to be disproven  
• Can be tested using a research design that is feasible, ethical, and practical   
• Specific and relevant to the research problem  
• Rooted in a thorough literature search  
• Can generate new knowledge or understanding.  

How to create an effective research hypothesis  

A study begins with the formulation of a research question. A researcher then performs background research. This background information forms the basis for building a good research hypothesis . The researcher then performs experiments, collects, and analyzes the data, interprets the findings, and ultimately, determines if the findings support or negate the original hypothesis.  

Let’s look at each step for creating an effective, testable, and good research hypothesis :  

• Identify a research problem or question: Start by identifying a specific research problem.   
• Review the literature: Conduct an in-depth review of the existing literature related to the research problem to grasp the current knowledge and gaps in the field.   
• Formulate a clear and testable hypothesis : Based on the research question, use existing knowledge to form a clear and testable hypothesis . The hypothesis should state a predicted relationship between two or more variables that can be measured and manipulated. Improve the original draft till it is clear and meaningful.  
• State the null hypothesis: The null hypothesis is a statement that there is no relationship between the variables you are studying.   
• Define the population and sample: Clearly define the population you are studying and the sample you will be using for your research.  
• Select appropriate methods for testing the hypothesis: Select appropriate research methods, such as experiments, surveys, or observational studies, which will allow you to test your research hypothesis .  

Remember that creating a research hypothesis is an iterative process, i.e., you might have to revise it based on the data you collect. You may need to test and reject several hypotheses before answering the research problem.  

How to write a research hypothesis  

When you start writing a research hypothesis , you use an “if–then” statement format, which states the predicted relationship between two or more variables. Clearly identify the independent variables (the variables being changed) and the dependent variables (the variables being measured), as well as the population you are studying. Review and revise your hypothesis as needed.  

An example of a research hypothesis in this format is as follows:  

“ If [athletes] follow [cold water showers daily], then their [endurance] increases.”  

Population: athletes  

Independent variable: daily cold water showers  

Dependent variable: endurance  

You may have understood the characteristics of a good hypothesis . But note that a research hypothesis is not always confirmed; a researcher should be prepared to accept or reject the hypothesis based on the study findings.  

Research hypothesis checklist  

Following from above, here is a 10-point checklist for a good research hypothesis :  

• Testable: A research hypothesis should be able to be tested via experimentation or observation.  
• Specific: A research hypothesis should clearly state the relationship between the variables being studied.  
• Based on prior research: A research hypothesis should be based on existing knowledge and previous research in the field.  
• Falsifiable: A research hypothesis should be able to be disproven through testing.  
• Clear and concise: A research hypothesis should be stated in a clear and concise manner.  
• Logical: A research hypothesis should be logical and consistent with current understanding of the subject.  
• Relevant: A research hypothesis should be relevant to the research question and objectives.  
• Feasible: A research hypothesis should be feasible to test within the scope of the study.  
• Reflects the population: A research hypothesis should consider the population or sample being studied.  
• Uncomplicated: A good research hypothesis is written in a way that is easy for the target audience to understand.  

By following this research hypothesis checklist , you will be able to create a research hypothesis that is strong, well-constructed, and more likely to yield meaningful results.  

Types of research hypothesis  

Different types of research hypothesis are used in scientific research:  

1. Null hypothesis:

A null hypothesis states that there is no change in the dependent variable due to changes to the independent variable. This means that the results are due to chance and are not significant. A null hypothesis is denoted as H0 and is stated as the opposite of what the alternative hypothesis states.   

Example: “ The newly identified virus is not zoonotic .”  

2. Alternative hypothesis:

This states that there is a significant difference or relationship between the variables being studied. It is denoted as H1 or Ha and is usually accepted or rejected in favor of the null hypothesis.  

Example: “ The newly identified virus is zoonotic .”  

3. Directional hypothesis :

This specifies the direction of the relationship or difference between variables; therefore, it tends to use terms like increase, decrease, positive, negative, more, or less.   

Example: “ The inclusion of intervention X decreases infant mortality compared to the original treatment .”   

4. Non-directional hypothesis:

While it does not predict the exact direction or nature of the relationship between the two variables, a non-directional hypothesis states the existence of a relationship or difference between variables but not the direction, nature, or magnitude of the relationship. A non-directional hypothesis may be used when there is no underlying theory or when findings contradict previous research.  

Example, “ Cats and dogs differ in the amount of affection they express .”  

5. Simple hypothesis :

A simple hypothesis only predicts the relationship between one independent and another independent variable.  

Example: “ Applying sunscreen every day slows skin aging .”  

6 . Complex hypothesis :

A complex hypothesis states the relationship or difference between two or more independent and dependent variables.   

Example: “ Applying sunscreen every day slows skin aging, reduces sun burn, and reduces the chances of skin cancer .” (Here, the three dependent variables are slowing skin aging, reducing sun burn, and reducing the chances of skin cancer.)  

7. Associative hypothesis:  

An associative hypothesis states that a change in one variable results in the change of the other variable. The associative hypothesis defines interdependency between variables.  

Example: “ There is a positive association between physical activity levels and overall health .”  

8 . Causal hypothesis:

A causal hypothesis proposes a cause-and-effect interaction between variables.  

Example: “ Long-term alcohol use causes liver damage .”  

Note that some of the types of research hypothesis mentioned above might overlap. The types of hypothesis chosen will depend on the research question and the objective of the study.  

Research hypothesis examples  

Here are some good research hypothesis examples :  

“The use of a specific type of therapy will lead to a reduction in symptoms of depression in individuals with a history of major depressive disorder.”  

“Providing educational interventions on healthy eating habits will result in weight loss in overweight individuals.”  

“Plants that are exposed to certain types of music will grow taller than those that are not exposed to music.”  

“The use of the plant growth regulator X will lead to an increase in the number of flowers produced by plants.”  

Characteristics that make a research hypothesis weak are unclear variables, unoriginality, being too general or too vague, and being untestable. A weak hypothesis leads to weak research and improper methods.   

Some bad research hypothesis examples (and the reasons why they are “bad”) are as follows:  

“This study will show that treatment X is better than any other treatment . ” (This statement is not testable, too broad, and does not consider other treatments that may be effective.)  

“This study will prove that this type of therapy is effective for all mental disorders . ” (This statement is too broad and not testable as mental disorders are complex and different disorders may respond differently to different types of therapy.)  

“Plants can communicate with each other through telepathy . ” (This statement is not testable and lacks a scientific basis.)  

Importance of testable hypothesis  

If a research hypothesis is not testable, the results will not prove or disprove anything meaningful. The conclusions will be vague at best. A testable hypothesis helps a researcher focus on the study outcome and understand the implication of the question and the different variables involved. A testable hypothesis helps a researcher make precise predictions based on prior research.  

To be considered testable, there must be a way to prove that the hypothesis is true or false; further, the results of the hypothesis must be reproducible.  

Frequently Asked Questions (FAQs) on research hypothesis  

1. What is the difference between research question and research hypothesis ?  

A research question defines the problem and helps outline the study objective(s). It is an open-ended statement that is exploratory or probing in nature. Therefore, it does not make predictions or assumptions. It helps a researcher identify what information to collect. A research hypothesis , however, is a specific, testable prediction about the relationship between variables. Accordingly, it guides the study design and data analysis approach.

2. When to reject null hypothesis ?

A null hypothesis should be rejected when the evidence from a statistical test shows that it is unlikely to be true. This happens when the test statistic (e.g., p -value) is less than the defined significance level (e.g., 0.05). Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it simply means that the evidence found is not compatible with the null hypothesis.  

3. How can I be sure my hypothesis is testable?  

A testable hypothesis should be specific and measurable, and it should state a clear relationship between variables that can be tested with data. To ensure that your hypothesis is testable, consider the following:  

• Clearly define the key variables in your hypothesis. You should be able to measure and manipulate these variables in a way that allows you to test the hypothesis.  
• The hypothesis should predict a specific outcome or relationship between variables that can be measured or quantified.   
• You should be able to collect the necessary data within the constraints of your study.  
• It should be possible for other researchers to replicate your study, using the same methods and variables.   
• Your hypothesis should be testable by using appropriate statistical analysis techniques, so you can draw conclusions, and make inferences about the population from the sample data.  
• The hypothesis should be able to be disproven or rejected through the collection of data.  

4. How do I revise my research hypothesis if my data does not support it?  

If your data does not support your research hypothesis , you will need to revise it or develop a new one. You should examine your data carefully and identify any patterns or anomalies, re-examine your research question, and/or revisit your theory to look for any alternative explanations for your results. Based on your review of the data, literature, and theories, modify your research hypothesis to better align it with the results you obtained. Use your revised hypothesis to guide your research design and data collection. It is important to remain objective throughout the process.  

5. I am performing exploratory research. Do I need to formulate a research hypothesis?  

As opposed to “confirmatory” research, where a researcher has some idea about the relationship between the variables under investigation, exploratory research (or hypothesis-generating research) looks into a completely new topic about which limited information is available. Therefore, the researcher will not have any prior hypotheses. In such cases, a researcher will need to develop a post-hoc hypothesis. A post-hoc research hypothesis is generated after these results are known.  

6. How is a research hypothesis different from a research question?

A research question is an inquiry about a specific topic or phenomenon, typically expressed as a question. It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis.

7. Can a research hypothesis change during the research process?

Yes, research hypotheses can change during the research process. As researchers collect and analyze data, new insights and information may emerge that require modification or refinement of the initial hypotheses. This can be due to unexpected findings, limitations in the original hypotheses, or the need to explore additional dimensions of the research topic. Flexibility is crucial in research, allowing for adaptation and adjustment of hypotheses to align with the evolving understanding of the subject matter.

8. How many hypotheses should be included in a research study?

The number of research hypotheses in a research study varies depending on the nature and scope of the research. It is not necessary to have multiple hypotheses in every study. Some studies may have only one primary hypothesis, while others may have several related hypotheses. The number of hypotheses should be determined based on the research objectives, research questions, and the complexity of the research topic. It is important to ensure that the hypotheses are focused, testable, and directly related to the research aims.

9. Can research hypotheses be used in qualitative research?

Yes, research hypotheses can be used in qualitative research, although they are more commonly associated with quantitative research. In qualitative research, hypotheses may be formulated as tentative or exploratory statements that guide the investigation. Instead of testing hypotheses through statistical analysis, qualitative researchers may use the hypotheses to guide data collection and analysis, seeking to uncover patterns, themes, or relationships within the qualitative data. The emphasis in qualitative research is often on generating insights and understanding rather than confirming or rejecting specific research hypotheses through statistical testing.

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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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How to Formulate a Hypothesis: Example and Explanation

A hypothesis is a smart guess about how things work. It helps scientists figure out what they think will happen in their experiments. Making a good hypothesis is important because it guides the research and helps find answers to questions. In this article, we will learn how to make a strong hypothesis, look at some examples, and understand why they matter.

Key Takeaways

• A hypothesis is an educated guess that can be tested through experiments.
• Good hypotheses are clear, precise, and can be proven wrong.
• There are different types of hypotheses, like simple, complex, null, and alternative.
• Variables play a big role in forming a hypothesis, including independent, dependent, and control variables.
• Testing and refining hypotheses are crucial steps in scientific research.

Understanding the Concept of a Hypothesis

Definition and importance.

A hypothesis is an idea you can test. It's a clear statement predicting the outcome of your study. It's not just a guess ; it should be based on what you already know. A good hypothesis helps you focus your research and guides your experiments.

Role in Scientific Research

In science, a hypothesis is very important. It gives you a starting point for your experiments. You can test it to see if it's true or false. This helps you understand more about the world. A clear, testable hypothesis is key to good research .

Common Misconceptions

Many people think a hypothesis is just a wild guess. This is not true. A hypothesis is based on existing knowledge and theories. Another common mistake is making the hypothesis too broad. A good hypothesis should be specific and testable.

Steps to Formulate a Hypothesis

Formulating a hypothesis is a critical step in the scientific method. It involves several key stages that help ensure your hypothesis is both testable and relevant to your research question. Here are the steps you should follow:

Gathering Observations

Start by collecting as many observations about your topic or problem as possible. These observations will form the foundation of your hypothesis. Good clinical research starts from a plausible hypothesis supported by contemporary scientific knowledge. Look for patterns or trends in the data that might suggest a possible explanation.

Identifying Variables

Next, identify the variables involved in your study. Variables are the elements that you will measure or manipulate in your research. There are typically three types of variables: independent, dependent, and control variables. Understanding these will help you design a more effective experiment.

Developing Possible Explanations

Once you have gathered your observations and identified your variables, the next step is to develop possible explanations for the patterns you have observed. This is where you start to formulate your hypothesis. Think of ways to confirm or disprove each possible explanation through experimentation. This process is known as falsifiability and is crucial for a robust hypothesis.

Characteristics of a Good Hypothesis

Testability and falsifiability.

A good hypothesis must be testable, meaning you can design an experiment to check if it's true or false. Testability is crucial because it allows you to gather evidence to support or refute your hypothesis. Additionally, a hypothesis should be falsifiable, which means there should be a possible outcome that can prove it wrong. This aligns with the falsification principle proposed by Karl Popper, which is fundamental in scientific research.

Clarity and Precision

Your hypothesis should be clear and precise, avoiding any vague language. This clarity helps in demystifying the concept of a thesis statement . A well-defined hypothesis makes it easier to design experiments and interpret results. For example, instead of saying "Plants grow better with more light," you could say, "If plants receive 8 hours of sunlight daily, then they will grow taller than plants that receive 4 hours of sunlight daily."

Relevance to Research Question

A good hypothesis should be directly related to your research question. It should provide a clear direction for your study and help you focus on specific variables. This relevance ensures that your hypothesis is not just a random guess but is grounded in existing knowledge and observations. Hypotheses have strong, arguably foundational, utility as a tool of science . They support the falsification principle, proposed by Karl Popper as fundamental in scientific research.

Types of Hypotheses in Research

When conducting research, it's crucial to understand the different types of hypotheses you might encounter. Each type serves a unique purpose and helps guide your study in specific ways. Knowing these types can enhance the clarity and focus of your research proposal .

Examples of Hypotheses

Simple hypothesis examples.

A simple hypothesis suggests a relationship between two variables: one independent and one dependent. For instance, "If students sleep for at least 8 hours, then their test scores will improve." This type of hypothesis is straightforward and easy to test.

Complex Hypothesis Examples

A complex hypothesis involves more than two variables. An example could be, "If students sleep for at least 8 hours and eat a healthy breakfast, then their test scores and overall well-being will improve." This type of hypothesis examines multiple factors and their combined effects.

Null and Alternative Hypothesis Examples

The null hypothesis states that there is no relationship between the variables. For example, "There is no difference in test scores between students who sleep for 8 hours and those who do not." The alternative hypothesis, on the other hand, suggests a relationship: "Students who sleep for 8 hours will have better test scores than those who do not."

Understanding these examples helps clarify how to structure your own hypotheses. Whether simple or complex, each type plays a crucial role in scientific research.

The Role of Variables in Hypothesis Formulation

When formulating a hypothesis, understanding the role of variables is crucial. Variables are the elements that you measure or manipulate in your research . They help you establish relationships and test your predictions effectively.

Testing Your Hypothesis

Designing experiments.

Designing an experiment is a crucial step in testing your hypothesis. A well-designed experiment ensures that you can accurately test your hypothesis and obtain reliable results. Start by defining your independent and dependent variables clearly. Make sure to control other factors that might influence the outcome. This is essential for maintaining the integrity of your experiment. You should also consider the ethical implications of your experiment to ensure it adheres to accepted standards.

Data Collection Methods

Once your experiment is designed, the next step is to collect data. Choose data collection methods that are appropriate for your research question and hypothesis. Common methods include surveys, observations, and experiments. Ensure that your data collection process is systematic and consistent to avoid any biases. Remember, the goal is to gather data that will either support or refute your hypothesis.

Analyzing Results

After collecting your data, the next step is to analyze the results. Use statistical methods to determine whether your data supports your hypothesis. This involves calculating the likelihood that your results are due to chance. If your data does not support your hypothesis, don't be discouraged. Unexpected findings can lead to new questions and further research. Always be open to conducting further experiments to validate and understand your findings.

Common Pitfalls in Hypothesis Formulation

When formulating a hypothesis, it's crucial to avoid common mistakes that can undermine your research. Here are some pitfalls to watch out for:

Overly Broad Hypotheses

One of the most frequent errors is creating a hypothesis that is too broad. A broad hypothesis can be difficult to test and may not provide meaningful results. Narrowing down your hypothesis to a specific aspect of your research question can make it more manageable and testable.

Lack of Testability

A hypothesis must be testable to be valid. If you can't design an experiment to test your hypothesis, it's not useful. Ensure that your hypothesis includes variables that can be measured and tested. This is essential for revolutionizing research: the secrets of effective experimental design .

Ignoring Alternative Explanations

Another common mistake is failing to consider other possible explanations for your observations. When you ignore alternative explanations, you risk missing out on important insights. Always evaluate assumptions, revise methodology, and consider alternative explanations to strengthen your hypothesis.

By being aware of these pitfalls, you can create a more robust and reliable hypothesis for your research.

Refining and Revising Hypotheses

When you conduct research, it’s common to find that your initial hypothesis may not hold true. This is a normal part of the scientific process. If your results do not support your original hypothesis, consider suggesting alternative options for future studies. This can help guide further research and improve understanding of the topic.

To ensure your hypothesis is strong, you can use a checklist to identify any weaknesses. Here are some questions to consider:

• Is the hypothesis clear and specific?
• Can it be tested through experiments?
• Does it relate to the research question?

By answering these questions, you can refine your hypothesis and make it more robust. Additionally, incorporating feedback from peers can provide new insights and help you adjust your hypothesis based on new data.

In summary, refining and revising your hypothesis is essential for advancing your research. It allows you to adapt to new findings and improve the clarity and focus of your work. Remember, the goal is to develop a hypothesis that can lead to meaningful conclusions and further exploration in your field.

In the context of educational research, a recent meta-analysis highlights the importance of understanding the relationship between psychological needs and student well-being. This shows how refining hypotheses can lead to better insights into complex issues. Similarly, a grounded theory study emphasizes the need for thorough reviews to identify key issues in research, which can also inform hypothesis revision.

Case Studies of Hypothesis Formulation

One of the most famous historical examples of hypothesis formulation is Gregor Mendel's work on pea plants. Mendel's hypothesis about inheritance patterns laid the groundwork for modern genetics. He observed the traits of pea plants and formulated hypotheses about how these traits were passed down through generations. His work is a classic example of how careful observation and hypothesis testing can lead to significant scientific breakthroughs.

In contemporary research, hypothesis formulation continues to play a crucial role. For instance, in the field of psychology, researchers often develop hypotheses to understand human behavior. A recent study on the effects of social media on mental health formulated the hypothesis that increased social media use leads to higher levels of anxiety and depression. This hypothesis was tested through surveys and data analysis, providing valuable insights into the relationship between social media and mental health.

From both historical and contemporary examples, several lessons can be learned about effective hypothesis formulation:

• Observation is key : Careful observation of phenomena is the first step in formulating a hypothesis.
• Clarity and precision : A good hypothesis should be clear and precise, making it easier to test.
• Testability: Ensure that your hypothesis can be tested through experiments or data analysis.
• Flexibility: Be prepared to revise your hypothesis based on new data or feedback.

By understanding these lessons, you can improve your own hypothesis formulation process and contribute to the advancement of scientific knowledge.

In our "Case Studies of Hypothesis Formulation" section, we dive into real-world examples that show how to create strong hypotheses. These case studies are designed to help you understand the process and apply it to your own work. If you're looking for more detailed guidance, visit our website for step-by-step instructions and special offers. Don't miss out on the chance to improve your research skills!

Formulating a hypothesis is a fundamental step in the scientific method that helps guide research and experimentation. By gathering observations, evaluating potential causes, and developing testable statements, researchers can create hypotheses that are both meaningful and falsifiable. This process not only aids in understanding the problem at hand but also in predicting outcomes and drawing conclusions based on empirical evidence. Remember, a well-crafted hypothesis is clear, concise, and provides a direction for future research. With practice and careful consideration, anyone can learn to formulate effective hypotheses that contribute to scientific knowledge.

Frequently Asked Questions

What is a hypothesis.

A hypothesis is an educated guess about how things work. It's a statement that can be tested to see if it's true or false.

Why is a hypothesis important in scientific research?

A hypothesis helps guide your experiments and research. It gives you a clear focus and helps you understand what you're trying to find out.

What are the steps to formulate a good hypothesis?

To create a good hypothesis, start by gathering observations, look for patterns, and identify variables. Then, come up with possible explanations that you can test.

What makes a hypothesis testable?

A testable hypothesis is one that you can prove or disprove through experiments or observations. It should be clear and specific.

Can a hypothesis be proven true?

A hypothesis can be supported by evidence, but it can't be proven true beyond all doubt. New evidence might change our understanding.

What are independent and dependent variables?

Independent variables are the ones you change in an experiment. Dependent variables are the ones you measure to see if they change because of the independent variable.

What is a null hypothesis?

A null hypothesis states that there is no relationship between the variables being studied. It's often used as a starting point for testing.

How can I avoid common pitfalls in hypothesis formulation?

To avoid problems, make sure your hypothesis is specific, testable, and based on observations. Avoid making it too broad or ignoring other possible explanations.

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How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

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.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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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.

What Is A Research (Scientific) Hypothesis? A plain-language explainer + examples

By:  Derek Jansen (MBA)  | Reviewed By: Dr Eunice Rautenbach | June 2020

If you’re new to the world of research, or it’s your first time writing a dissertation or thesis, you’re probably noticing that the words “research hypothesis” and “scientific hypothesis” are used quite a bit, and you’re wondering what they mean in a research context .

“Hypothesis” is one of those words that people use loosely, thinking they understand what it means. However, it has a very specific meaning within academic research. So, it’s important to understand the exact meaning before you start hypothesizing. 

Research Hypothesis 101

• What is a hypothesis ?
• What is a research hypothesis (scientific hypothesis)?
• Requirements for a research hypothesis
• Definition of a research hypothesis
• The null hypothesis

What is a hypothesis?

Let’s start with the general definition of a hypothesis (not a research hypothesis or scientific hypothesis), according to the Cambridge Dictionary:

Hypothesis: an idea or explanation for something that is based on known facts but has not yet been proved.

In other words, it’s a statement that provides an explanation for why or how something works, based on facts (or some reasonable assumptions), but that has not yet been specifically tested . For example, a hypothesis might look something like this:

Hypothesis: sleep impacts academic performance.

This statement predicts that academic performance will be influenced by the amount and/or quality of sleep a student engages in – sounds reasonable, right? It’s based on reasonable assumptions , underpinned by what we currently know about sleep and health (from the existing literature). So, loosely speaking, we could call it a hypothesis, at least by the dictionary definition.

But that’s not good enough…

Unfortunately, that’s not quite sophisticated enough to describe a research hypothesis (also sometimes called a scientific hypothesis), and it wouldn’t be acceptable in a dissertation, thesis or research paper . In the world of academic research, a statement needs a few more criteria to constitute a true research hypothesis .

What is a research hypothesis?

A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes – specificity , clarity and testability .

Let’s take a look at these more closely.

Need a helping hand?

Hypothesis Essential #1: Specificity & Clarity

A good research hypothesis needs to be extremely clear and articulate about both what’ s being assessed (who or what variables are involved ) and the expected outcome (for example, a difference between groups, a relationship between variables, etc.).

Let’s stick with our sleepy students example and look at how this statement could be more specific and clear.

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.

As you can see, the statement is very specific as it identifies the variables involved (sleep hours and test grades), the parties involved (two groups of students), as well as the predicted relationship type (a positive relationship). There’s no ambiguity or uncertainty about who or what is involved in the statement, and the expected outcome is clear.

Contrast that to the original hypothesis we looked at – “Sleep impacts academic performance” – and you can see the difference. “Sleep” and “academic performance” are both comparatively vague , and there’s no indication of what the expected relationship direction is (more sleep or less sleep). As you can see, specificity and clarity are key.

Hypothesis Essential #2: Testability (Provability)

A statement must be testable to qualify as a research hypothesis. In other words, there needs to be a way to prove (or disprove) the statement. If it’s not testable, it’s not a hypothesis – simple as that.

For example, consider the hypothesis we mentioned earlier:

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.  

We could test this statement by undertaking a quantitative study involving two groups of students, one that gets 8 or more hours of sleep per night for a fixed period, and one that gets less. We could then compare the standardised test results for both groups to see if there’s a statistically significant difference. 

Again, if you compare this to the original hypothesis we looked at – “Sleep impacts academic performance” – you can see that it would be quite difficult to test that statement, primarily because it isn’t specific enough. How much sleep? By who? What type of academic performance?

So, remember the mantra – if you can’t test it, it’s not a hypothesis 🙂

Defining A Research Hypothesis

You’re still with us? Great! Let’s recap and pin down a clear definition of a hypothesis.

A research hypothesis (or scientific hypothesis) is a statement about an expected relationship between variables, or explanation of an occurrence, that is clear, specific and testable.

So, when you write up hypotheses for your dissertation or thesis, make sure that they meet all these criteria. If you do, you’ll not only have rock-solid hypotheses but you’ll also ensure a clear focus for your entire research project.

What about the null hypothesis?

You may have also heard the terms null hypothesis , alternative hypothesis, or H-zero thrown around. At a simple level, the null hypothesis is the counter-proposal to the original hypothesis.

For example, if the hypothesis predicts that there is a relationship between two variables (for example, sleep and academic performance), the null hypothesis would predict that there is no relationship between those variables.

At a more technical level, the null hypothesis proposes that no statistical significance exists in a set of given observations and that any differences are due to chance alone.

And there you have it – hypotheses in a nutshell. 

If you have any questions, be sure to leave a comment below and we’ll do our best to help you. If you need hands-on help developing and testing your hypotheses, consider our private coaching service , where we hold your hand through the research journey.

17 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

Hi” best wishes to you and your very nice blog” 

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7 Types of Research Hypothesis: Examples, Significance and Step-By-Step Guide

Introduction.

In any research study, a research hypothesis plays a crucial role in guiding the investigation and providing a clear direction for the research. It is an essential component of a thesis as it helps to frame the research question and determine the methodology to be used.

This article will provide a detailed analysis of research hypotheses in a thesis, highlighting their significance and qualities. It will also explore different types of research hypotheses and provide illustrative examples. Additionally, a step-by-step guide to developing research hypotheses and methods for testing and validating them will be discussed. By the end of this article, readers will have a comprehensive understanding of research hypotheses and their role in a thesis.

Understanding Research Hypotheses in a Thesis

A research hypothesis is a statement of expectation or prediction that will be tested by research. In a thesis, a research hypothesis is formulated to address the research question or problem statement . It serves as a tentative answer or explanation to the research question. The research hypothesis guides the direction of the study and helps in determining the research design and methodology.

The research hypothesis is typically based on existing theories, previous research findings, or observations. It is formulated after a thorough review of the literature and understanding of the research area. A well-defined research hypothesis provides a clear focus for the study and helps in generating testable predictions. By testing the research hypothesis, researchers aim to gather evidence to support or reject the hypothesis. This process contributes to the advancement of knowledge in the field and helps in drawing meaningful conclusions.

Significance of Research Hypotheses in a Thesis

One of the key significance of research hypotheses is that they help in organizing and structuring the research study. By formulating a hypothesis, the researcher defines the specific research question and identifies the variables that will be investigated. This helps in narrowing down the scope of the study and ensures that the research is focused and targeted.

Moreover, research hypotheses provide a framework for data collection and analysis. They guide the researcher in selecting appropriate research methods , tools, and techniques to gather relevant data. The hypotheses also help in determining the statistical tests and analysis techniques that will be used to analyze the collected data.

Another significance of research hypotheses is that they contribute to the advancement of knowledge in a particular field. By formulating hypotheses and conducting research to test them, researchers are able to generate new insights, theories, and explanations. This contributes to the existing body of knowledge and helps in expanding the understanding of a specific phenomenon or topic.

Furthermore, research hypotheses are important for establishing the validity and reliability of the research findings. By formulating clear and testable hypotheses, researchers can ensure that their study is based on sound scientific principles. The hypotheses provide a basis for evaluating the accuracy and generalizability of the research results.

In addition, research hypotheses are essential for making informed decisions and recommendations based on the research findings. They help in drawing conclusions and making predictions about the relationship between variables. This information can be used to inform policy decisions, develop interventions, or guide future research in the field.

Qualities of an Effective Research Hypothesis in a Thesis

An effective research hypothesis in a thesis possesses several key qualities that contribute to its strength and validity. These qualities are essential for ensuring that the hypothesis can be tested and validated through empirical research. The following are some of the qualities that make a research hypothesis effective:

1. Specificity: A good research hypothesis is specific and clearly defines the variables and the relationship between them. It provides a clear direction for the research and allows for precise testing of the hypothesis.

2. Testability: An effective hypothesis in research is testable, meaning that it can be empirically examined and either supported or refuted through data analysis. It should be possible to design experiments or collect data that can provide evidence for or against the hypothesis.

3. Clarity: A research hypothesis should be written in clear and concise language. It should avoid ambiguity and ensure that the intended meaning is easily understood by the readers. Clear language helps in communicating the hypothesis effectively and facilitates its evaluation.

4. Falsifiability: A strong research hypothesis is falsifiable, which means that it is possible to prove it wrong. It should be formulated in a way that allows for the possibility of obtaining evidence that contradicts the hypothesis. This is important for the scientific process as it encourages critical thinking and the exploration of alternative explanations.

5. Relevance: An effective research hypothesis is relevant to the research question and the overall objectives of the study. It should address a significant gap in knowledge or contribute to the existing body of literature. A relevant hypothesis adds value to the research and increases its significance.

6. Novelty: A good research hypothesis is original and innovative. It should propose a new idea or approach that has not been extensively explored before. Novelty in the hypothesis increases the potential for new discoveries and contributes to the advancement of knowledge in the field.

7. Coherence: An effective research hypothesis should be coherent and consistent with existing theories, concepts, and empirical evidence. It should align with the current understanding of the topic and build upon previous research. Coherence ensures that the hypothesis is grounded in a solid foundation and enhances its credibility.

8. Measurability: A research hypothesis should be measurable, meaning that it can be quantitatively or qualitatively assessed. It should be possible to collect data or evidence that can be used to evaluate the hypothesis. Measurability allows for objective testing and increases the reliability of the research findings.

By incorporating these qualities into the formulation of a research hypothesis, researchers can enhance the validity and reliability of their study.

Different Types of Research Hypotheses in a Thesis

In a thesis, there are several different types of research hypotheses that can be used to test the relationship between variables. These hypotheses provide a framework for the research and guide the direction of the study. Understanding the different types of research hypotheses is essential for conducting a comprehensive and effective thesis.

Null Hypothesis

The null hypothesis is a statement that suggests there is no significant relationship between the variables being studied. It assumes that any observed differences or relationships are due to chance or random variation. The null hypothesis is denoted as H0 and is often used as a starting point for hypothesis testing.

Alternative Hypothesis

The alternative hypothesis, also known as the research hypothesis, is a statement that suggests there is a significant relationship between the variables being studied. It contradicts the null hypothesis and proposes that the observed differences or relationships are not due to chance.

Directional Hypothesis

A directional hypothesis is a specific type of alternative hypothesis that predicts the direction of the relationship between variables. It states that there is a positive or negative relationship between the variables, indicating the direction of the effect.

Non-Directional Hypothesis

In contrast to a directional hypothesis, a non-directional hypothesis does not predict the direction of the relationship between variables. It simply states that there is a relationship between the variables without specifying the direction of the effect.

Statistical Hypothesis

A statistical hypothesis is a hypothesis that is formulated based on statistical analysis. It involves using statistical tests to determine the likelihood of the observed data occurring under the null hypothesis.

Associative Hypothesis

An associative hypothesis suggests that there is a relationship between variables, but it does not imply causation. It indicates that changes in one variable are associated with changes in another variable.

Causal Hypothesis

A causal hypothesis proposes a cause-and-effect relationship between variables. It suggests that changes in one variable directly cause changes in another variable.

These different types of research hypotheses provide researchers with various options to explore and test the relationships between variables in a thesis. The choice of hypothesis depends on the research question, the nature of the variables, and the available data.

Illustrative Examples of Research Hypotheses in a Thesis

To better understand research hypotheses in a thesis, let’s explore some illustrative examples. These examples will demonstrate how hypotheses are formulated and tested in different research studies.

Example 1: Hypothesis for a study on the effects of exercise on weight loss:

Null Hypothesis (H0): There is no significant difference in weight loss between individuals who engage in regular exercise and those who do not.

Alternative Hypothesis (H1): Individuals who engage in regular exercise will experience greater weight loss compared to those who do not exercise.

Example 2: Hypothesis for a study on the impact of social media on self-esteem:

Null Hypothesis (H0): There is no significant relationship between social media usage and self-esteem levels.

Alternative Hypothesis (H1): Increased social media usage is associated with lower self-esteem levels.

Example 3: Hypothesis for a study on the effectiveness of a new teaching method in improving student performance:

Null Hypothesis (H0): There is no significant difference in student performance between the traditional teaching method and the new teaching method.

Alternative Hypothesis (H1): The new teaching method leads to improved student performance compared to the traditional teaching method.

These examples highlight the structure of research hypotheses, where the null hypothesis represents no effect or relationship, while the alternative hypothesis suggests the presence of an effect or relationship. It is important to note that these hypotheses are testable and can be analyzed using appropriate statistical methods.

Step-by-Step Guide to Developing Research Hypotheses in a Thesis

Developing a research hypothesis is a crucial step in the process of conducting a thesis. In this section, we will provide a step-by-step guide to developing research hypotheses in a thesis.

Step 1: Identify the Research Topic

The first step in developing a research hypothesis is to clearly identify the research topic. This involves understanding the research problem and determining the specific area of study.

Step 2: Conduct Preliminary Research

Once the research topic is identified, it is important to conduct preliminary research to gather relevant information. This helps in understanding the existing knowledge and identifying any gaps or areas that need further investigation.

Step 3: Formulate the Research Question

Based on the preliminary research, formulate a clear and concise research question. The research question should be specific and focused, addressing the research problem identified in step 1.

Step 4: Define the Variables

Identify the variables that will be studied in the research. Variables are the factors or concepts that are being measured or manipulated in the study. It is important to clearly define the variables to ensure the research hypothesis is specific and testable.

Step 5: Predict the Relationship and Outcome

The research hypothesis should propose a link between the variables and predict the expected outcome. It should clearly state the expected relationship between the variables and the anticipated result.

Step 6: Ensure Clarity and Conciseness

A good research hypothesis should be simple and concise, avoiding wordiness. It should be clear and free from ambiguity or assumptions about the readers’ knowledge. The hypothesis should also be observable and measurable.

Step 7: Validate the Hypothesis

Before finalizing the research hypothesis, it is important to validate it. This can be done through further research, literature review , or consultation with experts in the field. Validating the hypothesis ensures its relevance and novelty.

By following these step-by-step guidelines, researchers can develop effective research hypotheses for their theses. A well-developed hypothesis provides a solid foundation for the research and helps in generating meaningful results.

Methods for Testing and Validating Research Hypotheses in a Thesis

Hypothesis testing is a formal procedure for investigating our ideas about the world. It allows you to statistically test your predictions. The usual process is to make a hypothesis, create an experiment to test it, run the experiment, draw a conclusion, and then allow other researchers to replicate the study to validate the findings. There are several methods for testing and validating research hypotheses in a thesis.

Experimental Research

One common method is experimental research, where researchers manipulate variables and measure their effects on the dependent variable.

Observational Research

Another method is observational research, where researchers observe and record data without manipulating variables. This method is often used when it is not feasible or ethical to conduct experiments.

Survey Research

Survey research is another method that involves collecting data from a sample of individuals using questionnaires or interviews . This method is useful for studying attitudes, opinions, and behaviors.

Conducting Meta-analysis

In addition to these methods, researchers can also use existing data or conduct meta-analyses to test and validate research hypotheses. Existing data can be obtained from sources such as government databases, previous studies, or publicly available datasets. Meta-analysis involves combining the results of multiple studies to determine the overall effect size and to test the generalizability of findings across different populations and contexts. Once the data is collected, researchers can use statistical analysis techniques to analyze the data and test the research hypotheses. Common statistical tests include t-tests, analysis of variance (ANOVA), regression analysis, and chi-square tests.

The choice of statistical test depends on the research design, the type of data collected, and the specific research hypotheses being tested. It is important to note that testing and validating research hypotheses is an iterative process. Researchers may need to refine their hypotheses, modify their research design, or collect additional data based on the initial findings. By using rigorous methods for testing and validating research hypotheses, researchers can ensure the reliability and validity of their findings, contributing to the advancement of knowledge in their field.

In conclusion, research hypotheses are essential components of a thesis that guide the research process and contribute to the advancement of knowledge in a particular field. By formulating clear and testable hypotheses, researchers can make meaningful contributions to their field and address important research questions. It is important for researchers to carefully develop and validate their hypotheses to ensure the credibility and reliability of their findings.

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Research Questions & Hypotheses

Generally, in quantitative studies, reviewers expect hypotheses rather than research questions. However, both research questions and hypotheses serve different purposes and can be beneficial when used together.

Research Questions

Clarify the research’s aim (farrugia et al., 2010).

• Research often begins with an interest in a topic, but a deep understanding of the subject is crucial to formulate an appropriate research question.
• Descriptive: “What factors most influence the academic achievement of senior high school students?”
• Comparative: “What is the performance difference between teaching methods A and B?”
• Relationship-based: “What is the relationship between self-efficacy and academic achievement?”
• Increasing knowledge about a subject can be achieved through systematic literature reviews, in-depth interviews with patients (and proxies), focus groups, and consultations with field experts.
• Some funding bodies, like the Canadian Institute for Health Research, recommend conducting a systematic review or a pilot study before seeking grants for full trials.
• The presence of multiple research questions in a study can complicate the design, statistical analysis, and feasibility.
• It’s advisable to focus on a single primary research question for the study.
• The primary question, clearly stated at the end of a grant proposal’s introduction, usually specifies the study population, intervention, and other relevant factors.
• The FINER criteria underscore aspects that can enhance the chances of a successful research project, including specifying the population of interest, aligning with scientific and public interest, clinical relevance, and contribution to the field, while complying with ethical and national research standards.

• The P ICOT approach is crucial in developing the study’s framework and protocol, influencing inclusion and exclusion criteria and identifying patient groups for inclusion.

• Defining the specific population, intervention, comparator, and outcome helps in selecting the right outcome measurement tool.
• The more precise the population definition and stricter the inclusion and exclusion criteria, the more significant the impact on the interpretation, applicability, and generalizability of the research findings.
• A restricted study population enhances internal validity but may limit the study’s external validity and generalizability to clinical practice.
• A broadly defined study population may better reflect clinical practice but could increase bias and reduce internal validity.
• An inadequately formulated research question can negatively impact study design, potentially leading to ineffective outcomes and affecting publication prospects.

Checklist: Good research questions for social science projects (Panke, 2018)

Research Hypotheses

Present the researcher’s predictions based on specific statements.

• These statements define the research problem or issue and indicate the direction of the researcher’s predictions.
• Formulating the research question and hypothesis from existing data (e.g., a database) can lead to multiple statistical comparisons and potentially spurious findings due to chance.
• The research or clinical hypothesis, derived from the research question, shapes the study’s key elements: sampling strategy, intervention, comparison, and outcome variables.
• Hypotheses can express a single outcome or multiple outcomes.
• After statistical testing, the null hypothesis is either rejected or not rejected based on whether the study’s findings are statistically significant.
• Hypothesis testing helps determine if observed findings are due to true differences and not chance.
• Hypotheses can be 1-sided (specific direction of difference) or 2-sided (presence of a difference without specifying direction).
• 2-sided hypotheses are generally preferred unless there’s a strong justification for a 1-sided hypothesis.
• A solid research hypothesis, informed by a good research question, influences the research design and paves the way for defining clear research objectives.

Types of Research Hypothesis

• In a Y-centered research design, the focus is on the dependent variable (DV) which is specified in the research question. Theories are then used to identify independent variables (IV) and explain their causal relationship with the DV.
• Example: “An increase in teacher-led instructional time (IV) is likely to improve student reading comprehension scores (DV), because extensive guided practice under expert supervision enhances learning retention and skill mastery.”
• Hypothesis Explanation: The dependent variable (student reading comprehension scores) is the focus, and the hypothesis explores how changes in the independent variable (teacher-led instructional time) affect it.
• In X-centered research designs, the independent variable is specified in the research question. Theories are used to determine potential dependent variables and the causal mechanisms at play.
• Example: “Implementing technology-based learning tools (IV) is likely to enhance student engagement in the classroom (DV), because interactive and multimedia content increases student interest and participation.”
• Hypothesis Explanation: The independent variable (technology-based learning tools) is the focus, with the hypothesis exploring its impact on a potential dependent variable (student engagement).
• Probabilistic hypotheses suggest that changes in the independent variable are likely to lead to changes in the dependent variable in a predictable manner, but not with absolute certainty.
• Example: “The more teachers engage in professional development programs (IV), the more their teaching effectiveness (DV) is likely to improve, because continuous training updates pedagogical skills and knowledge.”
• Hypothesis Explanation: This hypothesis implies a probable relationship between the extent of professional development (IV) and teaching effectiveness (DV).
• Deterministic hypotheses state that a specific change in the independent variable will lead to a specific change in the dependent variable, implying a more direct and certain relationship.
• Example: “If the school curriculum changes from traditional lecture-based methods to project-based learning (IV), then student collaboration skills (DV) are expected to improve because project-based learning inherently requires teamwork and peer interaction.”
• Hypothesis Explanation: This hypothesis presumes a direct and definite outcome (improvement in collaboration skills) resulting from a specific change in the teaching method.
• Example : “Students who identify as visual learners will score higher on tests that are presented in a visually rich format compared to tests presented in a text-only format.”
• Explanation : This hypothesis aims to describe the potential difference in test scores between visual learners taking visually rich tests and text-only tests, without implying a direct cause-and-effect relationship.
• Example : “Teaching method A will improve student performance more than method B.”
• Explanation : This hypothesis compares the effectiveness of two different teaching methods, suggesting that one will lead to better student performance than the other. It implies a direct comparison but does not necessarily establish a causal mechanism.
• Example : “Students with higher self-efficacy will show higher levels of academic achievement.”
• Explanation : This hypothesis predicts a relationship between the variable of self-efficacy and academic achievement. Unlike a causal hypothesis, it does not necessarily suggest that one variable causes changes in the other, but rather that they are related in some way.

Tips for developing research questions and hypotheses for research studies

• Perform a systematic literature review (if one has not been done) to increase knowledge and familiarity with the topic and to assist with research development.
• Learn about current trends and technological advances on the topic.
• Seek careful input from experts, mentors, colleagues, and collaborators to refine your research question as this will aid in developing the research question and guide the research study.
• Use the FINER criteria in the development of the research question.
• Ensure that the research question follows PICOT format.
• Develop a research hypothesis from the research question.
• Ensure that the research question and objectives are answerable, feasible, and clinically relevant.

If your research hypotheses are derived from your research questions, particularly when multiple hypotheses address a single question, it’s recommended to use both research questions and hypotheses. However, if this isn’t the case, using hypotheses over research questions is advised. It’s important to note these are general guidelines, not strict rules. If you opt not to use hypotheses, consult with your supervisor for the best approach.

Farrugia, P., Petrisor, B. A., Farrokhyar, F., & Bhandari, M. (2010). Practical tips for surgical research: Research questions, hypotheses and objectives.  Canadian journal of surgery. Journal canadien de chirurgie ,  53 (4), 278–281.

Hulley, S. B., Cummings, S. R., Browner, W. S., Grady, D., & Newman, T. B. (2007). Designing clinical research. Philadelphia.

Panke, D. (2018). Research design & method selection: Making good choices in the social sciences.  Research Design & Method Selection , 1-368.

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Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing  is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.  

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

• Clear and precise
• Capable of being tested
• Able to relate to a variable
• Stated in simple terms
• Consistent with known facts
• Limited in scope and specific
• Tested in a limited timeframe
• Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A  null hypothesis  is a hypothesis when there is no significant relationship between the dependent and the participants’ independent  variables . 

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

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How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to  gather the data  obtained through a large number of samples from a specific population. 

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many  types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study 

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance. 

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

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Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the  significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided. 

If the significance level is minimum, then it prevents the researchers from false claims. 

The significance level is denoted by  P,  and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the  outcomes of your study . You need to ensure whether you have met the objectives of your research or not. 

In the discussion section and  conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis? 

Always remember that you either conclude to reject Ho in favor of Haor   do not reject Ho . It would help if you never rejected  Ha  or even  accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude  reject Ho in favor of Haor   do not reject Ho,  then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

• One-Sample Test : Compare sample data to a known population value.
• Two-Sample Test : Compare means between two sample groups.
• ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

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Experimental research refers to the experiments conducted in the laboratory or under observation in controlled conditions. Here is all you need to know about experimental research.

In historical research, a researcher collects and analyse the data, and explain the events that occurred in the past to test the truthfulness of observations.

A meta-analysis is a formal, epidemiological, quantitative study design that uses statistical methods to generalise the findings of the selected independent studies.

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5.5 Introduction to Hypothesis Tests

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter.

Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealership advertises that its new small truck gets 35 miles per gallon on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that female managers in their company earn an average of $60,000 per year. A statistician may want to make a decision about or evaluate these claims. A hypothesis test can be used to do this.

A hypothesis test involves collecting data from a sample and evaluating the data. Then the statistician makes a decision as to whether or not there is sufficient evidence to reject the null hypothesis based upon analyses of the data.

In this section, you will conduct hypothesis tests on single means when the population standard deviation is known.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will perform some variation of these steps:

• Define hypotheses.
• Collect and/or use the sample data to determine the correct distribution to use.
• Calculate test statistic.
• Make a decision.
• Write a conclusion.

Defining your hypotheses

The actual test begins by considering two hypotheses: the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis ( H 0 ) is often a statement of the accepted historical value or norm. This is your starting point that you must assume from the beginning in order to show an effect exists.

The alternative hypothesis ( H a ) is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision . There are two options for a decision. They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

The following table shows mathematical symbols used in H 0 and H a :

NOTE: H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol in the alternative hypothesis depends on the wording of the hypothesis test. Despite this, many researchers may use =, ≤, or ≥ in the null hypothesis. This practice is acceptable because our only decision is to reject or not reject the null hypothesis.

We want to test whether the mean GPA of students in American colleges is 2.0 (out of 4.0). The null hypothesis is: H 0 : μ = 2.0. What is the alternative hypothesis?

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

Using the Sample to Test the Null Hypothesis

Once you have defined your hypotheses, the next step in the process is to collect sample data. In a classroom context, the data or summary statistics will usually be given to you.

Then you will have to determine the correct distribution to perform the hypothesis test, given the assumptions you are able to make about the situation. Right now, we are demonstrating these ideas in a test for a mean when the population standard deviation is known using the z distribution. We will see other scenarios in the future.

Calculating a Test Statistic

Next you will start evaluating the data. This begins with calculating your test statistic , which is a measure of the distance between what you observed and what you are assuming to be true. In this context, your test statistic, z ο , quantifies the number of standard deviations between the sample mean, x, and the population mean, µ . Calculating the test statistic is analogous to the previously discussed process of standardizing observations with z -scores:

where µ o   is the value assumed to be true in the null hypothesis.

Making a Decision

Once you have your test statistic, there are two methods to use it to make your decision:

• Critical value method (discussed further in later chapters)
• p -value method (our current focus)

p -Value Method

To find a p -value , we use the test statistic to calculate the actual probability of getting the test result. Formally, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.

A large p -value calculated from the data indicates that we should not reject the null hypothesis. The smaller the p -value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis. We would reject the null hypothesis if the evidence is strongly against it.

Draw a graph that shows the p -value. The hypothesis test is easier to perform if you use a graph because you see the problem more clearly.

Suppose a baker claims that his bread height is more than 15 cm on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes ten loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm and the distribution of heights is normal.

The null hypothesis could be H 0 : μ ≤ 15.

The alternate hypothesis is H a : μ > 15.

The words “is more than” calls for the use of the > symbol, so “ μ > 15″ goes into the alternate hypothesis. The null hypothesis must contradict the alternate hypothesis.

Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm). Then, is the mean height (17 cm) calculated from the sample unexpectedly large? The hypothesis test works by asking how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm.

This means that the p -value is the probability that a sample mean is the same or greater than 17 cm when the population mean is, in fact, 15 cm. We can calculate this probability using the normal distribution for means.

A p -value of approximately zero tells us that it is highly unlikely that a loaf of bread rises no more than 15 cm on average. That is, almost 0% of all loaves of bread would be at least as high as 17 cm purely by CHANCE had the population mean height really been 15 cm. Because the outcome of 17 cm is so unlikely (meaning it is happening NOT by chance alone), we conclude that the evidence is strongly against the null hypothesis that the mean height would be at most 15 cm. There is sufficient evidence that the true mean height for the population of the baker’s loaves of bread is greater than 15 cm.

A normal distribution has a standard deviation of one. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5.

Find the p -value.

Decision and Conclusion

A systematic way to decide whether to reject or not reject the null hypothesis is to compare the p -value and a preset or preconceived α (also called a significance level ). A preset α is the probability of a type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem. If there is no given preconceived α , then use α = 0.05.

When you make a decision to reject or not reject H 0 , do as follows:

• If α > p -value, reject H 0 . The results of the sample data are statistically significant . You can say there is sufficient evidence to conclude that H 0 is an incorrect belief and that the alternative hypothesis, H a , may be correct.
• If α ≤ p -value, fail to reject H 0 . The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, H a , may be correct.

After you make your decision, write a thoughtful conclusion in the context of the scenario incorporating the hypotheses.

NOTE: When you “do not reject H 0 ,” it does not mean that you should believe that H 0 is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of H o .

When using the p -value to evaluate a hypothesis test, the following rhymes can come in handy:

If the p -value is low, the null must go.

If the p -value is high, the null must fly.

This memory aid relates a p -value less than the established alpha (“the p -value is low”) as rejecting the null hypothesis and, likewise, relates a p -value higher than the established alpha (“the p -value is high”) as not rejecting the null hypothesis.

Fill in the blanks:

• Reject the null hypothesis when              .
• The results of the sample data             .
• Do not reject the null when hypothesis when             .

It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:

• H 0 : p = 0.50, H a : p > 0.50
• p -value = 0.025

Interpret the results and state a conclusion in simple, non-technical terms.

Click here for more multimedia resources, including podcasts, videos, lecture notes, and worked examples.

Figure References

Figure 5.11: Alora Griffiths (2019). dalmatian puppy near man in blue shorts kneeling. Unsplash license. https://unsplash.com/photos/7aRQZtLsvqw

Figure 5.13: Kindred Grey (2020). Bread height probability. CC BY-SA 4.0.

A decision-making procedure for determining whether sample evidence supports a hypothesis

The claim that is assumed to be true and is tested in a hypothesis test

A working hypothesis that is contradictory to the null hypothesis

A measure of the difference between observations and the hypothesized (or claimed) value

The probability that an event will occur, assuming the null hypothesis is true

Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α

Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis

Significant Statistics Copyright © 2024 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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6 Week 5 Introduction to Hypothesis Testing Reading

An introduction to hypothesis testing.

What are you interested in learning about? Perhaps you’d like to know if there is a difference in average final grade between two different versions of a college class? Does the Fort Lewis women’s soccer team score more goals than the national Division II women’s average? Which outdoor sport do Fort Lewis students prefer the most?  Do the pine trees on campus differ in mean height from the aspen trees? For all of these questions, we can collect a sample, analyze the data, then make a statistical inference based on the analysis.  This means determining whether we have enough evidence to reject our null hypothesis (what was originally assumed to be true, until we prove otherwise). The process is called hypothesis testing .

A really good Khan Academy video to introduce the hypothesis test process: Khan Academy Hypothesis Testing . As you watch, please don’t get caught up in the calculations, as we will use SPSS to do these calculations.  We will also use SPSS p-values, instead of the referenced Z-table, to make statistical decisions.

The Six-Step Process

Hypothesis testing requires very specific, detailed steps.  Think of it as a mathematical lab report where you have to write out your work in a particular way.  There are six steps that we will follow for ALL of the hypothesis tests that we learn this semester.

1. Research Question

All hypothesis tests start with a research question.  This is literally a question that includes what you are trying to prove, like the examples earlier:  Which outdoor sport do Fort Lewis students prefer the most? Is there sufficient evidence to show that the Fort Lewis women’s soccer team scores more goals than the national Division 2 women’s average?

In this step, besides literally being a question, you’ll want to include:

• mention of your variable(s)
• wording specific to the type of test that you’ll be conducting (mean, mean difference, relationship, pattern)
• specific wording that indicates directionality (are you looking for a ‘difference’, are you looking for something to be ‘more than’ or ‘less than’ something else, or are you comparing one pattern to another?)

Consider this research question: Do the pine trees on campus differ in mean height from the aspen trees?

• The wording of this research question clearly mentions the variables being studied. The independent variable is the type of tree (pine or aspen), and these trees are having their heights compared, so the dependent variable is height.
• ‘Mean’ is mentioned, so this indicates a test with a quantitative dependent variable.
• The question also asks if the tree heights ‘differ’. This specific word indicates that the test being performed is a two-tailed (i.e. non-directional) test. More about the meaning of one/two-tailed will come later.

2. Statistical Hypotheses

A statistical hypothesis test has a null hypothesis, the status quo, what we assume to be true.  Notation is H 0, read as “H naught”.  The alternative hypothesis is what you are trying to prove (mentioned in your research question), H 1 or H A .  All hypothesis tests must include a null and an alternative hypothesis.  We also note which hypothesis test is being done in this step.

The notation for your statistical hypotheses will vary depending on the type of test that you’re doing. Writing statistical hypotheses is NOT the same as most scientific hypotheses. You are not writing sentences explaining what you think will happen in the study. Here is an example of what statistical hypotheses look like using the research question: Do the pine trees on campus differ in mean height from the aspen trees?

3. Decision Rule

In this step, you state which alpha value you will use, and when appropriate, the directionality, or tail, of the test.  You also write a statement: “I will reject the null hypothesis if p < alpha” (insert actual alpha value here).  In this introductory class, alpha is the level of significance, how willing we are to make the wrong statistical decision, and it will be set to 0.05 or 0.01.

Example of a Decision Rule:

Let alpha=0.01, two-tailed. I will reject the null hypothesis if p<0.01.

4. Assumptions, Analysis and Calculations

Quite a bit goes on in this step.  Assumptions for the particular hypothesis test must be done.  SPSS will be used to create appropriate graphs, and test output tables. Where appropriate, calculations of the test’s effect size will also be done in this step.

All hypothesis tests have assumptions that we hope to meet. For example, tests with a quantitative dependent variable consider a histogram(s) to check if the distribution is normal, and whether there are any obvious outliers. Each hypothesis test has different assumptions, so it is important to pay attention to the specific test’s requirements.

Required SPSS output will also depend on the test.

5. Statistical Decision

It is in Step 5 that we determine if we have enough statistical evidence to reject our null hypothesis.  We will consult the SPSS p-value and compare to our chosen alpha (from Step 3: Decision Rule).

Put very simply, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample. The p -value can also be thought of as the probability that the results (from the sample) that we are seeing are solely due to chance. This concept will be discussed in much further detail in the class notes.

Based on this numerical comparison between the p-value and alpha, we’ll either reject or retain our null hypothesis.  Note: You may NEVER ‘accept’ the null hypothesis. This is because it is impossible to prove a null hypothesis to be true.

Retaining the null means that you just don’t have enough evidence to prove your alternative hypothesis to be true, so you fall back to your null. (You retain the null when p is greater than or equal to alpha.)

Rejecting the null means that you did find enough evidence to prove your alternative hypothesis as true. (You reject the null when p is less than alpha.)

Example of a Statistical Decision:

Retain the null hypothesis, because p=0.12 > alpha=0.01.

The p-value will come from SPSS output, and the alpha will have already been determined back in Step 3. You must be very careful when you compare the decimal values of the p-value and alpha. If, for example, you mistakenly think that p=0.12 < alpha=0.01, then you will make the incorrect statistical decision, which will likely lead to an incorrect interpretation of the study’s findings.

6. Interpretation

The interpretation is where you write up your findings. The specifics will vary depending on the type of hypothesis test you performed, but you will always include a plain English, contextual conclusion of what your study found (i.e. what it means to reject or retain the null hypothesis in that particular study).  You’ll have statistics that you quote to support your decision.  Some of the statistics will need to be written in APA style citation (the American Psychological Association style of citation).  For some hypothesis tests, you’ll also include an interpretation of the effect size.

Some hypothesis tests will also require an additional (non-Parametric) test after the completion of your original test, if the test’s assumptions have not been met. These tests are also call “Post-Hoc tests”.

As previously stated, hypothesis testing is a very detailed process. Do not be concerned if you have read through all of the steps above, and have many questions (and are possibly very confused). It will take time, and a lot of practice to learn and apply these steps!

This Reading is just meant as an overview of hypothesis testing. Much more information is forthcoming in the various sets of Notes about the specifics needed in each of these steps. The Hypothesis Test Checklist will be a critical resource for you to refer to during homeworks and tests.

Student Course Learning Objectives

4.  Choose, administer and interpret the correct tests based on the situation, including identification of appropriate sampling and potential errors

c. Choose the appropriate hypothesis test given a situation

d. Describe the meaning and uses of alpha and p-values

e. Write the appropriate null and alternative hypotheses, including whether the alternative should be one-sided or two-sided

f. Determine and calculate the appropriate test statistic (e.g. z-test, multiple t-tests, Chi-Square, ANOVA)

g. Determine and interpret effect sizes.

h. Interpret results of a hypothesis test

• Use technology in the statistical analysis of data
• Communicate in writing the results of statistical analyses of data

Attributions

Adapted from “Week 5 Introduction to Hypothesis Testing Reading” by Sherri Spriggs and Sandi Dang is licensed under CC BY-NC-SA 4.0 .

Math 132 Introduction to Statistics Readings Copyright © by Sherri Spriggs is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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• Knowledge Base

Methodology

Research Methods | Definitions, Types, Examples

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

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

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

Second, decide how you will analyze the data .

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

Table of contents

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

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

Qualitative vs. quantitative data

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

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

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

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

Primary vs. secondary research

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

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

Descriptive vs. experimental data

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

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

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

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

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

Qualitative analysis methods

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

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

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

Quantitative analysis methods

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

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

• During an experiment .
• Using probability sampling methods .

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

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

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

Research bias

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

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

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

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

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

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

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

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

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

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

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

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

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Research Methods In Psychology

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

Research methods in psychology are systematic procedures used to observe, describe, predict, and explain behavior and mental processes. They include experiments, surveys, case studies, and naturalistic observations, ensuring data collection is objective and reliable to understand and explain psychological phenomena.

Hypotheses are statements about the prediction of the results, that can be verified or disproved by some investigation.

There are four types of hypotheses :

• Null Hypotheses (H0 ) – these predict that no difference will be found in the results between the conditions. Typically these are written ‘There will be no difference…’
• Alternative Hypotheses (Ha or H1) – these predict that there will be a significant difference in the results between the two conditions. This is also known as the experimental hypothesis.
• One-tailed (directional) hypotheses – these state the specific direction the researcher expects the results to move in, e.g. higher, lower, more, less. In a correlation study, the predicted direction of the correlation can be either positive or negative.
• Two-tailed (non-directional) hypotheses – these state that a difference will be found between the conditions of the independent variable but does not state the direction of a difference or relationship. Typically these are always written ‘There will be a difference ….’

All research has an alternative hypothesis (either a one-tailed or two-tailed) and a corresponding null hypothesis.

Once the research is conducted and results are found, psychologists must accept one hypothesis and reject the other. 

So, if a difference is found, the Psychologist would accept the alternative hypothesis and reject the null.  The opposite applies if no difference is found.

Sampling techniques

Sampling is the process of selecting a representative group from the population under study.

A sample is the participants you select from a target population (the group you are interested in) to make generalizations about.

Representative means the extent to which a sample mirrors a researcher’s target population and reflects its characteristics.

Generalisability means the extent to which their findings can be applied to the larger population of which their sample was a part.

• Volunteer sample : where participants pick themselves through newspaper adverts, noticeboards or online.
• Opportunity sampling : also known as convenience sampling , uses people who are available at the time the study is carried out and willing to take part. It is based on convenience.
• Random sampling : when every person in the target population has an equal chance of being selected. An example of random sampling would be picking names out of a hat.
• Systematic sampling : when a system is used to select participants. Picking every Nth person from all possible participants. N = the number of people in the research population / the number of people needed for the sample.
• Stratified sampling : when you identify the subgroups and select participants in proportion to their occurrences.
• Snowball sampling : when researchers find a few participants, and then ask them to find participants themselves and so on.
• Quota sampling : when researchers will be told to ensure the sample fits certain quotas, for example they might be told to find 90 participants, with 30 of them being unemployed.

Experiments always have an independent and dependent variable .

• The independent variable is the one the experimenter manipulates (the thing that changes between the conditions the participants are placed into). It is assumed to have a direct effect on the dependent variable.
• The dependent variable is the thing being measured, or the results of the experiment.

Operationalization of variables means making them measurable/quantifiable. We must use operationalization to ensure that variables are in a form that can be easily tested.

For instance, we can’t really measure ‘happiness’, but we can measure how many times a person smiles within a two-hour period. 

By operationalizing variables, we make it easy for someone else to replicate our research. Remember, this is important because we can check if our findings are reliable.

Extraneous variables are all variables which are not independent variable but could affect the results of the experiment.

It can be a natural characteristic of the participant, such as intelligence levels, gender, or age for example, or it could be a situational feature of the environment such as lighting or noise.

Demand characteristics are a type of extraneous variable that occurs if the participants work out the aims of the research study, they may begin to behave in a certain way.

For example, in Milgram’s research , critics argued that participants worked out that the shocks were not real and they administered them as they thought this was what was required of them. 

Extraneous variables must be controlled so that they do not affect (confound) the results.

Randomly allocating participants to their conditions or using a matched pairs experimental design can help to reduce participant variables. 

Situational variables are controlled by using standardized procedures, ensuring every participant in a given condition is treated in the same way

Experimental Design

Experimental design refers to how participants are allocated to each condition of the independent variable, such as a control or experimental group.

• Independent design ( between-groups design ): each participant is selected for only one group. With the independent design, the most common way of deciding which participants go into which group is by means of randomization. 
• Matched participants design : each participant is selected for only one group, but the participants in the two groups are matched for some relevant factor or factors (e.g. ability; sex; age).
• Repeated measures design ( within groups) : each participant appears in both groups, so that there are exactly the same participants in each group.
• The main problem with the repeated measures design is that there may well be order effects. Their experiences during the experiment may change the participants in various ways.
• They may perform better when they appear in the second group because they have gained useful information about the experiment or about the task. On the other hand, they may perform less well on the second occasion because of tiredness or boredom.
• Counterbalancing is the best way of preventing order effects from disrupting the findings of an experiment, and involves ensuring that each condition is equally likely to be used first and second by the participants.

If we wish to compare two groups with respect to a given independent variable, it is essential to make sure that the two groups do not differ in any other important way. 

Experimental Methods

All experimental methods involve an iv (independent variable) and dv (dependent variable)..

The researcher decides where the experiment will take place, at what time, with which participants, in what circumstances,  using a standardized procedure.

• Field experiments are conducted in the everyday (natural) environment of the participants. The experimenter still manipulates the IV, but in a real-life setting. It may be possible to control extraneous variables, though such control is more difficult than in a lab experiment.
• Natural experiments are when a naturally occurring IV is investigated that isn’t deliberately manipulated, it exists anyway. Participants are not randomly allocated, and the natural event may only occur rarely.

Case studies are in-depth investigations of a person, group, event, or community. It uses information from a range of sources, such as from the person concerned and also from their family and friends.

Many techniques may be used such as interviews, psychological tests, observations and experiments. Case studies are generally longitudinal: in other words, they follow the individual or group over an extended period of time. 

Case studies are widely used in psychology and among the best-known ones carried out were by Sigmund Freud . He conducted very detailed investigations into the private lives of his patients in an attempt to both understand and help them overcome their illnesses.

Case studies provide rich qualitative data and have high levels of ecological validity. However, it is difficult to generalize from individual cases as each one has unique characteristics.

Correlational Studies

Correlation means association; it is a measure of the extent to which two variables are related. One of the variables can be regarded as the predictor variable with the other one as the outcome variable.

Correlational studies typically involve obtaining two different measures from a group of participants, and then assessing the degree of association between the measures. 

The predictor variable can be seen as occurring before the outcome variable in some sense. It is called the predictor variable, because it forms the basis for predicting the value of the outcome variable.

Relationships between variables can be displayed on a graph or as a numerical score called a correlation coefficient.

• If an increase in one variable tends to be associated with an increase in the other, then this is known as a positive correlation .
• If an increase in one variable tends to be associated with a decrease in the other, then this is known as a negative correlation .
• A zero correlation occurs when there is no relationship between variables.

After looking at the scattergraph, if we want to be sure that a significant relationship does exist between the two variables, a statistical test of correlation can be conducted, such as Spearman’s rho.

The test will give us a score, called a correlation coefficient . This is a value between 0 and 1, and the closer to 1 the score is, the stronger the relationship between the variables. This value can be both positive e.g. 0.63, or negative -0.63.

A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. A correlation only shows if there is a relationship between variables.

Correlation does not always prove causation, as a third variable may be involved. 

Interview Methods

Interviews are commonly divided into two types: structured and unstructured.

A fixed, predetermined set of questions is put to every participant in the same order and in the same way. 

Responses are recorded on a questionnaire, and the researcher presets the order and wording of questions, and sometimes the range of alternative answers.

The interviewer stays within their role and maintains social distance from the interviewee.

There are no set questions, and the participant can raise whatever topics he/she feels are relevant and ask them in their own way. Questions are posed about participants’ answers to the subject

Unstructured interviews are most useful in qualitative research to analyze attitudes and values.

Though they rarely provide a valid basis for generalization, their main advantage is that they enable the researcher to probe social actors’ subjective point of view. 

Questionnaire Method

Questionnaires can be thought of as a kind of written interview. They can be carried out face to face, by telephone, or post.

The choice of questions is important because of the need to avoid bias or ambiguity in the questions, ‘leading’ the respondent or causing offense.

• Open questions are designed to encourage a full, meaningful answer using the subject’s own knowledge and feelings. They provide insights into feelings, opinions, and understanding. Example: “How do you feel about that situation?”
• Closed questions can be answered with a simple “yes” or “no” or specific information, limiting the depth of response. They are useful for gathering specific facts or confirming details. Example: “Do you feel anxious in crowds?”

Its other practical advantages are that it is cheaper than face-to-face interviews and can be used to contact many respondents scattered over a wide area relatively quickly.

Observations

There are different types of observation methods :

• Covert observation is where the researcher doesn’t tell the participants they are being observed until after the study is complete. There could be ethical problems or deception and consent with this particular observation method.
• Overt observation is where a researcher tells the participants they are being observed and what they are being observed for.
• Controlled : behavior is observed under controlled laboratory conditions (e.g., Bandura’s Bobo doll study).
• Natural : Here, spontaneous behavior is recorded in a natural setting.
• Participant : Here, the observer has direct contact with the group of people they are observing. The researcher becomes a member of the group they are researching.  
• Non-participant (aka “fly on the wall): The researcher does not have direct contact with the people being observed. The observation of participants’ behavior is from a distance

Pilot Study

A pilot  study is a small scale preliminary study conducted in order to evaluate the feasibility of the key s teps in a future, full-scale project.

A pilot study is an initial run-through of the procedures to be used in an investigation; it involves selecting a few people and trying out the study on them. It is possible to save time, and in some cases, money, by identifying any flaws in the procedures designed by the researcher.

A pilot study can help the researcher spot any ambiguities (i.e. unusual things) or confusion in the information given to participants or problems with the task devised.

Sometimes the task is too hard, and the researcher may get a floor effect, because none of the participants can score at all or can complete the task – all performances are low.

The opposite effect is a ceiling effect, when the task is so easy that all achieve virtually full marks or top performances and are “hitting the ceiling”.

Research Design

In cross-sectional research , a researcher compares multiple segments of the population at the same time

Sometimes, we want to see how people change over time, as in studies of human development and lifespan. Longitudinal research is a research design in which data-gathering is administered repeatedly over an extended period of time.

In cohort studies , the participants must share a common factor or characteristic such as age, demographic, or occupation. A cohort study is a type of longitudinal study in which researchers monitor and observe a chosen population over an extended period.

Triangulation means using more than one research method to improve the study’s validity.

Reliability

Reliability is a measure of consistency, if a particular measurement is repeated and the same result is obtained then it is described as being reliable.

• Test-retest reliability :  assessing the same person on two different occasions which shows the extent to which the test produces the same answers.
• Inter-observer reliability : the extent to which there is an agreement between two or more observers.

Meta-Analysis

Meta-analysis is a statistical procedure used to combine and synthesize findings from multiple independent studies to estimate the average effect size for a particular research question.

Meta-analysis goes beyond traditional narrative reviews by using statistical methods to integrate the results of several studies, leading to a more objective appraisal of the evidence.

This is done by looking through various databases, and then decisions are made about what studies are to be included/excluded.

• Strengths : Increases the conclusions’ validity as they’re based on a wider range.
• Weaknesses : Research designs in studies can vary, so they are not truly comparable.

Peer Review

A researcher submits an article to a journal. The choice of the journal may be determined by the journal’s audience or prestige.

The journal selects two or more appropriate experts (psychologists working in a similar field) to peer review the article without payment. The peer reviewers assess: the methods and designs used, originality of the findings, the validity of the original research findings and its content, structure and language.

Feedback from the reviewer determines whether the article is accepted. The article may be: Accepted as it is, accepted with revisions, sent back to the author to revise and re-submit or rejected without the possibility of submission.

The editor makes the final decision whether to accept or reject the research report based on the reviewers comments/ recommendations.

Peer review is important because it prevent faulty data from entering the public domain, it provides a way of checking the validity of findings and the quality of the methodology and is used to assess the research rating of university departments.

Peer reviews may be an ideal, whereas in practice there are lots of problems. For example, it slows publication down and may prevent unusual, new work being published. Some reviewers might use it as an opportunity to prevent competing researchers from publishing work.

Some people doubt whether peer review can really prevent the publication of fraudulent research.

The advent of the internet means that a lot of research and academic comment is being published without official peer reviews than before, though systems are evolving on the internet where everyone really has a chance to offer their opinions and police the quality of research.

Types of Data

• Quantitative data is numerical data e.g. reaction time or number of mistakes. It represents how much or how long, how many there are of something. A tally of behavioral categories and closed questions in a questionnaire collect quantitative data.
• Qualitative data is virtually any type of information that can be observed and recorded that is not numerical in nature and can be in the form of written or verbal communication. Open questions in questionnaires and accounts from observational studies collect qualitative data.
• Primary data is first-hand data collected for the purpose of the investigation.
• Secondary data is information that has been collected by someone other than the person who is conducting the research e.g. taken from journals, books or articles.

Validity means how well a piece of research actually measures what it sets out to, or how well it reflects the reality it claims to represent.

Validity is whether the observed effect is genuine and represents what is actually out there in the world.

• Concurrent validity is the extent to which a psychological measure relates to an existing similar measure and obtains close results. For example, a new intelligence test compared to an established test.
• Face validity : does the test measure what it’s supposed to measure ‘on the face of it’. This is done by ‘eyeballing’ the measuring or by passing it to an expert to check.
• Ecological validit y is the extent to which findings from a research study can be generalized to other settings / real life.
• Temporal validity is the extent to which findings from a research study can be generalized to other historical times.

Features of Science

• Paradigm – A set of shared assumptions and agreed methods within a scientific discipline.
• Paradigm shift – The result of the scientific revolution: a significant change in the dominant unifying theory within a scientific discipline.
• Objectivity – When all sources of personal bias are minimised so not to distort or influence the research process.
• Empirical method – Scientific approaches that are based on the gathering of evidence through direct observation and experience.
• Replicability – The extent to which scientific procedures and findings can be repeated by other researchers.
• Falsifiability – The principle that a theory cannot be considered scientific unless it admits the possibility of being proved untrue.

Statistical Testing

A significant result is one where there is a low probability that chance factors were responsible for any observed difference, correlation, or association in the variables tested.

If our test is significant, we can reject our null hypothesis and accept our alternative hypothesis.

If our test is not significant, we can accept our null hypothesis and reject our alternative hypothesis. A null hypothesis is a statement of no effect.

In Psychology, we use p < 0.05 (as it strikes a balance between making a type I and II error) but p < 0.01 is used in tests that could cause harm like introducing a new drug.

A type I error is when the null hypothesis is rejected when it should have been accepted (happens when a lenient significance level is used, an error of optimism).

A type II error is when the null hypothesis is accepted when it should have been rejected (happens when a stringent significance level is used, an error of pessimism).

Ethical Issues

• Informed consent is when participants are able to make an informed judgment about whether to take part. It causes them to guess the aims of the study and change their behavior.
• To deal with it, we can gain presumptive consent or ask them to formally indicate their agreement to participate but it may invalidate the purpose of the study and it is not guaranteed that the participants would understand.
• Deception should only be used when it is approved by an ethics committee, as it involves deliberately misleading or withholding information. Participants should be fully debriefed after the study but debriefing can’t turn the clock back.
• All participants should be informed at the beginning that they have the right to withdraw if they ever feel distressed or uncomfortable.
• It causes bias as the ones that stayed are obedient and some may not withdraw as they may have been given incentives or feel like they’re spoiling the study. Researchers can offer the right to withdraw data after participation.
• Participants should all have protection from harm . The researcher should avoid risks greater than those experienced in everyday life and they should stop the study if any harm is suspected. However, the harm may not be apparent at the time of the study.
• Confidentiality concerns the communication of personal information. The researchers should not record any names but use numbers or false names though it may not be possible as it is sometimes possible to work out who the researchers were.

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Speaker 1: Hello everyone, this is Dr. Wallace. Have you ever wondered why so much time and emphasis is placed on understanding research questions, hypothesis statements, and variables in a research methodology course? Let's face it, when you look at these three items in a research proposal, they do not take up a lot of space. We spend more time discussing our research methodology, data collection and analysis, and prior research on our topic than we do on these three components in a research proposal. However, these three components are the foundation upon which any good research study is conducted. I want to take a few minutes and explain, at a high level, the role of each in a research proposal and study, and then show you how they are connected to each other. I think the best way to examine this subject is to begin with an example research topic. I can then demonstrate how these three components are connected by using this research topic as an example. Let's keep things easy and formulate a very simple topic. For the purposes of our lesson, I am going to say that I want to examine the effects of a thermostat on room temperatures. Now, with this research topic established, let's begin by looking at our three components. Okay, let's kick things off by looking at research questions. What is a research question? The research question is the way we succinctly define what we hope the research study will show us. We have identified a problem or issue that we think is important to study. Now, the research question specifically identifies what part of that issue or problem we hope to answer or address. As implied by its name, our research question is presented in the form of a question. The type of question we are asking is often driven by the type of study we are conducting in our research methodology. Using our example topic, a potential research question that we might ask is, how does changing the thermostat setting impact a room's temperature? Now that we have a research question, let's go take a look at the role of the hypothesis. So, what is a hypothesis? A hypothesis is a prediction of what we believe the study will find, or put another way, the answer to the research question. A hypothesis is an empirical statement that can be verified based upon observation or experience. It is testable to be true or false through the research study findings. You will also sometimes hear reference to a null hypothesis, but let's save that for another lesson. Now, let's return to our research topic example and create a hypothesis. The hypothesis for our example study might be, changing the temperature setting on a thermostat, up or down, will cause the room temperature, where the thermostat is located, to change in the same way. We have made a prediction of how we think the research study will answer our question. Okay, let's move to the final piece of the puzzle, variables. Variables, my Achilles heel during my doctoral study days. That's right, I'll be the first to admit that this simple concept gave me a hard time when I was a student. Let me take a shot at breaking down variables as simply as possible in one slide. There are two types of variables, dependent and independent, also referred to as DV or IV. Okay, so what's the difference? Let's see if I can make this as simple as possible. The dependent variable is what we watch to see if a change is occurring, while the independent variable is the thing we manipulate to influence a change in the dependent variable. I understand this can get confusing. Perhaps if we go back to our example research topic, things will become a bit clearer. In this research study, the thermostat setting is my independent variable, because it is the thing I have the power to change or alter. I am going to manipulate the independent variable to see if it creates a change in my dependent variable. The thermostat setting influences the room temperature, which is my dependent variable. The room temperature is my dependent variable because it is the thing I am watching to see if a change occurs when I alter the independent variable. Now, I manipulate my thermostat setting by moving it to a different temperature. I have just made a change that I predicted would influence my dependent variable. I will now watch my dependent variable, the room temperature, to see if a change occurs that matches the change I made to the thermostat setting, my independent variable. This is what I predicted with my hypothesis, so I want to watch how the room temperature, my dependent variable, is impacted when I make changes to the thermostat setting, my independent variable. Okay, now that we have a high-level understanding of these three components of a research proposal and study, let's see how they all work together. Let's connect those dots. The research question or questions that we create for the study specified what we want to answer or find out in the study. In other words, they put meaning to why our study is important. The hypothesis is our prediction of what we believe the study will find, or put another way, our predicted answer to the research questions. With the hypothesis, you are looking into your magic ball and telling everyone what you think the research study will find when all is said and done. In many cases, the research questions and hypothesis will be closely related, with the primary difference being that the hypothesis is presented as a statement, while the research questions are, well to put this plainly, formatted as a question. Now let's see how the variables complete our puzzle. The independent and dependent variables are the components of our study that we manipulate and watch for outcomes. Since our hypothesis made a prediction, it is only logical that our variables have to be included in the hypothesis. Our hypothesis is where we show the relationship between the independent and dependent variables. While this is the logical flow for building many research studies, I cannot overstress the fact that a research proposal is a constantly evolving process. Until we have locked down all components of the research proposal and are ready to conduct the study, it is entirely possible that you may go back and tweak or change any one of these components based upon new information you uncover or updates that you make to one of the three components. Don't let this worry you though, because this is a natural occurrence when working the kinks out of your research strategy. Let's conclude by summarizing what we have covered. The research question is our way of stating what we hope the study will find or help us learn. Our hypothesis is our prediction statement of what we think the research study findings will show. Finally, our variables are the aspects of the study that we manipulate and observe to determine whether our hypothesis was correct. Thank you for taking the time to view this lesson. I hope the information that I have presented helps clarify why understanding research questions, hypothesis, and variables is so important in research methodology and how these three work together to establish a strong foundation for a research study.

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Home » Research Design – Types, Methods and Examples

Research Design – Types, Methods and Examples

Table of Contents

Research Design

Definition:

Research design refers to the overall strategy or plan for conducting a research study. It outlines the methods and procedures that will be used to collect and analyze data, as well as the goals and objectives of the study. Research design is important because it guides the entire research process and ensures that the study is conducted in a systematic and rigorous manner.

Types of Research Design

Types of Research Design are as follows:

Descriptive Research Design

This type of research design is used to describe a phenomenon or situation. It involves collecting data through surveys, questionnaires, interviews, and observations. The aim of descriptive research is to provide an accurate and detailed portrayal of a particular group, event, or situation. It can be useful in identifying patterns, trends, and relationships in the data.

Correlational Research Design

Correlational research design is used to determine if there is a relationship between two or more variables. This type of research design involves collecting data from participants and analyzing the relationship between the variables using statistical methods. The aim of correlational research is to identify the strength and direction of the relationship between the variables.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This type of research design involves manipulating one variable and measuring the effect on another variable. It usually involves randomly assigning participants to groups and manipulating an independent variable to determine its effect on a dependent variable. The aim of experimental research is to establish causality.

Quasi-experimental Research Design

Quasi-experimental research design is similar to experimental research design, but it lacks one or more of the features of a true experiment. For example, there may not be random assignment to groups or a control group. This type of research design is used when it is not feasible or ethical to conduct a true experiment.

Case Study Research Design

Case study research design is used to investigate a single case or a small number of cases in depth. It involves collecting data through various methods, such as interviews, observations, and document analysis. The aim of case study research is to provide an in-depth understanding of a particular case or situation.

Longitudinal Research Design

Longitudinal research design is used to study changes in a particular phenomenon over time. It involves collecting data at multiple time points and analyzing the changes that occur. The aim of longitudinal research is to provide insights into the development, growth, or decline of a particular phenomenon over time.

Structure of Research Design

The format of a research design typically includes the following sections:

• Introduction : This section provides an overview of the research problem, the research questions, and the importance of the study. It also includes a brief literature review that summarizes previous research on the topic and identifies gaps in the existing knowledge.
• Research Questions or Hypotheses: This section identifies the specific research questions or hypotheses that the study will address. These questions should be clear, specific, and testable.
• Research Methods : This section describes the methods that will be used to collect and analyze data. It includes details about the study design, the sampling strategy, the data collection instruments, and the data analysis techniques.
• Data Collection: This section describes how the data will be collected, including the sample size, data collection procedures, and any ethical considerations.
• Data Analysis: This section describes how the data will be analyzed, including the statistical techniques that will be used to test the research questions or hypotheses.
• Results : This section presents the findings of the study, including descriptive statistics and statistical tests.
• Discussion and Conclusion : This section summarizes the key findings of the study, interprets the results, and discusses the implications of the findings. It also includes recommendations for future research.
• References : This section lists the sources cited in the research design.

Example of Research Design

An Example of Research Design could be:

Research question: Does the use of social media affect the academic performance of high school students?

Research design:

• Research approach : The research approach will be quantitative as it involves collecting numerical data to test the hypothesis.
• Research design : The research design will be a quasi-experimental design, with a pretest-posttest control group design.
• Sample : The sample will be 200 high school students from two schools, with 100 students in the experimental group and 100 students in the control group.
• Data collection : The data will be collected through surveys administered to the students at the beginning and end of the academic year. The surveys will include questions about their social media usage and academic performance.
• Data analysis : The data collected will be analyzed using statistical software. The mean scores of the experimental and control groups will be compared to determine whether there is a significant difference in academic performance between the two groups.
• Limitations : The limitations of the study will be acknowledged, including the fact that social media usage can vary greatly among individuals, and the study only focuses on two schools, which may not be representative of the entire population.
• Ethical considerations: Ethical considerations will be taken into account, such as obtaining informed consent from the participants and ensuring their anonymity and confidentiality.

How to Write Research Design

Writing a research design involves planning and outlining the methodology and approach that will be used to answer a research question or hypothesis. Here are some steps to help you write a research design:

• Define the research question or hypothesis : Before beginning your research design, you should clearly define your research question or hypothesis. This will guide your research design and help you select appropriate methods.
• Select a research design: There are many different research designs to choose from, including experimental, survey, case study, and qualitative designs. Choose a design that best fits your research question and objectives.
• Develop a sampling plan : If your research involves collecting data from a sample, you will need to develop a sampling plan. This should outline how you will select participants and how many participants you will include.
• Define variables: Clearly define the variables you will be measuring or manipulating in your study. This will help ensure that your results are meaningful and relevant to your research question.
• Choose data collection methods : Decide on the data collection methods you will use to gather information. This may include surveys, interviews, observations, experiments, or secondary data sources.
• Create a data analysis plan: Develop a plan for analyzing your data, including the statistical or qualitative techniques you will use.
• Consider ethical concerns : Finally, be sure to consider any ethical concerns related to your research, such as participant confidentiality or potential harm.

When to Write Research Design

Research design should be written before conducting any research study. It is an important planning phase that outlines the research methodology, data collection methods, and data analysis techniques that will be used to investigate a research question or problem. The research design helps to ensure that the research is conducted in a systematic and logical manner, and that the data collected is relevant and reliable.

Ideally, the research design should be developed as early as possible in the research process, before any data is collected. This allows the researcher to carefully consider the research question, identify the most appropriate research methodology, and plan the data collection and analysis procedures in advance. By doing so, the research can be conducted in a more efficient and effective manner, and the results are more likely to be valid and reliable.

Purpose of Research Design

The purpose of research design is to plan and structure a research study in a way that enables the researcher to achieve the desired research goals with accuracy, validity, and reliability. Research design is the blueprint or the framework for conducting a study that outlines the methods, procedures, techniques, and tools for data collection and analysis.

Some of the key purposes of research design include:

• Providing a clear and concise plan of action for the research study.
• Ensuring that the research is conducted ethically and with rigor.
• Maximizing the accuracy and reliability of the research findings.
• Minimizing the possibility of errors, biases, or confounding variables.
• Ensuring that the research is feasible, practical, and cost-effective.
• Determining the appropriate research methodology to answer the research question(s).
• Identifying the sample size, sampling method, and data collection techniques.
• Determining the data analysis method and statistical tests to be used.
• Facilitating the replication of the study by other researchers.
• Enhancing the validity and generalizability of the research findings.

Applications of Research Design

There are numerous applications of research design in various fields, some of which are:

• Social sciences: In fields such as psychology, sociology, and anthropology, research design is used to investigate human behavior and social phenomena. Researchers use various research designs, such as experimental, quasi-experimental, and correlational designs, to study different aspects of social behavior.
• Education : Research design is essential in the field of education to investigate the effectiveness of different teaching methods and learning strategies. Researchers use various designs such as experimental, quasi-experimental, and case study designs to understand how students learn and how to improve teaching practices.
• Health sciences : In the health sciences, research design is used to investigate the causes, prevention, and treatment of diseases. Researchers use various designs, such as randomized controlled trials, cohort studies, and case-control studies, to study different aspects of health and healthcare.
• Business : Research design is used in the field of business to investigate consumer behavior, marketing strategies, and the impact of different business practices. Researchers use various designs, such as survey research, experimental research, and case studies, to study different aspects of the business world.
• Engineering : In the field of engineering, research design is used to investigate the development and implementation of new technologies. Researchers use various designs, such as experimental research and case studies, to study the effectiveness of new technologies and to identify areas for improvement.

Advantages of Research Design

Here are some advantages of research design:

• Systematic and organized approach : A well-designed research plan ensures that the research is conducted in a systematic and organized manner, which makes it easier to manage and analyze the data.
• Clear objectives: The research design helps to clarify the objectives of the study, which makes it easier to identify the variables that need to be measured, and the methods that need to be used to collect and analyze data.
• Minimizes bias: A well-designed research plan minimizes the chances of bias, by ensuring that the data is collected and analyzed objectively, and that the results are not influenced by the researcher’s personal biases or preferences.
• Efficient use of resources: A well-designed research plan helps to ensure that the resources (time, money, and personnel) are used efficiently and effectively, by focusing on the most important variables and methods.
• Replicability: A well-designed research plan makes it easier for other researchers to replicate the study, which enhances the credibility and reliability of the findings.
• Validity: A well-designed research plan helps to ensure that the findings are valid, by ensuring that the methods used to collect and analyze data are appropriate for the research question.
• Generalizability : A well-designed research plan helps to ensure that the findings can be generalized to other populations, settings, or situations, which increases the external validity of the study.

Research Design Vs Research Methodology

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A Good check on the Bayes factor

• Original Manuscript
• Open access
• Published: 04 September 2024

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• Nikola Sekulovski   ORCID: orcid.org/0000-0001-7032-1684 1 ,
• Maarten Marsman   ORCID: orcid.org/0000-0001-5309-7502 1 &
• Eric-Jan Wagenmakers   ORCID: orcid.org/0000-0003-1596-1034 1  

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Bayes factor hypothesis testing provides a powerful framework for assessing the evidence in favor of competing hypotheses. To obtain Bayes factors, statisticians often require advanced, non-standard tools, making it important to confirm that the methodology is computationally sound. This paper seeks to validate Bayes factor calculations by applying two theorems attributed to Alan Turing and Jack Good. The procedure entails simulating data sets under two hypotheses, calculating Bayes factors, and assessing whether their expected values align with theoretical expectations. We illustrate this method with an ANOVA example and a network psychometrics application, demonstrating its efficacy in detecting calculation errors and confirming the computational correctness of the Bayes factor results. This structured validation approach aims to provide researchers with a tool to enhance the credibility of Bayes factor hypothesis testing, fostering more robust and trustworthy scientific inferences.

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Introduction

The Bayes factor (Kass & Raftery, 1995 ; Jeffreys, 1935 ) serves as a valuable tool for testing scientific hypotheses by comparing the relative predictive adequacy of two competing statistical models. In recent decades, there has been a surge in the adoption of Bayes factors as a tool for hypothesis testing (e.g., in psychology, Heck et al., 2023 ; van de Schoot et al., 2017 ). This increasing trend towards Bayesian hypothesis testing and model comparison has been catalyzed by a growing critique of traditional frequentist null hypothesis significance testing methods (e.g., Wasserstein and Lazar, 2016 ; Wagenmakers, 2007 ; Cohen, 1994 ; Wagenmakers et al., 2018b ; Benjamin et al., 2018 ; for an early critique see Edwards et al., 1963 ). In addition, the emergence of user-friendly software packages (e.g., JASP Team, 2023 ; Morey and Rouder, 2022 ; Gu et al., 2021 ) and associated tutorial articles have played a crucial role in making the benefits of the Bayesian framework more accessible to applied researchers (e.g., van Doorn et al., 2021 ; Rouder et al., 2012 ; Hoijtink et al., 2019 ; Marsman and Wagenmakers, 2017 ; Wagenmakers et al., 2018b ; Wagenmakers et al., 2018a ). Overall, this upswing in Bayesian methodology has ushered in a new era of statistical analysis, offering researchers valuable alternatives to traditional approaches.

Although Bayes factors have gained popularity in scientific practice, calculating them can be challenging, especially when comparing the relative likelihood of two complex models, such as hierarchical or nonlinear models with a large number of parameters. In such cases, Bayes factors often need to be approximated using various numerical (sampling) techniques such as bridge sampling (Gronau et al., 2017 ) or path sampling (Zhou et al., 2012 ); for a general introduction to stochastic sampling in Bayesian inference see Gamerman and Lopes ( 2006 ). These techniques often require the user to specify proposal distributions or tune certain parameters within the sampler, which may lead to inaccuracies. There are also state-of-the-art sampling methods designed to obtain joint posterior probabilities over many models; some notable examples of these transdimensional methods are Reversible Jump MCMC (Green, 1995 ), MCMC with mixtures of mutually singular distributions (Gottardo & Raftery, 2008 ) and the product space method (Lodewyckx et al., 2011 ; Carlin & Chib, 1995 ). These methods, even though very powerful, are quite complex to implement in software and therefore error-prone. Therefore, despite their utility, the use of these numerical techniques can introduce errors, such as the one highlighted by Tsukamura and Okada ( 2023 ), who pointed out a common coding error when computing Bayes factors in certain settings in the Stan programming language (Stan Development Team, 2023 ). Recently, Schad and Vasishth ( 2024 ) showed that Bayes factor estimates can be biased in some commonly used factorial designs.

In addition to the potential inaccuracies of existing approac-hes, ongoing research is constantly advancing the methods used to compute Bayes factors; a recent development by Kim and Rockova ( 2023 ) introduces a deep learning estimator as an addition to the toolkit of techniques available for computing Bayes factors. While the diversity of computational approaches is crucial, it is important to note that the complexity of these tools can lead to inaccuracies in Bayes factor calculations in applied research contexts. Thus, the development of appropriate controls and checks becomes imperative.

Schad et al. ( 2022 ) highlight five key considerations that warrant attention when computing Bayes factors, two of which are (i) the Bayes factor estimates for complex statistical models can be unstable, and (ii) the Bayes factor estimates can be biased. Therefore, Schad et al. ( 2022 ) propose a structured approach based on simulation-based calibration, which was originally developed as a method to validate the computational correctness of applied Bayesian inference more generally, and use it to verify the accuracy of Bayes factor calculations (see Talts et al., 2018 ; Cook et al., 2006 ; Geweke, 2004 ). Their method is based on the idea that that the marginal expected posterior model probability is equal to the prior model probability. We provide a more detailed description of the method proposed by Schad et al. ( 2022 ) in one of the following sections.

Before proposing another formal Bayes factor check in the spirit of the one by Schad et al. ( 2022 ), we would like to mention two other methods that, while not explicitly described as Bayes factor checks, can be used for this purpose. For the first method, suppose a researcher is interested in computing the Bayes factor for the relative adequacy of two complex (possibly non-nested) models, \(\mathcal {H}_1\) and \(\mathcal {H}_{\text {2}}\) , and has already chosen a numerical method implemented in some software for computing \(\text {BF}_{12}\) . To check that the calculation has been carried out correctly, they can construct nested versions of each of the models by selecting a single parameter and setting it to its maximum likelihood estimate (MLE) value, which would act as a surrogate oracle null model. They can then use the Savage–Dickey density ratio (Dickey & Lientz, 1970 ; Wagenmakers et al., 2010 ) to compute \(\text {BF}_{\text {ou}}\) – the Bayes factor in favor of the oracle null over the unconstrained model – for both \(\mathcal {H}_1\) and \(\mathcal {H}_{\text {2}}\) . When both models have Savage–Dickey \(\text {BF}_{\text {ou}}\) ’s that match the \(\text {BF}_{\text {ou}}\) ’s obtained from the method under scrutiny, then this gives the researcher reason to believe that \(\text {BF}_{12}\) has been computed correctly. A similar approach has been implemented by Gronau et al. ( 2020 ) for computing the marginal likelihood in evidence accumulation models, achieved by introducing a Warp-III bridge sampling algorithm. A second method to check the Bayes factor is pragmatic and can be used whenever multiple computational methods are available for a specific application. The idea is that one can use all methods – if they agree, they will mutually reinforce the conclusion and provide evidence that the Bayes factor has been calculated correctly. Furthermore, a Bayes factor can be computed for this agreement. Given that the probability of two correct methods yielding the same outcome is 1, the Bayes factor is calculated as 1 divided by the probability of a chance agreement between two methods, assuming at least one is incorrect. Since the probability of two methods converging on the same wrong value is very small, the Bayes factor provides very strong evidence that both methods are correct.

In this paper, we draw attention to two theorems by Alan Turing and Jack Good (e.g., Good, 1950 , 1985 , 1994 ), which they proposed could be used to verify the computation of Bayes factors. We introduce a structured approach to perform this verification, aiming to revive and highlight an idea that, until now, has not received the attention it deserves.

The remainder of this paper is structured as follows. In the next section, we provide an overview of the material in Good ( 1985 ), where we discuss the theorems, introduce key concepts, and establish notation. Following this, we present a simple binomial model to illustrate the conditions under which these theorems apply. Next, we outline the workflow for the Bayes factor check tool and offer two numerical examples to demonstrate its application-one employing an ANOVA design and the other utilizing a complex psychometric network model. We conclude the paper by comparing the strengths and limitations of this method, as well as highlighting potential avenues for improvement.

Theoretical background

The weight of evidence.

Good ( 1985 ) points out that the concept of weight of evidence , which is used in many areas (e.g., in science, medicine, law, and daily life), is a function of the probabilities of the data under two hypotheses (see also Good, 1950 , 1965 , 1979 , 1994 , 1995 ). Formally, this relation takes the form

where \(\mathcal {W}(\mathcal {H}_1:\text {data})\) denotes the weight of evidence in favor of the hypothesis \(\mathcal {H}_1\) provided by the evidence (data), while \(p(\text {data} \mid \mathcal {H}_\cdot )\) denote the probabilities of the data under each of the hypotheses (i.e., what is usually called the marginal likelihood of the data). Good ( 1985 ) further points out that this function should be mathematically independent of \(p(\mathcal {H}_\cdot )\) , known as the prior probability of a hypothesis, but that \(p(\mathcal {H}_\cdot \mid \text {data})\) (i.e., the posterior probability) should depend both on the weight of evidence and the prior probability. This relationship can therefore be expressed as

Thus, the Bayes factor can be interpreted as the factor by which the initial odds are multiplied to give the final odds, or as the ratio of the posterior odds for \(\mathcal {H}_1\) to its prior odds. When \(\mathcal {H}_1\) and \(\mathcal {H}_2\) are simple (point) hypotheses the Bayes factor is equal to the likelihood ratio (Royall, 2017 ). Good defined the weight of evidence as the logarithm of the Bayes factor (Good, 1950 , 1985 , 1994 ), because it is additive and symmetric (e.g., \(\log (\text {BF} = 10) = 2.3\) and \(\log (\text {BF} = {1}/{10}) = -2.3\) , the average of which is 0). In contrast, the Bayes factor scale is not symmetric – the average of a Bayes factor of 10 and 1/10 is larger than 1. In writing about an appropriate metric for the weight of evidence, Good ( 1985 ) draws attention to a counterintuitive theorem about the Bayes factor, and suggested it may be used to check whether a particular procedure computes Bayes factors correctly. The theorem states that “the expected (Bayes) factor in favor of the false hypothesis is 1” . Good attributed this paradoxical insight to Alan Turing, whose team at Bletchley Park decrypted German naval messages during World War II (cf. Zabell, 2023 ).

In the following subsection, we first introduce Turing’s theorem. We then present another related theorem proposed by Good, which shows the relationship between higher-order moments of Bayes factors.

Moments of the Bayes factor

Theorem 1: the expected (bayes) factor in favor of the false hypothesis equals 1. – alan turing.

Suppose the possible outcomes of an experiment are \(E_1, E_2,...,E_M\) , where \(\mathcal {H}_t\) is the true hypothesis and \(\mathcal {H}_f\) is the false hypothesis. Footnote 1 Taking the expectation of the Bayes factor in favor of one of the hypotheses simply means calculating the weighted average of that Bayes factor where the weights are provided by the probability of the evidence given the true hypothesis (i.e., \(p(\text {E} \mid \mathcal {H}_t)\) ). Then the expected Bayes factor in favor of \(\mathcal {H}_f\) is given by

\(\square \)

The theorem states that the expected Bayes factor against the truth is 1, regardless of sample size. For example, consider a binomial experiment with \(n = 2\) trials and k successes, where \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Beta}(\alpha =1\text {, }\beta =1)\) . There are three possible outcomes for this experiment, \(E_1\text {: } k = 0\) , \(E_2\text {: } k = 1\) , and \(E_3\text {: } k = 2\) . It follows from the beta-binomial distribution that the probability is the same for each possible outcome under \(\mathcal {H}_1\) , which in this case is 1/3 \(\forall \ E_i\) . Under \(\mathcal {H}_0\) the probability of \(E_1\) and \(E_3\) is 1/4 and for \(E_2\) is 1/2. Assuming that \(\mathcal {H}_1\) is the correct hypotheses we have

As a Bayes factor of 1 indicates the complete absence of evidence, this theorem is paradoxical; intuition suggests that – especially for large sample sizes – the average Bayes factor against the truth should be much smaller than 1. As mentioned in the previous subsection, unlike the weight of evidence, the Bayes factor is not symmetric. For example, the mean of \(\text {BF}_{10} = {1}/{10}\) and \(\text {BF}_{10} = 10\) is 5.05 and not 1, whereas the mean of \(\log ({1}/{10})\) and \(\log (10)\) is 0. This theorem implies that the sampling distribution of the Bayes factor is skewed to the right. Therefore, Good ( 1985 ) suggests that the Bayes factor is likely to have a (roughly) log-normal distribution while the weight of evidence has a (roughly) normal distribution (see also, Good, 1994 ). Finally, Good ( 1985 ) shows that the expected weight of evidence in favor of the truth (i.e., \(\mathcal {W}(\mathcal {H}_t: \text {data})\) ) is non-negative and vanishes when the weight of evidence is 0. This again illustrates that the weight of evidence is additive and its expected value is more meaningful than that of the Bayes factor.

Until now, Theorem 1 has been used almost exclusively to establish the universal bound on obtaining misleading evidence (e.g., Royall, 2000 ; Sanborn and Hills, 2014 ). The universal bound states that the probability of obtaining a Bayes factor greater than or equal to \({1}/{\alpha }\) in favor of the false hypothesis is less than or equal to some threshold \(\alpha \) . For example, the probability of obtaining a Bayes factor of 100 in favor of the false hypothesis is less than or equal to \(1\%\) . This is related to the fact that a Bayes factor in favor of the false hypothesis is related to a non-negative test martingale where the expected value of the martingale at any point t is 1. Footnote 2 That is, the test martingale measures the evidence against a hypothesis \(\mathcal {H}\) , and its inverse at some point t is a Bayes factor in favor of \(\mathcal {H}\) (see e.g., Shafer et al., 2011 ; Grünwald et al., 2020 ). Footnote 3 These properties have also been used independently in sequential analysis by Abraham Wald (Wald, 1945 ). Since the concept of a martingale (Ville, 1939 ) predates the work of Good and Turing, this suggests that they were not the first to be (at least implicitly) aware of this theorem. However, Jack Good was apparently the first to propose that the theorem may be used to verify the computation of the Bayes factor (Good, 1985 , p. 255). This paper implements Good’s idea.

Theorem 1 shows that the first moment of the Bayes factor under the false hypothesis is equal to 1. This is the main result; however, Good ( 1985 ) shows that Theorem 1 is a special case of another theorem which shows the equivalence between higher-order moments of Bayes factors; we turn to this theorem next.

Theorem 2: Equivalence of moments for Bayes factors under \(\mathcal {H}_1\) and \(\mathcal {H}_2 \) . – Jack Good

The second theorem generalizes the first and states that

The theorem can be expressed as

Using the product law of exponents, the right-hand side of the equation above can be rewritten as

which immediately proves the result.

This theorem states that the \(k^{th}\) moment of the Bayes factor in favor of \(\mathcal {H}_1\) about the origin, given that \(\mathcal {H}_1\) is true is equal to the \((k+1)^{st}\) moment of the Bayes factor in favor of \(\mathcal {H}_1\) given that \(\mathcal {H}_2\) is true. Here we refer to the raw moments, that is the moments about the origin and not to the central moments (such as the variance, which is the second moment about the mean). When \(k = 0\) , this result reduces to that of the first theorem.

Considering the binomial example from earlier with \(n = 2\) and hypotheses \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Beta}(\alpha = 1\text {, } \beta = 1)\) one can see that

Numerical illustrations

Consider a sequence of n coin tosses that forms the basis of a test of the null hypothesis \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) against the alternative hypothesis \(\mathcal {H}_1\text {: } \theta \sim \text {Uniform}(0,1)\) , where \(\theta \) represents the probability of the coin landing heads. Footnote 4 Additionally, in the last part of this section, we consider a restricted (directional) hypothesis \(\mathcal {H}_{\text {r}}\text {: } \theta > {1}/{2}\) . We simulated a total of \(m = 100{,}000\) data sets either under \(\mathcal {H}_0\) , \(\mathcal {H}_1\) or \(\mathcal {H}_{\text {r}}\) for sample sizes of \(n = \{10, 50, 100\}\) . For each simulation setting, we averaged the \(m = 2, \dots , 100{,}000\) Bayes factors in favor of the wrong hypothesis. The code to reproduce the examples in this paper is publicly available in an OSF repository at https://osf.io/438vy/ .

The average Bayes factor in favor of the null hypothesis quickly converges to 1 for synthetic data sets generated under the alternative hypothesis. The figure depicts the average \(\text {BF}_{01}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_1\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The left panel plots the cumulative mean across \(m = 100{,}000\) data sets; the right panel zooms in on the first \(m = 1{,}000\) iterations

The average Bayes factor in favor of the alternative hypothesis does not converge to 1 as n increases for the synthetic data sets generated under the null hypothesis. The figure depicts the average \(\text {BF}_{10}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_0\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\)

Illustration of Theorem 1

Figure 1 illustrates the situation where \(\mathcal {H}_1\) is true and plots the mean Bayes factor in favor of \(\mathcal {H}_0\) , that is, the average \(\text {BF}_{01}\) . For all three values of n , the average \(\text {BF}_{01}\) quickly stabilizes towards 1. There is a slightly larger instability in the mean for larger sample sizes n ; however, the results quickly converge as m increases.

Figure 2 illustrates the situation where \(\mathcal {H}_0\) is true and plots the mean Bayes factor in favor of \(\mathcal {H}_1\) , that is, the average \(\text {BF}_{10}\) calculated for the data sets simulated under \(\mathcal {H}_0\) . It is immediately evident that for larger sample size n , the mean \(\text {BF}_{10}\) becomes unstable and moves away from 1. As m increases, the average appears to stabilize on values different from 1. This observation suggests that under \(\mathcal {H}_0\) , with a large sample size, a very large number of iterations would be necessary to obtain a mean \(\text {BF}_{10}\) that approaches 1. This phenomenon arises because, under \(\mathcal {H}_0\) , there exist rare outcomes that produce extreme \(\text {BF}_{10}\) values, a situation that does not occur with \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is the true hypothesis. The chance of encountering these extreme results under \(\mathcal {H}_0\) , which in turn yields extreme \(\text {BF}_{10}\) values, becomes less probable as the sample size n increases. Consequently, in this scenario the mean \(\text {BF}_{10}\) does not quickly converge to 1. We conclude that the Turing–Good theorems exhibit more robust performance in practice when the true hypothesis is not a point null hypothesis (i.e., when the more complicated hypothesis is true).

When the encompassing hypothesis is true, the average Bayes factor in favor of the restricted hypothesis rapidly converges to 1, whereas for when the restricted hypothesis is true the average Bayes factor in favor of the encompassing hypothesis does not converge to 1 when the sample size is large. The left panel shows the average \(\text {BF}_{\text {re}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {e}}\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The right panel shows the average \(\text {BF}_{\text {er}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {r}}\) , for \(n = 10, 50, 100\)

Illustration of Theorem 2

To illustrate the second theorem, we compare the first moment of the Bayes factor in favor of the true hypothesis with the second raw moment in favor of the false hypothesis. We first calculated these moments analytically for \(n = \{10, 50, 100\}\) with \(\mathcal {H}_0\text {: } \theta = {1}/{2}\) and \(\mathcal {H}_1\text {: } \theta \sim \text {Uniform}(0,1)\) . We then calculated the same moments for the Bayes factors based on the synthetic data. We calculated the second raw moments for the Bayes factors using the following formula:

The results are summarized in Table 1 .

The eighth column of Table 1 shows that, on average, the evidence for \(\mathcal {H}_0\) increases with the sample size n . Comparing the seventh and eighth columns (shaded in gray) confirms that the mean of \(\text {BF}_{01}\) when \(\mathcal {H}_0\) is true is approximately equal to the second raw moment of \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true, regardless of sample size.

When the restricted hypothesis is true, the Bayes factor in favor of the null hypothesis rapidly converges to 1, whereas when the null hypothesis is true the Bayes factor in favor of the restricted hypothesis does not converge to 1 when the sample size is large. The left panel shows the average \(\text {BF}_{\text {0r}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_{\text {r}}\) , for \(n = 10, 50, 100\) ; the black solid line is for \(n = 10\) , the red dashed line is for \(n = 50\) , and the green dotted line is for \(n = 100\) . The right panel shows the average \(\text {BF}_{\text {r0}}\) as a function of the number of synthetic data sets m generated under \(\mathcal {H}_0\) , for \(n = 10, 50, 100\)

The sixth column of Table 1 shows that the expected evidence in favor of \(\mathcal {H}_1\) becomes extreme as n increases; contrasting this with the second moment of \(\text {BF}_{10}\) when \(\mathcal {H}_0\) shows that the values are equal for \(n = 10\) , but as n increases these values diverge. These instabilities are due to the same reasons highlighted in the previous subsection. Note, however, that the theorems still hold in this situation, and for a very large number of iterations m the moments are expected to eventually converge. This is supported by the analytical solutions presented in columns 2 through 6. However, the results computed from the synthetic data suggest that in practice, when dealing with a point null hypothesis, one should compute the first moment from the data generated under \(\mathcal {H}_0\) and compare it with the second raw moment computed from the data generated under \(\mathcal {H}_1\) .

It is also possible to compare, for example, the second and third raw moments. In the results from the simulation, the second raw moments of \(\text {BF}_{01}\) for the data sets generated under \(\mathcal {H}_0\) are 4.28, 19, and 37.32, for \(n = 10, 50\) , and 100, respectively. And the third raw moments of \(\text {BF}_{01}\) for the data sets generated under \(\mathcal {H}_1\) are 4.3, 18.8 and 37.1. These results illustrate that the second theorem holds for higher-order moments in general.

Directional hypotheses

In this subsection, we examine how the Bayes factor behaves when one of the hypotheses under consideration is a directional (i.e., inequality constrained or restricted) hypothesis. Hypotheses that consist of a combination of inequality and equality constraints among the parameters are known as informative hypotheses (Hoijtink, 2011 ). Informative hypotheses allow researchers to express their substantive theory and expectations and have become popular in recent years; therefore, it is important to also consider how inequality constrained hypotheses perform under the two theorems.

We make use of the restricted hypothesis \(\mathcal {H}_{\text {r}}: \theta > {1}/{2}\) , which we specify as \(\mathcal {H}_{\text {r}}: \theta \sim \text {Uniform}(0.5, 1)\) . This is equivalent to setting a truncated Beta distribution from 0.5 to 1 for the probability \(\theta \) . We then compare \(\mathcal {H}_{\text {r}}\) with the alternative hypothesis ( \(\mathcal {H}_1\) ) and the null hypothesis ( \(\mathcal {H}_0\) ) from the previous subsections. In line with previous literature (e.g., Klugkist et al., 2005 ), we rename the alternative hypothesis ( \(\mathcal {H}_1\) ) to the encompassing hypothesis and denote it as \(\mathcal {H}_{\text {e}}\) , as both \(\mathcal {H}_0\) and \(\mathcal {H}_{\text {r}}\) are nested under this encompassing hypothesis.

Figure 3 illustrates the situation of comparing \(\mathcal {H}_{\text {e}}\) and \(\mathcal {H}_{\text {r}}\) . In the left plot, the average \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {e}}\) is the true hypothesis quickly stabilizes towards 1 for all three sample size values. Note also that the initial fluctuations are all greater than 1; this is because half of the outcomes expected under \(\mathcal {H}_{\text {e}}\) are also plausible under \(\mathcal {H}_{\text {r}}\) . The right panel of Fig. 3 illustrates the reverse situation, where \(\mathcal {H}_{\text {r}}\) is the true hypothesis. As can be seen, the Bayes factor now does not quickly converge to 1 for larger sample sizes, because under \(\mathcal {H}_{\text {r}}\) , outcomes that produce large \(\text {BF}_{\text {er}}\) ’s are highly improbable; similar to the case when considering \(\text {BF}_{10}\) when \(\mathcal {H}_0\) is true (cf. Figure 2 ).

Figure 4 illustrates the situation of comparing \(\mathcal {H}_0\) with \(\mathcal {H}_{\text {r}}\) . In the left panel, the average \(\text {BF}_{0r}\) when \(\mathcal {H}_{\text {r}}\) is the true hypothesis approaches 1 for all three sample size values; note, however, that for \(n = 100\) it takes a considerable number of iterations for the average \(\text {BF}_{\text {0r}}\) to converge to 1. The right panel of Fig. 4 illustrates the situation when \(\mathcal {H}_0\) is the true hypothesis; as was the case in Fig. 2 , when the point (null) hypothesis is the true hypothesis, for a finite number of iterations, the average Bayes factor in favor of the false hypothesis does not converge to 1 as the sample size increases. Again, this is due to the fact that under \(\mathcal {H}_0\) very few outcomes produce large \(\text {BF}_{\text {r0}}\) .

Examining the third and fourth columns of Table 2 , we see that the second raw moment of \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {e}}\) is true is equal to the mean of \(\text {BF}_{\text {re}}\) when \(\mathcal {H}_{\text {r}}\) is true. A similar observation can be made when comparing the sixth and ninth columns. This illustrates that the second theorem also holds for inequality-constrained hypotheses. However, if we compare the mean of \(\text {BF}_{\text {er}}\) when \(\mathcal {H}_{\text {e}}\) is true with the second moment of \(\text {BF}_{\text {er}}\) when \(\mathcal {H}_0\) is true, we observe that these values diverge, especially as the sample size increases. The same divergence occurs when we compare the mean of \(\text {BF}_{12}\) when \(\mathcal {H}_1\) is true with the second moment of \(\text {BF}_{12}\) when \(\mathcal {H}_0\) is true (cf. Table 1 ).

These results illustrate that both theorems are applicable to directional hypotheses and can be used as a general method for checking Bayes factors. Furthermore, generalizing from all the examples, the first theorem shows more robust performance when the more general (encompassing) hypothesis is true. For the second theorem, the (more) specific hypothesis should be set to true, and the average Bayes factor in favor of the more specific hypothesis should be compared with the second moment of the Bayes factor in favor of the more specific hypothesis when the more general hypothesis is true.

An exception to the rule

In the philosophy of science, a universal generalization is a hypothesis stating that a parameter or characteristic is true for the entire population without exceptions (e.g., all ravens are black). So for the binomial example, this would be equivalent to \(\mathcal {H}_0\text {: } \theta = 1\) . The two theorems do not hold in this situation, since they require that the true hypothesis (in this case \(\mathcal {H}_0\) ) must assign a non-zero prior mass to all events that are considered plausible under the false hypothesis. In other words, both hypotheses must assign non-zero mass to the same sample space.

A formal approach for checking the Bayes factor calculation

In their method for checking the calculation of the Bayes factor, Schad et al. ( 2022 ) recommend simulating multiple data sets from statistical models (with predefined prior model probabilities) and then obtaining Bayes factors and posterior model probabilities using the same method that is to be used to calculate the Bayes factor(s) on the empirical data. This method represents a structured approach based on simulation-based calibration (Geweke, 2004 ; Cook et al., 2006 ). The idea is based on the fact that the expected posterior model probability should equal the prior model probability (see e.g., Skyrms, 1997 ; Goldstein, 1983 ; Huttegger, 2017 ). Therefore, if the average posterior model probability across the simulated data sets is equal to the prior model probability, then the calculation of the Bayes factor (and the posterior model probability) should be considered accurate.

For the correctly specified calculation the average \(\text {BF}_{01}\) rapidly converges to 1, whereas for the misspecified calculation, it does not. The figure depicts average \(\text {BF}_{01}\) calculated for the data generated under \(\mathcal {H}_1\) as a function of the number of synthetic data sets m . The Bayes factor is calculated using two different values for the scale of the scaled inverse chi-squared distribution

In this paper, we follow the approach by Schad et al. ( 2022 ) and propose a new method for checking the Bayes factor, based on Turing and Good’s theorems described in the previous sections. The check (steps 1-4) assumes that if the calculation of the Bayes factor is executed correctly and if all the assumptions are met, then its expected value in favor of the wrong hypothesis should be (approximately) equal to 1. Additionally, it is possible to extend this check by comparing higher-order moments (steps 5-6). After collecting the data and selecting the appropriate analysis, the proposed methodology can be summarized as follows:

Specify two rival models; since the prior can be seen as an integral part of the model (e.g., Vanpaemel, 2010 ; Vanpaemel and Lee, 2012 ), this step includes the assignment of prior distributions to the model parameters.

Calculate the Bayes factor based on the observed data using the computational methodology of interest.

Select one of the models to generate simulated data from – we strongly recommend this to be the more complex model; in nested models, one should therefore simulate from the alternative hypothesis and not from the null hypothesis.

Sample data from the prior predictive distribution. This could, for example, be done by selecting a parameter (vector) from the joint prior distribution and use this to generate a synthetic data set of the same length as the observed data (although it could be any length in principle).

Compute the Bayes factor in favor of the false hypothesis over the true hypothesis for the synthetic data set, using the same computational technique used for the observed data (step 2).

Repeat steps b-c m times, yielding m Bayes factors in favor of the false hypothesis.

Calculate the average Bayes factor in favor of the false hypothesis across the m Bayes factors obtained in the previous step. If this mean value is close to 1 for a sufficiently large number of simulations m , this provides strong evidence that the Bayes factor calculation has been executed correctly. Then one can confidently report the value obtained in step 2.

Additionally, simulate data as described in step 3, but this time set the other hypothesis under consideration (e.g., \(\mathcal {H}_0\) ) to true. Calculate the Bayes factor in favor of the true hypothesis. Repeat this step m times and calculate the average Bayes factor in favor of the true hypothesis.

Compare the mean Bayes factor from step 5 with the second moment of the Bayes factor in favor of the wrong hypothesis based on the data generated in step 3. If these two values are approximately equal, this provides additional evidence that the Bayes factor calculation was performed correctly.

This step-by-step approach helps validate the Bayes factor calculations and ensures that the results obtained are reliable. More specifically, if the Bayes factor calculation is done correctly, we should be confident that there were no issues with the calculation of the Bayes factor. In the following two subsections, we illustrate these steps with two concrete examples.

Note that the purpose of the following examples-one using a simple Bayes factor for an intervention effect in an ANOVA design, and another using a transdimensional Bayes factor for the inclusion of an edge in a graphical model-is to demonstrate how to perform the proposed check. A comprehensive review of the performance of various software packages in calculating Bayes factors is beyond the scope of this paper.

Example 1: A Bayes factor test for an intervention effect in one-way ANOVA

Consider a one-way ANOVA model where the standard alternative hypothesis ( \(\mathcal {H}_1\) ), which states that not all means between the 3 groups are equal, is tested against the null hypothesis ( \(\mathcal {H}_0\) ), which states that the means are equal. The model can be expressed as

where \(y_i\) is the value of the dependent variable for participant i , \(\alpha \) is the intercept, \(x_i\) is the factor variable denoting the group membership, \(\beta \) is the parameter representing the effect of the experimental manipulation, and \(\epsilon _i\) is the residual term normally distributed around 0 with variance \(\sigma ^2\) . To calculate the Bayes factor on the empirical data one can use the default settings in the R package BayesFactor (Morey & Rouder, 2022 ). The function anovaBF assigns Jeffreys priors to the intercept and residual variance, and a normal prior to the main effect

where g is given an independent scaled inverse-chi-squared hyperprior with 1 degree of freedom. The interested reader is referred to Rouder et al. ( 2012 ) for the details of the prior specifications. We now illustrate how the check can be performed for the current example.

Suppose we have collected data from 150 participants (50 participants in each of the 3 groups) and we wish to test \(\mathcal {H}_1\) versus \(\mathcal {H}_0\) . We simulate \(m = 200{,}000\) data sets under \(\mathcal {H}_1\) by sampling the parameter \(\beta \) from its prior distribution, employing the same default specification as used in the package (i.e., applying a scaled inverse-chi-squared hyperprior for g with a scale of 1/2 and Jeffreys priors on \(\alpha \) and \(\sigma ^2\) with a value of \(\sigma ^2 = 0.5\) ). Additionally, we generate m datasets under \(\mathcal {H}_0\) by setting \(\beta = 0\) . In both cases, we calculate the Bayes factors using the default settings as described above. To illustrate what happens when the Bayes factor calculation is misspecified, we re-calculate the Bayes factor for the data generated under \(\mathcal {H}_1\) by altering the default value for the scale of the inverse chi-squared distribution. Specifically, we change the scale from medium to ultrawide , corresponding to values of 1/2 and 1, respectively. For the Bayes factors calculated on the data sets where \(\mathcal {H}_1\) is true, approximately 0.28% of the Bayes factors calculations failed due to computational difficulties.

Figure 5 depicts the cumulative mean for \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true. Notably, for the Bayes factors calculated using the default settings of the package, which precisely mirror how the data was generated, the average \(\text {BF}_{01}\) rapidly converges to 1. However, when there is a discrepancy between the data and the Bayes factor calculation, which for the purpose of this example was achieved by altering the scale of the inverse chi-squared hyperprior from 1/2 to 1, we notice that the average Bayes factor deviates significantly from 1. It eventually stabilizes at a value of approximately 3.16, illustrating the sensitivity of the Bayes factor when its calculation is misspecified.

For the second set of synthetic data generated under \(\mathcal {H}_0\) , we calculate the average \(\text {BF}_{01}\) , which yields a value of 8.18, which we can compare with the second raw moment of \(\text {BF}_{01}\) from the data sets where the alternative hypothesis is true, which yields a value of 8.15. This result provides additional proof that the calculation of the Bayes factor was done correctly.

Example 2: A Bayes factor test for conditional independence in a Markov random field model

Network psychometrics is a relatively new subdiscipline in which psychological constructs (e.g., intelligence, mental disorders) are conceptualized as complex systems of behavioral and cognitive factors (Marsman & Rhemtulla, 2022 ; Borsboom & Cramer, 2013 ). Psychometric network analysis is then used to infer the structure of such systems from multivariate psychological data (Borsboom et al., 2021 ). These analyses use graphical models known as Markov Random Fields (MRFs, Kindermann and Snell, 1980 ; Rozanov, 1982 ) in which psychological variables assume the role of the network nodes. The edges of the network express the direct influence of one variable on another given the remaining network variables, that is, that they are conditionally dependent , and the absence of an edge implies that the two variables are conditionally independent (Lauritzen, 2004 ). The Bayesian approach to analyzing these graphical models (Mohammadi & Wit, 2015 ; Marsman et al., 2015 ; Marsman, 2022 ; Marsman et al., 2023 ; Williams, 2021 ; Williams & Mulder, 2020 ) allows researchers to quantify the evidence in the data for the presence or absence of edges, and thus to formally test for conditional (in)dependence (see Sekulovski et al., 2024 , for an overview of three Bayesian methods for testing conditional independence).

Sekulovski et al. ( 2024 ) discuss two types of Bayes factor tests for conditional independence. In one test, the predictive success of a particular network structure with the relationship of interest is compared against the same network structure with the relationship of interest removed. One problem with testing for conditional independence in this way is that even for relatively small networks, there are many possible structures to consider, and as Sekulovski et al. ( 2024 ) have shown, Bayes factor tests for conditional independence can be highly sensitive to the choice of that network structure. In the second Bayes factor test, we use Bayesian model averaging (BMA, Hoeting et al., 1999 ; Hinne et al., 2020 ) and contrast the predictive success of all structures with the relationship of interest against the predictive success of all structures without that relationship. This is known as the inclusion Bayes factor (Marsman, 2022 ; Marsman et al., 2023 ). Sekulovski et al. ( 2024 ) showed that the inclusion Bayes factor is robust to variations in the structures underlying the rest of the network. However, the BMA methods for psychometric network analysis required to estimate the inclusion Bayes factor are much more complex and thus more prone to the computational problems identified above. For an accessible introduction to BMA with a specific example on network models, see Hinne et al. ( 2020 ) and for an accessible introduction to BMA analysis of psychometric network models, see Huth et al. ( 2023 ) and Sekulovski et al. ( 2024 ).

The average \(\text {BF}_{01}\) converges to 1. The figure depicts the average inclusion \(\text {BF}_{01}\) calculated for the data generated under \(\mathcal {H}_1\) as a function of the number of synthetic data sets m

In this paper, we scrutinize the Bayesian edge selection method developed by Marsman et al. ( 2023 ) for analyzing MRF models for binary and ordinal data, and which can be used to estimate the inclusion Bayes factor. This method, implemented in the R package bgms (Marsman et al., 2023 ), stipulates a discrete spike and slab prior distribution on the edge weights of the MRF, and models the inclusion and exclusion of pairwise relations in the model with an edge indicator ( \(\gamma \) ), which when present designates the corresponding edge weight a diffuse prior and when absent sets it to 0. That is, for a single edge weight \(\theta _{ij}\) , between variables i and j , the prior distribution can be expressed as

The transdimensional Markov chain Monte Carlo method proposed by Gottardo and Raftery ( 2008 ) is used to simulate from the multivariate posterior distribution of the MRF’s parameters and edge indicators. The output of this approach can be used to compute the inclusion Bayes factor which is defined as

Since the inclusion Bayes factor is an extension of the classical Bayes factor presented in Eq.  1 and involves a much more complex calculation, we wish to verify that its computation is performed correctly using the newly proposed methodology. Therefore, we simulated \(m = 30{,}000\) datasets with \(p = 5\) binary variables and \(N = 500\) observations each. We focus on testing whether the first two variables are conditionally independent, that is, we compare \(\mathcal {H}_0\text {: } \theta _{12} = 0\) with \(\mathcal {H}_1\text {: } \theta _{12} \ne 0\) . For the case where \(\mathcal {H}_1\) is true, we simulated data where all ten possible edges have an edge weight value of \(\theta _{ij} = 0.5\) . Additionally, for the case where \(\mathcal {H}_0\) is true, we simulated a second set of data by setting the focal edge weight parameter \(\theta _{12}\) to 0 and leaving the values of the nine remaining edge weights unchanged. We estimated the graphical model for each simulated data set using the R package bgms . We used a unit information prior for \(f_{slab}\) ; a Dirac measure at 0 for \(f_{spike}\) , and an independent Bernoulli distribution for each \(\gamma _{ij}\) with a prior inclusion probability of 1/2 (see Sekulovski et al., 2024 , for a detailed analysis of the prior distributions for these models). Under this prior specification, the prior inclusion odds are equal to 1. In cases where the posterior inclusion probability was equal to 1, we obtained undefined values for the inclusion Bayes factor (i.e., 1/0). For the data sets where \(\mathcal {H}_1\) was true, there were 9,345 Bayes factors with undefined values (31%), and for the data sets where \(\mathcal {H}_0\) was true, there were 53 undefined values (0.2%). To work around this problem, we set all undefined values to 1 + the highest observed finite value of the inclusion Bayes factor.

Figure 6 shows the cumulative mean of the inclusion \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true (i.e., there is an edge between variables 1 and 2). As the number of simulations increases, the mean inclusion \(\text {BF}_{01}\) stabilizes around 1 (1.01 at the last iteration), indicating that the inclusion Bayes factor obtained with this approach was computed correctly. In addition, we computed the mean \(\text {BF}_{01}\) when \(\mathcal {H}_0\) is true, which was 11.5, and compared it to the second moment of \(\text {BF}_{01}\) when \(\mathcal {H}_1\) is true, which was 9.96. These values are not equal. However, we suspect that the reason for this is twofold: first, the sample size N in each of the simulated data sets was quite large, and second, since the calculation of this Bayes factor is more involved, it probably takes many more iterations m to be sure that the moments are equal. Estimating these models takes much more time than estimating other more standard statistical models, so it was not computationally feasible to do more than \(m = 30{,}000\) repetitions under each of the hypotheses. In addition, we must consider the sampling variability of the simulated data sets. In other words, due to variability, not all of the simulated data sets will show support for the hypothesis under which they were simulated, further reducing the number of “effective” data sets. These reasons also justify the choice to recode the undefined inclusion Bayes factor values as we did, rather than omitting them altogether.

This paper presents a structured approach to checking the accuracy of Bayes factor calculations based on the theorems of Turing and Good. The approach provides researchers with a general and practical method for confirming that their Bayes factor results are reliable. Application to two concrete examples demonstrated the effectiveness of this approach in verifying the correctness of Bayes factor calculations. In particular, if the method of calculating the Bayes factor is consistent with the data generation process, the mean Bayes factor in favor of the false hypothesis converges to approximately 1, in accordance with the first theorem. Furthermore, comparing the first and second moments of the Bayes factors under different hypotheses provides additional evidence for correct calculations. However, as we have seen in the second example when dealing with more complex models, the second theorem requires many more iterations. Due to the variability of the second moment, one can only be sure that the second theorem approximately holds for a finite number of simulations. Therefore, we recommend that researchers focus primarily on the first theorem and perform the additional check based on the second theorem whenever practically possible. This would also make the check less computationally expensive since it would only require simulating data under one of the hypotheses.

Finally, we have demonstrated that for practical applications of the first theorem, it is best to simulate under the more general hypothesis and take the average Bayes factor in favor of the more specific hypothesis. For the second theorem, the optimal approach can be summarized as follows. First, compute the mean Bayes factor in favor of the more specific hypothesis for data where that hypothesis is true. Second, compare this to the second raw moment in favor of the more specific hypothesis computed on data simulated under the more general hypothesis.

Limitations & Possible extensions

While the proposed approach provides a practical way to validate Bayes factor calculations, it is not without limitations. In cases with large sample sizes, or when dealing with highly complex models, the convergence of the values for the higher-order moments may require a significant number of iterations. In such cases, as we have seen, the second moments may not match very closely. In situations where Bayes factors are used for comparing highly complex models, different methods of checking their calculation might be more appropriate, such as the method proposed by Schad et al. ( 2022 ).

However, for certain Bayes factors, particularly those based on Bayesian model averaging (BMA), such as the inclusion Bayes factor for including an edge in a graphical model or a predictor in linear regression, the method proposed in this paper can be straightforwardly applied to verify these calculations. This is because the other two methods are more suitable for checking classical (i.e., non-BMA) Bayes factors, which compare two competing statistical models (see, Sekulovski et al., 2024 , for a discussion of the difference between these two Bayes factors)

One of the reviewers of the paper suggested that the check proposed in this paper could be incorporated as an additional step within the approach proposed by Schad et al. ( 2022 ). This would mean that at the start of the simulation exercise, we would have to (a) assign prior probabilities to two competing models and then randomly select one of those models, (b) simulate synthetic data under the sampled model, (c) compute the Bayes factor and the posterior model probability, and then repeat these steps m times. Then, step 4 would be split into two, where we filter out the data sets generated by only one of the models, and filter out the associated Bayes factors. For each resulting set of Bayes factors, we would compute the mean in favor of the false hypothesis, where we expect both means to be approximately equal to one.

Providing a structured and systematic way to evaluate Bayes factor calculations helps to increase the credibility and rigor of Bayesian hypothesis testing in applied research. The proposed methods serve as a valuable tool for researchers working with Bayes factors, providing a means to validate their results and ensure the robustness of their statistical inferences. We encourage researchers to consider this approach when using Bayes factors in their analyses, thereby fostering greater confidence in the validity of their conclusions.

Code Availability

The data and materials for all simulation examples are available at the OSF repository https://osf.io/438vy/ .

Availability of data and materials

Not applicable.

We use E and ‘data’ interchangeably.

A martingale is a sequence of random variables where the conditional expected value of the next value, given all prior values, equals the current value. For instance, consider a coin flip game where a player starts with 100 euros, winning one euro for heads and losing one euro for tails; in this scenario, the expected amount of money after each flip remains equal to the player’s current amount. Consequently, regardless of the number of flips, the expected future value is always equal to the present value, exemplifying the martingale property.

It should be noted that the marginal Bayes factor (i.e., a Bayes factor not conditioned on the false hypothesis) is not a martingale.

Note that the specification of \(\mathcal {H}_0\) and \(\mathcal {H}_1\) is the same as in the binomial example from the previous section with \(n = 2\) .

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Acknowledgements

The authors would like to thank Wolf Vanpaemel for providing the idea and example script for merging the Good check with the check proposed by Schad et al. ( 2022 ), as well as two other reviewers and the Associate Editor for their comments on earlier versions of the manuscript.

NS and MM were supported by the European Union (ERC, BAYESIAN P-NETS, #101040876). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.

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