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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

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 .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, 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 types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

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 ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize 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.

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

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.

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 .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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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).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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

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Statistics By Jim

Making statistics intuitive

Statistical Hypothesis Testing Overview

By Jim Frost 59 Comments

In this blog post, I explain why you need to use statistical hypothesis testing and help you navigate the essential terminology. Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables.

This post provides an overview of statistical hypothesis testing. If you need to perform hypothesis tests, consider getting my book, Hypothesis Testing: An Intuitive Guide .

Why You Should Perform Statistical Hypothesis Testing

Hypothesis testing is a form of inferential statistics that allows us to draw conclusions about an entire population based on a representative sample. You gain tremendous benefits by working with a sample. In most cases, it is simply impossible to observe the entire population to understand its properties. The only alternative is to collect a random sample and then use statistics to analyze it.

While samples are much more practical and less expensive to work with, there are trade-offs. When you estimate the properties of a population from a sample, the sample statistics are unlikely to equal the actual population value exactly.  For instance, your sample mean is unlikely to equal the population mean. The difference between the sample statistic and the population value is the sample error.

Differences that researchers observe in samples might be due to sampling error rather than representing a true effect at the population level. If sampling error causes the observed difference, the next time someone performs the same experiment the results might be different. Hypothesis testing incorporates estimates of the sampling error to help you make the correct decision. Learn more about Sampling Error .

For example, if you are studying the proportion of defects produced by two manufacturing methods, any difference you observe between the two sample proportions might be sample error rather than a true difference. If the difference does not exist at the population level, you won’t obtain the benefits that you expect based on the sample statistics. That can be a costly mistake!

Let’s cover some basic hypothesis testing terms that you need to know.

Background information : Difference between Descriptive and Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics

Hypothesis Testing

Hypothesis testing is a statistical analysis that uses sample data to assess two mutually exclusive theories about the properties of a population. Statisticians call these theories the null hypothesis and the alternative hypothesis. A hypothesis test assesses your sample statistic and factors in an estimate of the sample error to determine which hypothesis the data support.

When you can reject the null hypothesis, the results are statistically significant, and your data support the theory that an effect exists at the population level.

The effect is the difference between the population value and the null hypothesis value. The effect is also known as population effect or the difference. For example, the mean difference between the health outcome for a treatment group and a control group is the effect.

Typically, you do not know the size of the actual effect. However, you can use a hypothesis test to help you determine whether an effect exists and to estimate its size. Hypothesis tests convert your sample effect into a test statistic, which it evaluates for statistical significance. Learn more about Test Statistics .

An effect can be statistically significant, but that doesn’t necessarily indicate that it is important in a real-world, practical sense. For more information, read my post about Statistical vs. Practical Significance .

Null Hypothesis

The null hypothesis is one of two mutually exclusive theories about the properties of the population in hypothesis testing. Typically, the null hypothesis states that there is no effect (i.e., the effect size equals zero). The null is often signified by H 0 .

In all hypothesis testing, the researchers are testing an effect of some sort. The effect can be the effectiveness of a new vaccination, the durability of a new product, the proportion of defect in a manufacturing process, and so on. There is some benefit or difference that the researchers hope to identify.

However, it’s possible that there is no effect or no difference between the experimental groups. In statistics, we call this lack of an effect the null hypothesis. Therefore, if you can reject the null, you can favor the alternative hypothesis, which states that the effect exists (doesn’t equal zero) at the population level.

You can think of the null as the default theory that requires sufficiently strong evidence against in order to reject it.

For example, in a 2-sample t-test, the null often states that the difference between the two means equals zero.

When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .

Related post : Understanding the Null Hypothesis in More Detail

Alternative Hypothesis

The alternative hypothesis is the other theory about the properties of the population in hypothesis testing. Typically, the alternative hypothesis states that a population parameter does not equal the null hypothesis value. In other words, there is a non-zero effect. If your sample contains sufficient evidence, you can reject the null and favor the alternative hypothesis. The alternative is often identified with H 1 or H A .

For example, in a 2-sample t-test, the alternative often states that the difference between the two means does not equal zero.

You can specify either a one- or two-tailed alternative hypothesis:

If you perform a two-tailed hypothesis test, the alternative states that the population parameter does not equal the null value. For example, when the alternative hypothesis is H A : μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative has more power to detect an effect but it can test for a difference in only one direction. For example, H A : μ > 0 can only test for differences that are greater than zero.

Related posts : Understanding T-tests and One-Tailed and Two-Tailed Hypothesis Tests Explained

P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is correct. In simpler terms, p-values tell you how strongly your sample data contradict the null. Lower p-values represent stronger evidence against the null. You use P-values in conjunction with the significance level to determine whether your data favor the null or alternative hypothesis.

Related post : Interpreting P-values Correctly

Significance Level (Alpha)

For instance, a significance level of 0.05 signifies a 5% risk of deciding that an effect exists when it does not exist.

Use p-values and significance levels together to help you determine which hypothesis the data support. If the p-value is less than your significance level, you can reject the null and conclude that the effect is statistically significant. In other words, the evidence in your sample is strong enough to be able to reject the null hypothesis at the population level.

Related posts : Graphical Approach to Significance Levels and P-values and Conceptual Approach to Understanding Significance Levels

Types of Errors in Hypothesis Testing

Statistical hypothesis tests are not 100% accurate because they use a random sample to draw conclusions about entire populations. There are two types of errors related to drawing an incorrect conclusion.

• False positives: You reject a null that is true. Statisticians call this a Type I error . The Type I error rate equals your significance level or alpha (α).
• False negatives: You fail to reject a null that is false. Statisticians call this a Type II error. Generally, you do not know the Type II error rate. However, it is a larger risk when you have a small sample size , noisy data, or a small effect size. The type II error rate is also known as beta (β).

Statistical power is the probability that a hypothesis test correctly infers that a sample effect exists in the population. In other words, the test correctly rejects a false null hypothesis. Consequently, power is inversely related to a Type II error. Power = 1 – β. Learn more about Power in Statistics .

Related posts : Types of Errors in Hypothesis Testing and Estimating a Good Sample Size for Your Study Using Power Analysis

Which Type of Hypothesis Test is Right for You?

There are many different types of procedures you can use. The correct choice depends on your research goals and the data you collect. Do you need to understand the mean or the differences between means? Or, perhaps you need to assess proportions. You can even use hypothesis testing to determine whether the relationships between variables are statistically significant.

To choose the proper statistical procedure, you’ll need to assess your study objectives and collect the correct type of data . This background research is necessary before you begin a study.

Related Post : Hypothesis Tests for Continuous, Binary, and Count Data

Statistical tests are crucial when you want to use sample data to make conclusions about a population because these tests account for sample error. Using significance levels and p-values to determine when to reject the null hypothesis improves the probability that you will draw the correct conclusion.

To see an alternative approach to these traditional hypothesis testing methods, learn about bootstrapping in statistics !

If you want to see examples of hypothesis testing in action, I recommend the following posts that I have written:

• How Effective Are Flu Shots? This example shows how you can use statistics to test proportions.
• Fatality Rates in Star Trek . This example shows how to use hypothesis testing with categorical data.
• Busting Myths About the Battle of the Sexes . A fun example based on a Mythbusters episode that assess continuous data using several different tests.
• Are Yawns Contagious? Another fun example inspired by a Mythbusters episode.

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Reader Interactions

January 14, 2024 at 8:43 am

Hello professor Jim, how are you doing! Pls. What are the properties of a population and their examples? Thanks for your time and understanding.

January 14, 2024 at 12:57 pm

Please read my post about Populations vs. Samples for more information and examples.

Also, please note there is a search bar in the upper-right margin of my website. Use that to search for topics.

July 5, 2023 at 7:05 am

Hello, I have a question as I read your post. You say in p-values section

“P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is correct. In simpler terms, p-values tell you how strongly your sample data contradict the null. Lower p-values represent stronger evidence against the null.”

But according to your definition of effect, the null states that an effect does not exist, correct? So what I assume you want to say is that “P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is **incorrect**.”

July 6, 2023 at 5:18 am

Hi Shrinivas,

The correct definition of p-value is that it is a probability that exists in the context of a true null hypothesis. So, the quotation is correct in stating “if the null hypothesis is correct.”

Essentially, the p-value tells you the likelihood of your observed results (or more extreme) if the null hypothesis is true. It gives you an idea of whether your results are surprising or unusual if there is no effect.

Hence, with sufficiently low p-values, you reject the null hypothesis because it’s telling you that your sample results were unlikely to have occurred if there was no effect in the population.

I hope that helps make it more clear. If not, let me know I’ll attempt to clarify!

May 8, 2023 at 12:47 am

Thanks a lot Ny best regards

May 7, 2023 at 11:15 pm

Hi Jim Can you tell me something about size effect? Thanks

May 8, 2023 at 12:29 am

Here’s a post that I’ve written about Effect Sizes that will hopefully tell you what you need to know. Please read that. Then, if you have any more specific questions about effect sizes, please post them there. Thanks!

January 7, 2023 at 4:19 pm

Hi Jim, I have only read two pages so far but I am really amazed because in few paragraphs you made me clearly understand the concepts of months of courses I received in biostatistics! Thanks so much for this work you have done it helps a lot!

January 10, 2023 at 3:25 pm

Thanks so much!

June 17, 2021 at 1:45 pm

Can you help in the following question: Rocinante36 is priced at ₹7 lakh and has been designed to deliver a mileage of 22 km/litre and a top speed of 140 km/hr. Formulate the null and alternative hypotheses for mileage and top speed to check whether the new models are performing as per the desired design specifications.

April 19, 2021 at 1:51 pm

Its indeed great to read your work statistics.

I have a doubt regarding the one sample t-test. So as per your book on hypothesis testing with reference to page no 45, you have mentioned the difference between “the sample mean and the hypothesised mean is statistically significant”. So as per my understanding it should be quoted like “the difference between the population mean and the hypothesised mean is statistically significant”. The catch here is the hypothesised mean represents the sample mean.

Please help me understand this.

Regards Rajat

April 19, 2021 at 3:46 pm

Thanks for buying my book. I’m so glad it’s been helpful!

The test is performed on the sample but the results apply to the population. Hence, if the difference between the sample mean (observed in your study) and the hypothesized mean is statistically significant, that suggests that population does not equal the hypothesized mean.

For one sample tests, the hypothesized mean is not the sample mean. It is a mean that you want to use for the test value. It usually represents a value that is important to your research. In other words, it’s a value that you pick for some theoretical/practical reasons. You pick it because you want to determine whether the population mean is different from that particular value.

I hope that helps!

November 5, 2020 at 6:24 am

Jim, you are such a magnificent statistician/economist/econometrician/data scientist etc whatever profession. Your work inspires and simplifies the lives of so many researchers around the world. I truly admire you and your work. I will buy a copy of each book you have on statistics or econometrics. Keep doing the good work. Remain ever blessed

November 6, 2020 at 9:47 pm

Hi Renatus,

Thanks so much for you very kind comments. You made my day!! I’m so glad that my website has been helpful. And, thanks so much for supporting my books! 🙂

November 2, 2020 at 9:32 pm

Hi Jim, I hope you are aware of 2019 American Statistical Association’s official statement on Statistical Significance: https://www.tandfonline.com/doi/full/10.1080/00031305.2019.1583913 In case you do not bother reading the full article, may I quote you the core message here: “We conclude, based on our review of the articles in this special issue and the broader literature, that it is time to stop using the term “statistically significant” entirely. Nor should variants such as “significantly different,” “p < 0.05,” and “nonsignificant” survive, whether expressed in words, by asterisks in a table, or in some other way."

With best wishes,

November 3, 2020 at 2:09 am

I’m definitely aware of the debate surrounding how to use p-values most effectively. However, I need to correct you on one point. The link you provide is NOT a statement by the American Statistical Association. It is an editorial by several authors.

There is considerable debate over this issue. There are problems with p-values. However, as the authors state themselves, much of the problem is over people’s mindsets about how to use p-values and their incorrect interpretations about what statistical significance does and does not mean.

If you were to read my website more thoroughly, you’d be aware that I share many of their concerns and I address them in multiple posts. One of the authors’ key points is the need to be thoughtful and conduct thoughtful research and analysis. I emphasize this aspect in multiple posts on this topic. I’ll ask you to read the following three because they all address some of the authors’ concerns and suggestions. But you might run across others to read as well.

Five Tips for Using P-values to Avoid Being Misled How to Interpret P-values Correctly P-values and the Reproducibility of Experimental Results

September 24, 2020 at 11:52 pm

HI Jim, i just want you to know that you made explanation for Statistics so simple! I should say lesser and fewer words that reduce the complexity. All the best! 🙂

September 25, 2020 at 1:03 am

Thanks, Rene! Your kind words mean a lot to me! I’m so glad it has been helpful!

September 23, 2020 at 2:21 am

Honestly, I never understood stats during my entire M.Ed course and was another nightmare for me. But how easily you have explained each concept, I have understood stats way beyond my imagination. Thank you so much for helping ignorant research scholars like us. Looking forward to get hardcopy of your book. Kindly tell is it available through flipkart?

September 24, 2020 at 11:14 pm

I’m so happy to hear that my website has been helpful!

I checked on flipkart and it appears like my books are not available there. I’m never exactly sure where they’re available due to the vagaries of different distribution channels. They are available on Amazon in India.

Introduction to Statistics: An Intuitive Guide (Amazon IN) Hypothesis Testing: An Intuitive Guide (Amazon IN)

July 26, 2020 at 11:57 am

Dear Jim I am a teacher from India . I don’t have any background in statistics, and still I should tell that in a single read I can follow your explanations . I take my entire biostatistics class for botany graduates with your explanations. Thanks a lot. May I know how I can avail your books in India

July 28, 2020 at 12:31 am

Right now my books are only available as ebooks from my website. However, soon I’ll have some exciting news about other ways to obtain it. Stay tuned! I’ll announce it on my email list. If you’re not already on it, you can sign up using the form that is in the right margin of my website.

June 22, 2020 at 2:02 pm

Also can you please let me if this book covers topics like EDA and principal component analysis?

June 22, 2020 at 2:07 pm

This book doesn’t cover principal components analysis. Although, I wouldn’t really classify that as a hypothesis test. In the future, I might write a multivariate analysis book that would cover this and others. But, that’s well down the road.

My Introduction to Statistics covers EDA. That’s the largely graphical look at your data that you often do prior to hypothesis testing. The Introduction book perfectly leads right into the Hypothesis Testing book.

June 22, 2020 at 1:45 pm

Thanks for the detailed explanation. It does clear my doubts. I saw that your book related to hypothesis testing has the topics that I am studying currently. I am looking forward to purchasing it.

Regards, Take Care

June 19, 2020 at 1:03 pm

For this particular article I did not understand a couple of statements and it would great if you could help: 1)”If sample error causes the observed difference, the next time someone performs the same experiment the results might be different.” 2)”If the difference does not exist at the population level, you won’t obtain the benefits that you expect based on the sample statistics.”

I discovered your articles by chance and now I keep coming back to read & understand statistical concepts. These articles are very informative & easy to digest. Thanks for the simplifying things.

June 20, 2020 at 9:53 pm

I’m so happy to hear that you’ve found my website to be helpful!

To answer your questions, keep in mind that a central tenant of inferential statistics is that the random sample that a study drew was only one of an infinite number of possible it could’ve drawn. Each random sample produces different results. Most results will cluster around the population value assuming they used good methodology. However, random sampling error always exists and makes it so that population estimates from a sample almost never exactly equal the correct population value.

So, imagine that we’re studying a medication and comparing the treatment and control groups. Suppose that the medicine is truly not effect and that the population difference between the treatment and control group is zero (i.e., no difference.) Despite the true difference being zero, most sample estimates will show some degree of either a positive or negative effect thanks to random sampling error. So, just because a study has an observed difference does not mean that a difference exists at the population level. So, on to your questions:

1. If the observed difference is just random error, then it makes sense that if you collected another random sample, the difference could change. It could change from negative to positive, positive to negative, more extreme, less extreme, etc. However, if the difference exists at the population level, most random samples drawn from the population will reflect that difference. If the medicine has an effect, most random samples will reflect that fact and not bounce around on both sides of zero as much.

2. This is closely related to the previous answer. If there is no difference at the population level, but say you approve the medicine because of the observed effects in a sample. Even though your random sample showed an effect (which was really random error), that effect doesn’t exist. So, when you start using it on a larger scale, people won’t benefit from the medicine. That’s why it’s important to separate out what is easily explained by random error versus what is not easily explained by it.

I think reading my post about how hypothesis tests work will help clarify this process. Also, in about 24 hours (as I write this), I’ll be releasing my new ebook about Hypothesis Testing!

May 29, 2020 at 5:23 am

Hi Jim, I really enjoy your blog. Can you please link me on your blog where you discuss about Subgroup analysis and how it is done? I need to use non parametric and parametric statistical methods for my work and also do subgroup analysis in order to identify potential groups of patients that may benefit more from using a treatment than other groups.

May 29, 2020 at 2:12 pm

Hi, I don’t have a specific article about subgroup analysis. However, subgroup analysis is just the dividing up of a larger sample into subgroups and then analyzing those subgroups separately. You can use the various analyses I write about on the subgroups.

Alternatively, you can include the subgroups in regression analysis as an indicator variable and include that variable as a main effect and an interaction effect to see how the relationships vary by subgroup without needing to subdivide your data. I write about that approach in my article about comparing regression lines . This approach is my preferred approach when possible.

April 19, 2020 at 7:58 am

sir is confidence interval is a part of estimation?

April 17, 2020 at 3:36 pm

Sir can u plz briefly explain alternatives of hypothesis testing? I m unable to find the answer

April 18, 2020 at 1:22 am

Assuming you want to draw conclusions about populations by using samples (i.e., inferential statistics ), you can use confidence intervals and bootstrap methods as alternatives to the traditional hypothesis testing methods.

March 9, 2020 at 10:01 pm

Hi JIm, could you please help with activities that can best teach concepts of hypothesis testing through simulation, Also, do you have any question set that would enhance students intuition why learning hypothesis testing as a topic in introductory statistics. Thanks.

March 5, 2020 at 3:48 pm

Hi Jim, I’m studying multiple hypothesis testing & was wondering if you had any material that would be relevant. I’m more trying to understand how testing multiple samples simultaneously affects your results & more on the Bonferroni Correction

March 5, 2020 at 4:05 pm

I write about multiple comparisons (aka post hoc tests) in the ANOVA context . I don’t talk about Bonferroni Corrections specifically but I cover related types of corrections. I’m not sure if that exactly addresses what you want to know but is probably the closest I have already written. I hope it helps!

January 14, 2020 at 9:03 pm

Thank you! Have a great day/evening.

January 13, 2020 at 7:10 pm

Any help would be greatly appreciated. What is the difference between The Hypothesis Test and The Statistical Test of Hypothesis?

January 14, 2020 at 11:02 am

They sound like the same thing to me. Unless this is specialized terminology for a particular field or the author was intending something specific, I’d guess they’re one and the same.

April 1, 2019 at 10:00 am

so these are the only two forms of Hypothesis used in statistical testing?

April 1, 2019 at 10:02 am

Are you referring to the null and alternative hypothesis? If so, yes, that’s those are the standard hypotheses in a statistical hypothesis test.

April 1, 2019 at 9:57 am

year very insightful post, thanks for the write up

October 27, 2018 at 11:09 pm

hi there, am upcoming statistician, out of all blogs that i have read, i have found this one more useful as long as my problem is concerned. thanks so much

October 27, 2018 at 11:14 pm

Hi Stano, you’re very welcome! Thanks for your kind words. They mean a lot! I’m happy to hear that my posts were able to help you. I’m sure you will be a fantastic statistician. Best of luck with your studies!

October 26, 2018 at 11:39 am

Dear Jim, thank you very much for your explanations! I have a question. Can I use t-test to compare two samples in case each of them have right bias?

October 26, 2018 at 12:00 pm

Hi Tetyana,

You’re very welcome!

The term “right bias” is not a standard term. Do you by chance mean right skewed distributions? In other words, if you plot the distribution for each group on a histogram they have longer right tails? These are not the symmetrical bell-shape curves of the normal distribution.

If that’s the case, yes you can as long as you exceed a specific sample size within each group. I include a table that contains these sample size requirements in my post about nonparametric vs parametric analyses .

Bias in statistics refers to cases where an estimate of a value is systematically higher or lower than the true value. If this is the case, you might be able to use t-tests, but you’d need to be sure to understand the nature of the bias so you would understand what the results are really indicating.

I hope this helps!

April 2, 2018 at 7:28 am

Simple and upto the point 👍 Thank you so much.

April 2, 2018 at 11:11 am

Hi Kalpana, thanks! And I’m glad it was helpful!

March 26, 2018 at 8:41 am

Am I correct if I say: Alpha – Probability of wrongly rejection of null hypothesis P-value – Probability of wrongly acceptance of null hypothesis

March 28, 2018 at 3:14 pm

You’re correct about alpha. Alpha is the probability of rejecting the null hypothesis when the null is true.

Unfortunately, your definition of the p-value is a bit off. The p-value has a fairly convoluted definition. It is the probability of obtaining the effect observed in a sample, or more extreme, if the null hypothesis is true. The p-value does NOT indicate the probability that either the null or alternative is true or false. Although, those are very common misinterpretations. To learn more, read my post about how to interpret p-values correctly .

March 2, 2018 at 6:10 pm

I recently started reading your blog and it is very helpful to understand each concept of statistical tests in easy way with some good examples. Also, I recommend to other people go through all these blogs which you posted. Specially for those people who have not statistical background and they are facing to many problems while studying statistical analysis.

Thank you for your such good blogs.

March 3, 2018 at 10:12 pm

Hi Amit, I’m so glad that my blog posts have been helpful for you! It means a lot to me that you took the time to write such a nice comment! Also, thanks for recommending by blog to others! I try really hard to write posts about statistics that are easy to understand.

January 17, 2018 at 7:03 am

I recently started reading your blog and I find it very interesting. I am learning statistics by my own, and I generally do many google search to understand the concepts. So this blog is quite helpful for me, as it have most of the content which I am looking for.

January 17, 2018 at 3:56 pm

Hi Shashank, thank you! And, I’m very glad to hear that my blog is helpful!

January 2, 2018 at 2:28 pm

thank u very much sir.

January 2, 2018 at 2:36 pm

You’re very welcome, Hiral!

November 21, 2017 at 12:43 pm

Thank u so much sir….your posts always helps me to be a #statistician

November 21, 2017 at 2:40 pm

Hi Sachin, you’re very welcome! I’m happy that you find my posts to be helpful!

November 19, 2017 at 8:22 pm

great post as usual, but it would be nice to see an example.

November 19, 2017 at 8:27 pm

Thank you! At the end of this post, I have links to four other posts that show examples of hypothesis tests in action. You’ll find what you’re looking for in those posts!

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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.

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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.

Psst... there’s more!

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

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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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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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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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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Research Hypothesis In Psychology: Types, & Examples

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.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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Quantitative Data Analysis

5 Hypothesis Testing in Quantitative Research

Mikaila Mariel Lemonik Arthur

Statistical reasoning is built on the assumption that data are normally distributed , meaning that they will be distributed in the shape of a bell curve as discussed in the chapter on Univariate Analysis . While real life often—perhaps even usually—does not resemble a bell curve, basic statistical analysis assumes that if all possible random samples from a population were drawn and the mean taken from each sample, the distribution of sample means, when plotted on a graph, would be normally distributed (this assumption is called the Central Limit Theorem ). Given this assumption, we can use the mathematical techniques developed for the study of probability to determine the likelihood that the relationships or patterns we observe in our data occurred due to random chance rather than due some actual real-world connection, which we call statistical significance.

Statistical significance is not the same as practical significance. The fact that we have determined that a given result is unlikely to have occurred due to random chance does not mean that this given result is important, that it matters, or that it is useful. Similarly, we might observe a relationship or result that is very important in practical terms, but that we cannot claim is statistically significant—perhaps because our sample size is too small, for instance. Such a result might have occurred by chance, but ignoring it might still be a mistake. Let’s consider some examples to make this a bit clearer. Assume we were interested in the impacts of diet on health outcomes and found the statistically significant result that people who eat a lot of citrus fruit end up having pinky fingernails that are, on average, 1.5 millimeters longer than those who tend not to eat any citrus fruit. Should anyone change their diet due to this finding? Probably not, even those it is statistically significant. On the other hand, if we found that the people who ate the diets highest in processed sugar died on average five years sooner than those who ate the least processed sugar, even in the absence of a statistically significant result we might want to advise that people consider limiting sugar in their diet. This latter result has more practical significance (lifespan matters more than the length of your pinky fingernail) as well as a larger effect size or association (5 years of life as opposed to 1.5 millimeters of length), a factor that will be discussed in the chapter on association .

While people generally use the shorthand of “the likelihood that the results occurred by chance” when talking about statistical significance, it is actually a bit more complicated than that. What statistical significance is really telling us is the likelihood (or probability ) that a result equal to or more “extreme [1] ” is true in the real world, rather than our results having occurred due to random chance or sampling error . Testing for statistical significance, then, requires us to understand something about probability.

A Brief Review of Probability

You might remember having studied probability in a math class, with questions about coin flips or drawing marbles out of a jar. Such exercises can make probability seem very abstract. But in reality, computations of probability are deeply important for a wide variety of activities, ranging from gambling and stock trading to weather forecasts and, yes, statistical significance.

Probability is represented as a proportion (or decimal number) somewhere between 0 and 1. At 0, there is absolutely no likelihood that the event or pattern of interest would occur; at 1, it is absolutely certain that the event or pattern of interest will occur. We indicate that we are talking about probability by using the symbol [latex]p[/latex]. For example, if something has a 50% chance of occurring, we would write [latex]p=0.5[/latex] or [latex]\frac {1}{2}[/latex]. If we want to represent the likelihood of something not occurring, we can write [latex]1-p[/latex].

Check your thinking: Assume you were flipping coins, and you called heads. The probability of getting heads on a coin flip using a fair coin (in other words, a normal coin that has not been weighted to bias the result) is 0.5. Thus, in 50% of coin flips you should get heads. Consider the following probability questions and write down your answers so you can check them against the discussion below.

• Imagine you have flipped the coin 29 times and you have gotten heads each time. What is the probability you will get heads on flip 30?
• What is the probability that you will get heads on all of the first five coin flips?
• What is the probability that you will get heads on at least one of the first five coin flips?

There are a few basic concepts from the mathematical study of probability that are important for beginner data analysts to know, and we will review them here.

Probability over Repeated Trials : The probability of the outcome of interest is the same in each trial or test, regardless of the results of the prior test. So, if we flip a coin 29 times and get heads each time, what happens when we flip it the 29th time? The probability of heads is still 0.5! The belief that “this time it must be tails because it has been heads so many times” or “this coin just wants to come up heads” is simply superstition, and—assuming a fair coin—the results of prior trials do not influence the results of this one.

Probability of Multiple Events : The probability that the outcome of interest will occur repeatedly across multiple trials is the product [2] of the probability of the outcome on each individual trial. This is called the multiplication theorem . Thinking about the multiplication theorem requires that we keep in mind the fact that when we multiply decimal numbers together, those numbers get smaller— thus, the probability that a series of outcomes will occur is smaller than the probability of any one of those outcomes occurring on its own. So, what is the probability that we will get heads on all five of our coin flips? Well, to figure that out, we need to multiply the probability of getting heads on each of our coin flips together. The math looks like this (and produces a very small probability indeed):

[latex]\frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} \cdot \frac {1}{2} = 0.03125[/latex]

Probability of One of Many Events : Determining the probability that the outcome of interest will occur on at least one out of a series of events or repeated trials is a little bit more complicated. Mathematicians use the addition theorem to refer to this, because the basic way to calculate it is to calculate the probability of each sequence of events (say, heads-heads-heads, heads-heads-tails, heads-tails-heads, and so on) and add them together. But the greater the number of repeated trials, the more complicated that gets, so there is a simpler way to do it. Consider that the probability of getting  no heads is the same as the probability of getting all tails (which would be the same as the probability of getting all heads that we calculated above). And the only circumstance in which we would not have at least one flip resulting in heads would be a circumstance in which all flips had resulted in tails. Therefore, what we need to do in order to calculate the probability that we get at least one heads is to subtract the probability that we get no heads from 1—and as you can imagine, this procedure shows us that the probability of the outcome of interest occurring at least once over repeated trials is higher than the probability of the occurrence on any given trial. The math would look like this:

[latex]1- (\frac{1}{2})^5=0.9688[/latex]

So why is this digression into the math of probability important? Well, when we test for statistical significance, what we are really doing is determining the probability that the outcome we observed—or one that is more extreme than that which we observed—occurred by chance. We perform this analysis via a procedure called Null Hypothesis Significance Testing.

Null Hypothesis Significance Testing

Null hypothesis significance testing , or NHST , is a method of testing for statistical significance by comparing observed data to the data we would expect to see if there were no relationship between the variables or phenomena in question. NHST can take a little while to wrap one’s head around, especially because it relies on a logic of double negatives: first, we state a hypothesis we believe not to be true (there is no relationship between the variables in question) and then, we look for evidence that disconfirms this hypothesis. In other words, we are assuming that there is no relationship between the variables—even though our research hypothesis states that we think there is a relationship—and then looking to see if there is any evidence to suggest there is not no relationship. Confusing, right?

So why do we use the null hypothesis significance testing approach?

• The null hypothesis—that there is no relationship between the variables we are exploring—would be what we would generally accept as true in the absence of other information,
• It means we are assuming that differences or patterns occur due to chance unless there is strong evidence to suggest otherwise,
• It provides a benchmark for comparing observed outcomes, and
• It means we are searching for evidence that disconforms our hypothesis, making it less likely that we will accept a conclusion that turns out to be untrue.

Thus, NHST helps us avoid making errors in our interpretation of the result. In particular, it helps us avoid Type 2 error , as discussed in the chapter on Bivariate Analyses . As a reminder, Type 2 error is error where you accept a hypothesis as true when in fact it was false (while Type 1 error is error where you reject the hypothesis when in fact it was true). For example, you are making a Type 1 error if you decide not to study for a test because you assume you are so bad at the subject that studying simply cannot help you, when in fact we know from research that studying does lead to higher grades. And you are making a Type 2 error if your boss tells you that she is going to promote you if you do enough overtime and you then work lots of overtime in response, when actually your boss is just trying to make you work more hours and already had someone else in mind to promote.

We can never remove all sources of error from our analyses, though larger sample sizes help reduce error. Looking at the formula for computing standard error , we can see that the standard error ([latex]SE[/latex]) would get smaller as the sample size ([latex]N[/latex]) gets larger. Note: σ is the symbol we use to represent standard deviation.

[latex]SE = \frac{\sigma}{\sqrt N}[/latex]

Besides making our samples larger, another thing that we can do is that we can choose whether we are more willing to accept Type 1 error or Type 2 error and adjust our strategies accordingly. In most research, we would prefer to accept more Type 1 error, because we are more willing to miss out on a finding than we are to make a finding that turns out later to be inaccurate (though, of course, lots of research does eventually turn out to be inaccurate).

Performing NHST

Performing NHST requires that our data meet several assumptions:

• Our sample must be a random sample—statistical significance testing and other inferential and explanatory statistical methods are generally not appropriate for non-random samples [3] —as well as representative and of a sufficient size (see the Central Limit Theorem above).
• Observations must be independent of other observations, or else additional statistical manipulation must be performed. For instance, a dataset of data about siblings would need to be handled differently due to the fact that siblings affect one another, so data on each person in the dataset is not truly independent.
• You must determine the rules for your significance test, including the level of uncertainty you are willing to accept (significance level) and whether or not you are interested in the direction of the result (one-tailed versus two-tailed tests, to be discussed below), in advance of performing any analysis.
• The number of significance tests you run should be limited, because the more tests you run, the greater the likelihood that one of your tests will result in an error. To make this more clear, if you are willing to accept a 5% probability that you will make the error of accepting a hypothesis as true when it is really false, and you run 20 tests, one of those tests (5% of them!) is pretty likely to have produced an incorrect result.

If our data has met these assumptions, we can move forward with the process of conducting an NHST. This requires us to make three decisions: determining our null hypothesis , our confidence level (or acceptable significance level), and whether we will conduct a one-tailed or a two-tailed test. In keeping with Assumption 3 above, we must make these decisions before performing our analysis. The null hypothesis is the hypothesis that there is no relationship between the variables in question. So, for example, if our research hypothesis was that people who spend more time with their friends are happier, our null hypothesis would be that there is no relationship between how much time people spend with their friends and their happiness.

Our confidence level is the level of risk we are willing to accept that our results could have occurred by chance. Typically, in social science research, researchers use p<0.05 (we are willing to accept up to a 5% risk that our results occurred by chance), p<0.01 (we are willing to accept up to a 1% risk that our results occurred by chance), and/or p<0.001 (we are willing to accept up to a 0.1% risk that our results occurred by chance). P, as was noted above, is the mathematical notation for probability, and that’s why we use a p-value to indicate the probability that our results may have occurred by chance. A higher p-value increases the likelihood that we will accept as accurate a result that really occurred by chance; a lower p-value increases the likelihood that we will assume a result occurred by chance when actually it was real. Remember, what the p-value tells us is not the probability that our own research hypothesis is true, but rather this: assuming that the null hypothesis is correct, what is the probability that the data we observed—or data more extreme than the data we observed—would have occurred by chance.

Whether we choose a one-tailed or a two-tailed test tells us what we mean when we say “data more extreme than.” Remember that normal curve? A two-tailed test is agnostic as to the direction of our results—and many of the most common tests for statistical significance that we perform, like the Chi square, are two-tailed by default. However, if you are only interested in a result that occurs in a particular direction, you might choose a one-tailed test. For instance, if you were testing a new blood pressure medication, you might only care if the blood pressure of those taking the medication is significantly lower than those not taking the medication—having blood pressure significantly higher would not be a good or helpful result, so you might not want to test for that.

Having determined the parameters for our analysis, we then compute our test of statistical significance. There are different tests of statistical significance for different variables (for example, the Chi square discussed in the chapter on bivariate analyses ), as you will see in other chapters of this text, but all of them produce results in a similar format. We then compare this result to the p value we already selected. If the p value produced by our analysis is lower than the confidence level we selected, we can reject the null hypothesis, as the probability that our result occurred by chance is very low. If, on the other hand, the p value produced by our analysis is higher than the confidence level we selected, we fail to reject the null hypothesis, as the probability that our result occurred by chance is too high to accept. Keep in mind this is what we do even when the p value produced by our analysis is quite close to the threshold we have selected. So, for instance, if we have selected the confidence level of p<0.05 and the p value produced by our analysis is p=0.0501, we still fail to reject the null hypothesis and proceed as if there is not any support for our research hypothesis.

Thus, the process of null hypothesis significance testing proceeds according to the following steps:

• Determine the null hypothesis
• Set the confidence level and whether this will be a one-tailed or two-tailed test
• Compute the test value for the appropriate significance test
• Compare the test value to the critical value of that test statistic for the confidence level you selected
• Determine whether or not to reject the null hypothesis

Your statistical analysis software will perform steps 3 and 4 for you (before there was computer software to do this, researchers had to do the calculations by hand and compare their results to figures on published tables of critical values). But you as the researcher must perform steps 1, 2, and 5 yourself.

Confidence Intervals & Margins of Error

When talking about statistical significance, some researchers also use the terms confidence intervals and margins of error . Confidence intervals are ranges of probabilities within which we can assume the true population parameter lies. Most typically, analysts aim for 95% confidence intervals, meaning that in 95 out of 100 cases, the population parameter will lie within the upper and lower levels specified by your confidence interval. These are calculated by your statistics software as well. The margin of error, then, is the range of values within the confidence interval. So, for instance, a 2021 survey of Americans conducted by the Robert Wood Johnson Foundation and the Harvard T.H. Chan School of Public Health found that 71% of respondents favor substantially increasing federal spending on public health programs. This poll had a 95% confidence interval with a +/- 3.6 margin of error. What this tells us is that there is a 95% probability (19 in 20) that between 67.4% (71-3.6) and 74.6% (71+3.6) of Americans favored increasing federal public health spending at the time the poll was conducted. When a figure reflects an overwhelming majority, such as this one, the margin of error may seem of little relevance. But consider a similar poll with the same margin of error that sought to predict support for a political candidate and found that 51.5% of people said they would vote for that candidate. In that case, we would have found that there was a 95% probability that between 47.9% and 55.1% of people intended to vote for the candidate—which means the race is total tossup and we really would have no idea what to expect. For some people, thinking in terms of confidence intervals and margins of error is easier to understand than thinking in terms of p values; confidence intervals and margins of error are more frequently used in analyses of polls while p values are found more often in academic research. But basically, both approaches are doing the same fundamental analysis—they are determining the likelihood that the results we observed or a similarly-meaningful result would have occurred by chance.

What Does Significance Testing Tell Us?

One of the most important things to remember about significance testing is that, while the word “significance” is used in ordinary speech to mean importance, significance testing does not tell us whether our results are important—or even whether they are interesting. A full understanding of the relationship between a given set of variables requires looking at statistical significance as well as association and the theoretical importance of the findings. Table 1 provides a perspective on using the combination of significance and association to determine how important the results of statistical analysis are—but even using Table 1 as a guide, evaluating findings based on theoretical importance remains key. So: make sure that when you are conducting analyses, you avoid being misled into assuming that significant results are sufficient for making broad claims about the importance and meaning of results. And remember as well that significance only tells us the likelihood that the pattern of relationships we observe occurred by chance—not whether that pattern is causal. For, after all, quantitative research can never eliminate all plausible alternative explanations for the phenomenon in question (one of the three elements of causation, along with association and temporal order).

• Getting 7 heads on 7 coin flips
• Getting 5 heads on 7 coin flips
• Getting 1 head on 10 coin flips

Then check your work using the Coin Flip Probability Calculator .

• As the advertised hourly pay for a job goes up, the number of job applicants increases.
• Teenagers who watch more hours of makeup tutorial videos on TikTok have, on average, lower self-esteem.
• Couples who share hobbies in common are less likely to get divorced.
• Assume a research conducted a study that found that people wearing green socks type on average one word per minute faster than people who are not wearing green socks, and that this study found a p value of p<0.01. Is this result statistically significant? Is this result practically significant? Explain your answers.
• If we conduct a political poll and have a 95% confidence interval and a margin of error of +/- 2.3%, what can we conclude about support for Candidate X if 49.3% of respondents tell us they will vote for Candidate X? If 24.7% do? If 52.1% do? If 83.7% do?
• One way to think about this is to imagine that your result has been plotted on a bell curve. Statistical significance tells us the probability that the "real" result—the thing that is true in the real world and not due to random chance—is at the same point as or further along the skinny tails of the bell curve than the result we have plotted. ↵
• In other words, what you get when you multiply. ↵
• They also are not appropriate for censuses—but you do not need inferential statistics in a census because you are looking at the entire population rather than a sample, so you can simply describe the relationships that do exist. ↵

A distribution of values that is symmetrical and bell-shaped.

A graph showing a normal distribution—one that is symmetrical with a rounded top that then falls away towards the extremes in the shape of a bell

The sum of all the values in a list divided by the number of such values.

The theorem that states that if you take a series of sufficiently large random samples from the population (replacing people back into the population so they can be reselected each time you draw a new sample), the distribution of the sample means will be approximately normally distributed.

A statistical measure that suggests that sample results can be generalized to the larger population, based on a low probability of having made a Type 1 error.

How likely something is to happen; also, a branch of mathematics concerned with investigating the likelihood of occurrences.

Measurement error created due to the fact that even properly-constructed random samples are do not have precisely the same characteristics as the larger population from which they were drawn.

The theorem in probability about the likelihood of a given outcome occurring repeatedly over multiple trials; this is determined by multiplying the probabilities together.

The theorem addressing the determination of the probability of a given outcome occurring at least once across a series of trials; it is determined by adding the probability of each possible series of outcomes together.

A method of testing for statistical significance in which an observed relationship, pattern, or figure is tested against a hypothesis that there is no relationship or pattern among the variables being tested

Null hypothesis significance testing.

The error you make when you do not infer a relationship exists in the larger population when it actually does exist; in other words, a false negative conclusion.

The error made if one infers that a relationship exists in a larger population when it does not really exist; in other words, a false positive error.

A measure of accuracy of sample statistics computed using the standard deviation of the sampling distribution.

The hypothesis that there is no relationship between the variables in question.

The probability that the sample statistics we observe holds true for the larger population.

A measure of statistical significance used in crosstabulation to determine the generalizability of results.

A range of estimates into which it is highly probable that an unknown population parameter falls.

A suggestion of how far away from the actual population parameter a sample statistic is likely to be.

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

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Research Hypothesis: What It Is, Types + How to Develop?

A research study starts with a question. Researchers worldwide ask questions and create research hypotheses. The effectiveness of research relies on developing a good research hypothesis. Examples of research hypotheses can guide researchers in writing effective ones.

In this blog, we’ll learn what a research hypothesis is, why it’s important in research, and the different types used in science. We’ll also guide you through creating your research hypothesis and discussing ways to test and evaluate it.

What is a Research Hypothesis?

A hypothesis is like a guess or idea that you suggest to check if it’s true. A research hypothesis is a statement that brings up a question and predicts what might happen.

It’s really important in the scientific method and is used in experiments to figure things out. Essentially, it’s an educated guess about how things are connected in the research.

A research hypothesis usually includes pointing out the independent variable (the thing they’re changing or studying) and the dependent variable (the result they’re measuring or watching). It helps plan how to gather and analyze data to see if there’s evidence to support or deny the expected connection between these variables.

Importance of Hypothesis in Research

Hypotheses are really important in research. They help design studies, allow for practical testing, and add to our scientific knowledge. Their main role is to organize research projects, making them purposeful, focused, and valuable to the scientific community. Let’s look at some key reasons why they matter:

• A research hypothesis helps test theories.

A hypothesis plays a pivotal role in the scientific method by providing a basis for testing existing theories. For example, a hypothesis might test the predictive power of a psychological theory on human behavior.

• It serves as a great platform for investigation activities.

It serves as a launching pad for investigation activities, which offers researchers a clear starting point. A research hypothesis can explore the relationship between exercise and stress reduction.

• Hypothesis guides the research work or study.

A well-formulated hypothesis guides the entire research process. It ensures that the study remains focused and purposeful. For instance, a hypothesis about the impact of social media on interpersonal relationships provides clear guidance for a study.

• Hypothesis sometimes suggests theories.

In some cases, a hypothesis can suggest new theories or modifications to existing ones. For example, a hypothesis testing the effectiveness of a new drug might prompt a reconsideration of current medical theories.

• It helps in knowing the data needs.

A hypothesis clarifies the data requirements for a study, ensuring that researchers collect the necessary information—a hypothesis guiding the collection of demographic data to analyze the influence of age on a particular phenomenon.

• The hypothesis explains social phenomena.

Hypotheses are instrumental in explaining complex social phenomena. For instance, a hypothesis might explore the relationship between economic factors and crime rates in a given community.

• Hypothesis provides a relationship between phenomena for empirical Testing.

Hypotheses establish clear relationships between phenomena, paving the way for empirical testing. An example could be a hypothesis exploring the correlation between sleep patterns and academic performance.

• It helps in knowing the most suitable analysis technique.

A hypothesis guides researchers in selecting the most appropriate analysis techniques for their data. For example, a hypothesis focusing on the effectiveness of a teaching method may lead to the choice of statistical analyses best suited for educational research.

Characteristics of a Good Research Hypothesis

A hypothesis is a specific idea that you can test in a study. It often comes from looking at past research and theories. A good hypothesis usually starts with a research question that you can explore through background research. For it to be effective, consider these key characteristics:

• Clear and Focused Language: A good hypothesis uses clear and focused language to avoid confusion and ensure everyone understands it.
• Related to the Research Topic: The hypothesis should directly relate to the research topic, acting as a bridge between the specific question and the broader study.
• Testable: An effective hypothesis can be tested, meaning its prediction can be checked with real data to support or challenge the proposed relationship.
• Potential for Exploration: A good hypothesis often comes from a research question that invites further exploration. Doing background research helps find gaps and potential areas to investigate.
• Includes Variables: The hypothesis should clearly state both the independent and dependent variables, specifying the factors being studied and the expected outcomes.
• Ethical Considerations: Check if variables can be manipulated without breaking ethical standards. It’s crucial to maintain ethical research practices.
• Predicts Outcomes: The hypothesis should predict the expected relationship and outcome, acting as a roadmap for the study and guiding data collection and analysis.
• Simple and Concise: A good hypothesis avoids unnecessary complexity and is simple and concise, expressing the essence of the proposed relationship clearly.
• Clear and Assumption-Free: The hypothesis should be clear and free from assumptions about the reader’s prior knowledge, ensuring universal understanding.
• Observable and Testable Results: A strong hypothesis implies research that produces observable and testable results, making sure the study’s outcomes can be effectively measured and analyzed.

When you use these characteristics as a checklist, it can help you create a good research hypothesis. It’ll guide improving and strengthening the hypothesis, identifying any weaknesses, and making necessary changes. Crafting a hypothesis with these features helps you conduct a thorough and insightful research study.

Types of Research Hypotheses

The research hypothesis comes in various types, each serving a specific purpose in guiding the scientific investigation. Knowing the differences will make it easier for you to create your own hypothesis. Here’s an overview of the common types:

01. Null Hypothesis

The null hypothesis states that there is no connection between two considered variables or that two groups are unrelated. As discussed earlier, a hypothesis is an unproven assumption lacking sufficient supporting data. It serves as the statement researchers aim to disprove. It is testable, verifiable, and can be rejected.

For example, if you’re studying the relationship between Project A and Project B, assuming both projects are of equal standard is your null hypothesis. It needs to be specific for your study.

02. Alternative Hypothesis

The alternative hypothesis is basically another option to the null hypothesis. It involves looking for a significant change or alternative that could lead you to reject the null hypothesis. It’s a different idea compared to the null hypothesis.

When you create a null hypothesis, you’re making an educated guess about whether something is true or if there’s a connection between that thing and another variable. If the null view suggests something is correct, the alternative hypothesis says it’s incorrect. 

For instance, if your null hypothesis is “I’m going to be $1000 richer,” the alternative hypothesis would be “I’m not going to get $1000 or be richer.”

03. Directional Hypothesis

The directional hypothesis predicts the direction of the relationship between independent and dependent variables. They specify whether the effect will be positive or negative.

If you increase your study hours, you will experience a positive association with your exam scores. This hypothesis suggests that as you increase the independent variable (study hours), there will also be an increase in the dependent variable (exam scores).

04. Non-directional Hypothesis

The non-directional hypothesis predicts the existence of a relationship between variables but does not specify the direction of the effect. It suggests that there will be a significant difference or relationship, but it does not predict the nature of that difference.

For example, you will find no notable difference in test scores between students who receive the educational intervention and those who do not. However, once you compare the test scores of the two groups, you will notice an important difference.

05. Simple Hypothesis

A simple hypothesis predicts a relationship between one dependent variable and one independent variable without specifying the nature of that relationship. It’s simple and usually used when we don’t know much about how the two things are connected.

For example, if you adopt effective study habits, you will achieve higher exam scores than those with poor study habits.

06. Complex Hypothesis

A complex hypothesis is an idea that specifies a relationship between multiple independent and dependent variables. It is a more detailed idea than a simple hypothesis.

While a simple view suggests a straightforward cause-and-effect relationship between two things, a complex hypothesis involves many factors and how they’re connected to each other.

For example, when you increase your study time, you tend to achieve higher exam scores. The connection between your study time and exam performance is affected by various factors, including the quality of your sleep, your motivation levels, and the effectiveness of your study techniques.

If you sleep well, stay highly motivated, and use effective study strategies, you may observe a more robust positive correlation between the time you spend studying and your exam scores, unlike those who may lack these factors.

07. Associative Hypothesis

An associative hypothesis proposes a connection between two things without saying that one causes the other. Basically, it suggests that when one thing changes, the other changes too, but it doesn’t claim that one thing is causing the change in the other.

For example, you will likely notice higher exam scores when you increase your study time. You can recognize an association between your study time and exam scores in this scenario.

Your hypothesis acknowledges a relationship between the two variables—your study time and exam scores—without asserting that increased study time directly causes higher exam scores. You need to consider that other factors, like motivation or learning style, could affect the observed association.

08. Causal Hypothesis

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

For example, when you increase your study time, you experience higher exam scores. This hypothesis suggests a direct cause-and-effect relationship, indicating that the more time you spend studying, the higher your exam scores. It assumes that changes in your study time directly influence changes in your exam performance.

09. Empirical Hypothesis

An empirical hypothesis is a statement based on things we can see and measure. It comes from direct observation or experiments and can be tested with real-world evidence. If an experiment proves a theory, it supports the idea and shows it’s not just a guess. This makes the statement more reliable than a wild guess.

For example, if you increase the dosage of a certain medication, you might observe a quicker recovery time for patients. Imagine you’re in charge of a clinical trial. In this trial, patients are given varying dosages of the medication, and you measure and compare their recovery times. This allows you to directly see the effects of different dosages on how fast patients recover.

This way, you can create a research hypothesis: “Increasing the dosage of a certain medication will lead to a faster recovery time for patients.”

10. Statistical Hypothesis

A statistical hypothesis is a statement or assumption about a population parameter that is the subject of an investigation. It serves as the basis for statistical analysis and testing. It is often tested using statistical methods to draw inferences about the larger population.

In a hypothesis test, statistical evidence is collected to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.

For example, let’s say you’re testing a new medicine. Your hypothesis could be that the medicine doesn’t really help patients get better. So, you collect data and use statistics to see if your guess is right or if the medicine actually makes a difference.

If the data strongly shows that the medicine does help, you say your guess was wrong, and the medicine does make a difference. But if the proof isn’t strong enough, you can stick with your original guess because you didn’t get enough evidence to change your mind.

How to Develop a Research Hypotheses?

Step 1: identify your research problem or topic..

Define the area of interest or the problem you want to investigate. Make sure it’s clear and well-defined.

Start by asking a question about your chosen topic. Consider the limitations of your research and create a straightforward problem related to your topic. Once you’ve done that, you can develop and test a hypothesis with evidence.

Step 2: Conduct a literature review

Review existing literature related to your research problem. This will help you understand the current state of knowledge in the field, identify gaps, and build a foundation for your hypothesis. Consider the following questions:

• What existing research has been conducted on your chosen topic?
• Are there any gaps or unanswered questions in the current literature?
• How will the existing literature contribute to the foundation of your research?

Step 3: Formulate your research question

Based on your literature review, create a specific and concise research question that addresses your identified problem. Your research question should be clear, focused, and relevant to your field of study.

Step 4: Identify variables

Determine the key variables involved in your research question. Variables are the factors or phenomena that you will study and manipulate to test your hypothesis.

• Independent Variable: The variable you manipulate or control.
• Dependent Variable: The variable you measure to observe the effect of the independent variable.

Step 5: State the Null hypothesis

The null hypothesis is a statement that there is no significant difference or effect. It serves as a baseline for comparison with the alternative hypothesis.

Step 6: Select appropriate methods for testing the hypothesis

Choose research methods that align with your study objectives, such as experiments, surveys, or observational studies. The selected methods enable you to test your research hypothesis effectively.

Creating a research hypothesis usually takes more than one try. Expect to make changes as you collect data. It’s normal to test and say no to a few hypotheses before you find the right answer to your research question.

Testing and Evaluating Hypotheses

Testing hypotheses is a really important part of research. It’s like the practical side of things. Here, real-world evidence will help you determine how different things are connected. Let’s explore the main steps in hypothesis testing:

• State your research hypothesis.

Before testing, clearly articulate your research hypothesis. This involves framing both a null hypothesis, suggesting no significant effect or relationship, and an alternative hypothesis, proposing the expected outcome.

• Collect data strategically.

Plan how you will gather information in a way that fits your study. Make sure your data collection method matches the things you’re studying.

Whether through surveys, observations, or experiments, this step demands precision and adherence to the established methodology. The quality of data collected directly influences the credibility of study outcomes.

• Perform an appropriate statistical test.

Choose a statistical test that aligns with the nature of your data and the hypotheses being tested. Whether it’s a t-test, chi-square test, ANOVA, or regression analysis, selecting the right statistical tool is paramount for accurate and reliable results.

• Decide if your idea was right or wrong.

Following the statistical analysis, evaluate the results in the context of your null hypothesis. You need to decide if you should reject your null hypothesis or not.

• Share what you found.

When discussing what you found in your research, be clear and organized. Say whether your idea was supported or not, and talk about what your results mean. Also, mention any limits to your study and suggest ideas for future research.

The Role of QuestionPro to Develop a Good Research Hypothesis

QuestionPro is a survey and research platform that provides tools for creating, distributing, and analyzing surveys. It plays a crucial role in the research process, especially when you’re in the initial stages of hypothesis development. Here’s how QuestionPro can help you to develop a good research hypothesis:

• Survey design and data collection: You can use the platform to create targeted questions that help you gather relevant data.
• Exploratory research: Through surveys and feedback mechanisms on QuestionPro, you can conduct exploratory research to understand the landscape of a particular subject.
• Literature review and background research: QuestionPro surveys can collect sample population opinions, experiences, and preferences. This data and a thorough literature evaluation can help you generate a well-grounded hypothesis by improving your research knowledge.
• Identifying variables: Using targeted survey questions, you can identify relevant variables related to their research topic.
• Testing assumptions: You can use surveys to informally test certain assumptions or hypotheses before formalizing a research hypothesis.
• Data analysis tools: QuestionPro provides tools for analyzing survey data. You can use these tools to identify the collected data’s patterns, correlations, or trends.
• Refining your hypotheses: As you collect data through QuestionPro, you can adjust your hypotheses based on the real-world responses you receive.

A research hypothesis is like a guide for researchers in science. It’s a well-thought-out idea that has been thoroughly tested. This idea is crucial as researchers can explore different fields, such as medicine, social sciences, and natural sciences. The research hypothesis links theories to real-world evidence and gives researchers a clear path to explore and make discoveries.

QuestionPro Research Suite is a helpful tool for researchers. It makes creating surveys, collecting data, and analyzing information easily. It supports all kinds of research, from exploring new ideas to forming hypotheses. With a focus on using data, it helps researchers do their best work.

Are you interested in learning more about QuestionPro Research Suite? Take advantage of QuestionPro’s free trial to get an initial look at its capabilities and realize the full potential of your research efforts.

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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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In today’s data-driven world, decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis & hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

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What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life - 

• A teacher assumes that 60% of his college's students come from lower-middle-class families.
• A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

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Null Hypothesis and Alternate Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average. 

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

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Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine that their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps of Hypothesis Testing

Hypothesis testing is a statistical method to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here’s a breakdown of the typical steps involved in hypothesis testing:

Formulate Hypotheses

• Null Hypothesis (H0): This hypothesis states that there is no effect or difference, and it is the hypothesis you attempt to reject with your test.
• Alternative Hypothesis (H1 or Ha): This hypothesis is what you might believe to be true or hope to prove true. It is usually considered the opposite of the null hypothesis.

Choose the Significance Level (α)

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. Common choices for α are 0.05 (5%), 0.01 (1%), and 0.10 (10%).

Select the Appropriate Test

Choose a statistical test based on the type of data and the hypothesis. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis. The selection depends on data type, distribution, sample size, and whether the hypothesis is one-tailed or two-tailed.

Collect Data

Gather the data that will be analyzed in the test. This data should be representative of the population to infer conclusions accurately.

Calculate the Test Statistic

Based on the collected data and the chosen test, calculate a test statistic that reflects how much the observed data deviates from the null hypothesis.

Determine the p-value

The p-value is the probability of observing test results at least as extreme as the results observed, assuming the null hypothesis is correct. It helps determine the strength of the evidence against the null hypothesis.

Make a Decision

Compare the p-value to the chosen significance level:

• If the p-value ≤ α: Reject the null hypothesis, suggesting sufficient evidence in the data supports the alternative hypothesis.
• If the p-value > α: Do not reject the null hypothesis, suggesting insufficient evidence to support the alternative hypothesis.

Report the Results

Present the findings from the hypothesis test, including the test statistic, p-value, and the conclusion about the hypotheses.

Perform Post-hoc Analysis (if necessary)

Depending on the results and the study design, further analysis may be needed to explore the data more deeply or to address multiple comparisons if several hypotheses were tested simultaneously.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

Chi-Square 

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

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Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

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Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

• The null hypothesis is (H0 <= 90) or less change.
• A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true]. 

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

Level of Significance

The alpha value is a criterion for determining whether a test statistic is statistically significant. In a statistical test, Alpha represents an acceptable probability of a Type I error. Because alpha is a probability, it can be anywhere between 0 and 1. In practice, the most commonly used alpha values are 0.01, 0.05, and 0.1, which represent a 1%, 5%, and 10% chance of a Type I error, respectively (i.e. rejecting the null hypothesis when it is in fact correct).

A p-value is a metric that expresses the likelihood that an observed difference could have occurred by chance. As the p-value decreases the statistical significance of the observed difference increases. If the p-value is too low, you reject the null hypothesis.

Here you have taken an example in which you are trying to test whether the new advertising campaign has increased the product's sales. The p-value is the likelihood that the null hypothesis, which states that there is no change in the sales due to the new advertising campaign, is true. If the p-value is .30, then there is a 30% chance that there is no increase or decrease in the product's sales.  If the p-value is 0.03, then there is a 3% probability that there is no increase or decrease in the sales value due to the new advertising campaign. As you can see, the lower the p-value, the chances of the alternate hypothesis being true increases, which means that the new advertising campaign causes an increase or decrease in sales.

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Why Is Hypothesis Testing Important in Research Methodology?

Hypothesis testing is crucial in research methodology for several reasons:

• Provides evidence-based conclusions: It allows researchers to make objective conclusions based on empirical data, providing evidence to support or refute their research hypotheses.
• Supports decision-making: It helps make informed decisions, such as accepting or rejecting a new treatment, implementing policy changes, or adopting new practices.
• Adds rigor and validity: It adds scientific rigor to research using statistical methods to analyze data, ensuring that conclusions are based on sound statistical evidence.
• Contributes to the advancement of knowledge: By testing hypotheses, researchers contribute to the growth of knowledge in their respective fields by confirming existing theories or discovering new patterns and relationships.

When Did Hypothesis Testing Begin?

Hypothesis testing as a formalized process began in the early 20th century, primarily through the work of statisticians such as Ronald A. Fisher, Jerzy Neyman, and Egon Pearson. The development of hypothesis testing is closely tied to the evolution of statistical methods during this period.

• Ronald A. Fisher (1920s): Fisher was one of the key figures in developing the foundation for modern statistical science. In the 1920s, he introduced the concept of the null hypothesis in his book "Statistical Methods for Research Workers" (1925). Fisher also developed significance testing to examine the likelihood of observing the collected data if the null hypothesis were true. He introduced p-values to determine the significance of the observed results.
• Neyman-Pearson Framework (1930s): Jerzy Neyman and Egon Pearson built on Fisher’s work and formalized the process of hypothesis testing even further. In the 1930s, they introduced the concepts of Type I and Type II errors and developed a decision-making framework widely used in hypothesis testing today. Their approach emphasized the balance between these errors and introduced the concepts of the power of a test and the alternative hypothesis.

The dialogue between Fisher's and Neyman-Pearson's approaches shaped the methods and philosophy of statistical hypothesis testing used today. Fisher emphasized the evidential interpretation of the p-value. At the same time, Neyman and Pearson advocated for a decision-theoretical approach in which hypotheses are either accepted or rejected based on pre-determined significance levels and power considerations.

The application and methodology of hypothesis testing have since become a cornerstone of statistical analysis across various scientific disciplines, marking a significant statistical development.

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

• It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
• Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
• Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
• Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

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After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore the Post Graduate Program in Data Science.

If you have any questions regarding this ‘Hypothesis Testing In Statistics’ tutorial, do share them in the comment section. Our subject matter expert will respond to your queries. Happy learning!

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is H0 and H1 in statistics?

In statistics, H0​ and H1​ represent the null and alternative hypotheses. The null hypothesis, H0​, is the default assumption that no effect or difference exists between groups or conditions. The alternative hypothesis, H1​, is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data.

3. What is a simple hypothesis with an example?

A simple hypothesis is a specific statement predicting a single relationship between two variables. It posits a direct and uncomplicated outcome. For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here, the hypothesis suggests a direct relationship between the amount of sunlight (independent variable) and the growth rate of sunflowers (dependent variable), with no additional variables considered.

4. What are the 2 types of hypothesis testing?

• One-tailed (or one-sided) test: Tests for the significance of an effect in only one direction, either positive or negative.
• Two-tailed (or two-sided) test: Tests for the significance of an effect in both directions, allowing for the possibility of a positive or negative effect.

The choice between one-tailed and two-tailed tests depends on the specific research question and the directionality of the expected effect.

5. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

• Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
• Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
• Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

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Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

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What Is Hypothesis Testing?

• How It Works

4 Step Process

The bottom line.

• Fundamental Analysis

Hypothesis Testing: 4 Steps and Example

Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population or a data-generating process. The word "population" will be used for both of these cases in the following descriptions.

Key Takeaways

• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
• The test provides evidence concerning the plausibility of the hypothesis, given the data.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.
• The four steps of hypothesis testing include stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

How Hypothesis Testing Works

In hypothesis testing, an  analyst  tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.

The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis. Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.

The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.

• State the hypotheses.
• Formulate an analysis plan, which outlines how the data will be evaluated.
• Carry out the plan and analyze the sample data.
• Analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

Example of Hypothesis Testing

If an individual wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct. Mathematically, the null hypothesis is represented as Ho: P = 0.5. The alternative hypothesis is shown as "Ha" and is identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.

A random sample of 100 coin flips is taken, and the null hypothesis is tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.

If there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."

When Did Hypothesis Testing Begin?

Some statisticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”

What are the Benefits of Hypothesis Testing?

Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.

What are the Limitations of Hypothesis Testing?

Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.

Hypothesis testing refers to a statistical process that helps researchers determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. All hypothesis testing methods have the same four-step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

Sage. " Introduction to Hypothesis Testing ," Page 4.

Elder Research. " Who Invented the Null Hypothesis? "

Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples ."

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What is Hypothesis Testing? Types and Methods

• Soumyaa Rawat
• Jul 23, 2021

Hypothesis Testing  

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not. 

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number. 

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true. 

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started! 

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing. 

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence. 

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it. 

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis. 

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction. 

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa. 

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables. 

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa. 

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics. 

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not. 

(Related blog: z-test vs t-test )

Performing Hypothesis Testing  

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner. 

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure. 

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test. 

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful. 

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%. 

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing. 

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis. 

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size. 

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples. 

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples. 

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis. 

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible. 

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data. 

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST). 

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s. 

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis. 

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand. 

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis. 

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.  

(Also read - Introduction to Bayesian Statistics ) 

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach. 

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing. 

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis. 

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How to write a research hypothesis

Last updated

19 January 2023

Reviewed by

Miroslav Damyanov

Start with a broad subject matter that excites you, so your curiosity will motivate your work. Conduct a literature search to determine the range of questions already addressed and spot any holes in the existing research.

Narrow the topics that interest you and determine your research question. Rather than focusing on a hole in the research, you might choose to challenge an existing assumption, a process called problematization. You may also find yourself with a short list of questions or related topics.

Use the FINER method to determine the single problem you'll address with your research. FINER stands for:

I nteresting

You need a feasible research question, meaning that there is a way to address the question. You should find it interesting, but so should a larger audience. Rather than repeating research that others have already conducted, your research hypothesis should test something novel or unique. 

The research must fall into accepted ethical parameters as defined by the government of your country and your university or college if you're an academic. You'll also need to come up with a relevant question since your research should provide a contribution to the existing research area.

This process typically narrows your shortlist down to a single problem you'd like to study and the variable you want to test. You're ready to write your hypothesis statements.

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• Types of research hypotheses

It is important to narrow your topic down to one idea before trying to write your research hypothesis. You'll only test one problem at a time. To do this, you'll write two hypotheses – a null hypothesis (H0) and an alternative hypothesis (Ha).

You'll come across many terms related to developing a research hypothesis or referring to a specific type of hypothesis. Let's take a quick look at these terms.

Null hypothesis

The term null hypothesis refers to a research hypothesis type that assumes no statistically significant relationship exists within a set of observations or data. It represents a claim that assumes that any observed relationship is due to chance. Represented as H0, the null represents the conjecture of the research.

Alternative hypothesis

The alternative hypothesis accompanies the null hypothesis. It states that the situation presented in the null hypothesis is false or untrue, and claims an observed effect in your test. This is typically denoted by Ha or H(n), where “n” stands for the number of alternative hypotheses. You can have more than one alternative hypothesis. 

Simple hypothesis

The term simple hypothesis refers to a hypothesis or theory that predicts the relationship between two variables - the independent (predictor) and the dependent (predicted). 

Complex hypothesis

The term complex hypothesis refers to a model – either quantitative (mathematical) or qualitative . A complex hypothesis states the surmised relationship between two or more potentially related variables.

Directional hypothesis

When creating a statistical hypothesis, the directional hypothesis (the null hypothesis) states an assumption regarding one parameter of a population. Some academics call this the “one-sided” hypothesis. The alternative hypothesis indicates whether the researcher tests for a positive or negative effect by including either the greater than (">") or less than ("<") sign.

Non-directional hypothesis

We refer to the alternative hypothesis in a statistical research question as a non-directional hypothesis. It includes the not equal ("≠") sign to show that the research tests whether or not an effect exists without specifying the effect's direction (positive or negative).

Associative hypothesis

The term associative hypothesis assumes a link between two variables but stops short of stating that one variable impacts the other. Academic statistical literature asserts in this sense that correlation does not imply causation. So, although the hypothesis notes the correlation between two variables – the independent and dependent - it does not predict how the two interact.

Logical hypothesis

Typically used in philosophy rather than science, researchers can't test a logical hypothesis because the technology or data set doesn't yet exist. A logical hypothesis uses logic as the basis of its assumptions. 

In some cases, a logical hypothesis can become an empirical hypothesis once technology provides an opportunity for testing. Until that time, the question remains too expensive or complex to address. Note that a logical hypothesis is not a statistical hypothesis.

Empirical hypothesis

When we consider the opposite of a logical hypothesis, we call this an empirical or working hypothesis. This type of hypothesis considers a scientifically measurable question. A researcher can consider and test an empirical hypothesis through replicable tests, observations, and measurements.

Statistical hypothesis

The term statistical hypothesis refers to a test of a theory that uses representative statistical models to test relationships between variables to draw conclusions regarding a large population. This requires an existing large data set, commonly referred to as big data, or implementing a survey to obtain original statistical information to form a data set for the study. 

Testing this type of hypothesis requires the use of random samples. Note that the null and alternative hypotheses are used in statistical hypothesis testing.

Causal hypothesis

The term causal hypothesis refers to a research hypothesis that tests a cause-and-effect relationship. A causal hypothesis is utilized when conducting experimental or quasi-experimental research.

Descriptive hypothesis

The term descriptive hypothesis refers to a research hypothesis used in non-experimental research, specifying an influence in the relationship between two variables.

• What makes an effective research hypothesis?

An effective research hypothesis offers a clearly defined, specific statement, using simple wording that contains no assumptions or generalizations, and that you can test. A well-written hypothesis should predict the tested relationship and its outcome. It contains zero ambiguity and offers results you can observe and test. 

The research hypothesis should address a question relevant to a research area. Overall, your research hypothesis needs the following essentials:

Hypothesis Essential #1: Specificity & Clarity

Hypothesis Essential #2: Testability (Provability)

• How to develop a good research hypothesis

In developing your hypothesis statements, you must pre-plan some of your statistical analysis. Once you decide on your problem to examine, determine three aspects:

the parameter you'll test

the test's direction (left-tailed, right-tailed, or non-directional)

the hypothesized parameter value

Any quantitative research includes a hypothesized parameter value of a mean, a proportion, or the difference between two proportions. Here's how to note each parameter:

Single mean (μ)

Paired means (μd)

Single proportion (p)

Difference between two independent means (μ1−μ2)

Difference between two proportions (p1−p2)

Simple linear regression slope (β)

Correlation (ρ)

Defining these parameters and determining whether you want to test the mean, proportion, or differences helps you determine the statistical tests you'll conduct to analyze your data. When writing your hypothesis, you only need to decide which parameter to test and in what overarching way.

The null research hypothesis must include everyday language, in a single sentence, stating the problem you want to solve. Write it as an if-then statement with defined variables. Write an alternative research hypothesis that states the opposite.

• What is the correct format for writing a hypothesis?

The following example shows the proper format and textual content of a hypothesis. It follows commonly accepted academic standards.

Null hypothesis (H0): High school students who participate in varsity sports as opposed to those who do not, fail to score higher on leadership tests than students who do not participate.

Alternative hypothesis (H1): High school students who play a varsity sport as opposed to those who do not participate in team athletics will score higher on leadership tests than students who do not participate in athletics.

The research question tests the correlation between varsity sports participation and leadership qualities expressed as a score on leadership tests. It compares the population of athletes to non-athletes.

• What are the five steps of a hypothesis?

Once you decide on the specific problem or question you want to address, you can write your research hypothesis. Use this five-step system to hone your null hypothesis and generate your alternative hypothesis.

Step 1 : Create your research question. This topic should interest and excite you; answering it provides relevant information to an industry or academic area.

Step 2 : Conduct a literature review to gather essential existing research.

Step 3 : Write a clear, strong, simply worded sentence that explains your test parameter, test direction, and hypothesized parameter.

Step 4 : Read it a few times. Have others read it and ask them what they think it means. Refine your statement accordingly until it becomes understandable to everyone. While not everyone can or will comprehend every research study conducted, any person from the general population should be able to read your hypothesis and alternative hypothesis and understand the essential question you want to answer.

Step 5 : Re-write your null hypothesis until it reads simply and understandably. Write your alternative hypothesis.

What is the Red Queen hypothesis?

Some hypotheses are well-known, such as the Red Queen hypothesis. Choose your wording carefully, since you could become like the famed scientist Dr. Leigh Van Valen. In 1973, Dr. Van Valen proposed the Red Queen hypothesis to describe coevolutionary activity, specifically reciprocal evolutionary effects between species to explain extinction rates in the fossil record. 

Essentially, Van Valen theorized that to survive, each species remains in a constant state of adaptation, evolution, and proliferation, and constantly competes for survival alongside other species doing the same. Only by doing this can a species avoid extinction. Van Valen took the hypothesis title from the Lewis Carroll book, "Through the Looking Glass," which contains a key character named the Red Queen who explains to Alice that for all of her running, she's merely running in place.

• Getting started with your research

In conclusion, once you write your null hypothesis (H0) and an alternative hypothesis (Ha), you’ve essentially authored the elevator pitch of your research. These two one-sentence statements describe your topic in simple, understandable terms that both professionals and laymen can understand. They provide the starting point of your research project.

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• Published: 26 July 2024

Exploring the nexus between national innovation performance and happiness

• Irina Alina Popescu   ORCID: orcid.org/0000-0003-1303-5264 1 &
• Paulo Jorge Reis Mourão   ORCID: orcid.org/0000-0001-6046-645X 2  

Humanities and Social Sciences Communications volume  11 , Article number:  960 ( 2024 ) Cite this article

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• Science, technology and society

The study of happiness in economics has started to gain considerable momentum. Social policy factors are currently being recognized as determinants of national competitiveness, while innovation is an important factor to ensure economic growth and societal well-being. In order to shed light on the complex relationship between innovation performance and societal happiness, an examination was conducted in 130 countries that covered observations from 2011 to 2022. The analysis aims to uncover the degree to which these two dimensions are interconnected and to discern whether one may be identified as the causal factor of the other. The results derived from the SGMM regressions reveal that spaces characterized by elevated levels of innovation also tend to exhibit correspondingly higher indicators of resident happiness. Notably, this relationship is particularly pronounced in countries with observed real income per capita. Consequently, this study supports the hypothesis that innovation fosters improvements in resident well-being, despite ongoing debates. In light of these results, understanding the positive association between innovation and happiness has significant policy implications for fostering economic growth and enhancing quality of life on a national scale.

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Introduction.

The significance of happiness within the larger framework of economic and social advancement has recently attracted substantial attention. Through an economic lens, happiness transcends conventional economic indicators by focusing on individuals’ subjective experiences and well-being. Economists have progressively acknowledged that conventional economic metrics, such as the gross domestic product (GDP), fail to adequately represent the complex range of individual’s experiences and quality of life. Consequently, their focus has shifted toward investigating happiness as an important measure of societal progress and individual well-being. On the contrary, innovation remains a deeply embedded concept within the academic discourse of economics. It has undergone a comprehensive examination as a pivotal catalyst for economic growth, development, and competitiveness. Scholars have explored various dimensions of innovation, including its determinants, effects, and implications for businesses, industries, and entire economies.

In recent years, there has been a growing interest in policies that consider human happiness and innovation performance as important factors in assessing and improving national competitiveness. Some countries, such as the United Arab Emirates, have appointed ministers of happiness or well-being to focus on improving citizens’ quality of life. These positions often work on policies related to education, healthcare, community development, and work-life balance. Happy citizens are more productive (Cabanas and Illouz 2019 ), and increases in productivity improve national competitiveness (O’Mahony and Van Ark 2003 ).

However, the relationship between happiness and innovation has recently attracted increased research attention among economists. To date, investigations into causality and effects have yielded inconsistent findings, necessitating further empirical exploration and theoretical development. Prior scholarly inquiry has predominantly examined either the influence of innovation performance on happiness (e.g., Huntsinger and Raoul 2019 ; Su and Muhammad 2023 ) or the reciprocal influence of happiness levels on innovation (e.g., Ji and Wang 2022 ; Li and Shen 2022 ; Wang et al. 2017 ; Bani-Melhem et al. 2018 ). In particular, these studies have been conducted in a single national context. Cross-national analyses investigating the correlation between happiness and innovation on a national scale remain conspicuously absent within the existing scholarly literature.

To address this research gap, this study investigates the causal relationship between happiness and innovation in 130 countries over the period 2011–2022. Our examination involves the assessment of national-level happiness levels according to the World Happiness Report (United Nations) (Helliwell et al. 2023 ) and the evaluation of innovation performance using the innovation score from the Global Innovation Index.

Our findings show that the most supported hypothesis regarding causality is that innovation serves as a driver of happiness. Countries exhibiting greater innovation tendencies also tend to exhibit correspondingly higher values on the happiness indicator. Although innovation processes inherently have the potential to benefit all nations and economies that, in subsequent years, adopt the outcomes derived from innovation, there exists a significant statistical correlation at play here, which warrants careful consideration.

The paper unfolds as follows. Section Theoretical background provides the conceptual groundwork and offers a synthesis of the outcomes from pivotal research studies pertinent to our pursuit. Section Methodology describes the dataset and delineates the methodology employed. Subsequently, Results and Discussion showcase the empirical findings and engage in discourse vis-à-vis earlier studies. The paper ends with concluding remarks and policy recommendations.

Theoretical background

Over the past decades, human happiness has emerged as a prominent subject in the literature (Kahneman and Krueger 2006 ; Clark et al. 2008 ). Social scientists have sought to understand the determinants and associations of happiness, as well as its implications for a country’s economic and social realms. The substantial expansion in both scope and rigor of this literature has contributed to the establishment of an emerging field known as the ‘economics of happiness’ (Easterlin 2004 ). Within the economics literature, happiness is equated with subjective well-being (Engelbrecht 2015 ).

Recognizing the complexity and significance of happiness for humanity, Layard ( 2005 ) emphasized the imperative for an ‘academic revolution,’ urging all social researchers to strive for a deeper understanding of the determinants of happiness. Broadly speaking, happiness has been linked to economic growth, economic freedom, institutional quality, cultural factors, social support, a healthy living environment, and physical well-being (Voukelatou et al. 2021 ; Veenhoven 2012 ).

Intuitively, economic growth has been posited to positively impact happiness (Aldieri et al. 2019 ). Empirical evidence supporting the notion that economic growth enhances happiness has also been presented (Hagerty and Veenhoven 2003 ; Inglehart 2017 ). Recent rigorous studies have demonstrated that happiness co-varies with several macroeconomic variables, including GDP, GDP growth, income, and unemployment (Aldieri et al. 2021 ; Di Tella et al. 2003 ; Helliwell 2003 ; Alesina et al. 2004 ). However, the positive effect of economic growth on happiness appears to plateau beyond a certain threshold. Furthermore, the Easterlin paradox (Easterlin 1974 , 1995 ) has established that, at the national level, average happiness remains relatively constant over time despite substantial increases in GNP per capita. Similarly, Dwyer ( 2020 ) documented the disconnect between GDP and self-reported life satisfaction levels.

The economic development of a nation has been unequivocally intertwined with numerous psychological shifts that impact human happiness. Economic growth triggers a shift in societal priorities, transitioning from the pursuit of maximum wealth to the pursuit of maximum well-being (Inglehart 2017 ; Pugno 2019 ). Happiness is related to pro-social values and behaviors, fostering trust and exhibiting a robust correlation with social participation and social capital (Layous et al. 2017 ; Guven 2011 ).

Within the scholarly discourse, there exists a consensus that economic development finds its base in innovation (Reznakova and Stefankova 2022 ; Fuertes-Callen and Cuellar-Fernandez 2019 ; Mourao and Popescu 2023 ; Popescu et al. 2023 ). Innovation has claimed a pivotal role in economic growth models, notably through the seminal contributions of Schumpeter ( 1934 ), whose ideas laid the groundwork for subsequent economic growth paradigms. Innovation performance acts as a catalyst for enhanced productivity growth, while simultaneously fostering improvements across various macroeconomic dimensions (Huong et al. 2021 ).

The nexus between innovation and happiness remains shrouded in ambiguity with respect to its effects, direction, and magnitude. As posited by Dolan and Metcalfe ( 2012 ), the available evidence on the link between happiness and innovation is exceedingly scarce. While the prevailing body of research acknowledges a positive correlation between innovation and happiness (e.g. Derclaye 2014 ), a cohort of scholars have acknowledged that innovation-driven growth could also be implicated in unemployment and inequalities, which could potentially impinge on happiness and well-being (Vivarelli 2014 ; Brynjolfsson and McAfee 2014 ).

Additionally, the direction of the relationship between innovation and happiness remains a subject of ongoing debate. Previous research has examined the impact of innovation performance on human happiness (e.g., Huntsinger and Raoul 2019 ; Su and Muhammad 2023 ) or the influence of happiness levels on innovation performance (e.g., Ji and Wang 2022 ; Li and Shen 2022 ; Wang et al. 2017 ; Bani-Melhem et al. 2018 ).

On the one hand, earlier studies have verified that innovation performance can indeed impact human happiness , although it is only one of several factors influencing overall happiness levels within a country. It is imperative to acknowledge, from the outset, that innovation embodies a dual nature, as underscored by Schubert ( 2012 ). Concerns about the ramifications of technological innovation (e.g., automation, digitization) on work are pervasive within economic literature and society. A spectrum of effects, both directly positive (e.g., creation of higher-quality jobs, enhanced worker skills, increased job satisfaction) and negative (e.g., heightened uncertainty, anxiety, devaluation of human capital, displacement, status erosion), have been proposed. In exploring these trade-offs, several scholars have emphasized that innovation can lead to imbalanced wealth distribution, potentially reducing employment, and increasing inequality, two factors intrinsically linked to determining happiness (Vivarelli 2014 ; Brynjolfsson and McAfee 2014 ).

However, given innovation’s pivotal role in economic development and societal advancement, the indirect positive effects of innovation on societal-level happiness have garnered substantial recognition (Castellacci 2022 ). For example, Engelbrecht ( 2015 ) formulated a comprehensive model outlining the nexus between innovation and happiness (subjective well-being). This model encompasses multiple dimensions, including the workplace and labor market, the product market, the material standard of living, objective well-being indicators (e.g., health, education, social indicators), and the natural environment. Spaces characterized by robust innovation performance tend to experience heightened economic growth rates and increased employment opportunities (Nelson 1996 ). This, in turn, leads to better living standards, better access to essential necessities, and increased disposable income (Aldieri et al. 2019 ), all of which can positively impact overall happiness. In the context of product markets, innovation drives the development of new and enhanced products and services, such as advanced healthcare technologies, improved infrastructure, and more efficient transportation systems (Barrett et al. 2015 ). These advancements in consumption can improve the quality of life and well-being, contributing to higher levels of happiness (Veenhoven et al. 2021 ). On the contrary, the purchase of financial products does not necessarily have a positive effect on happiness.

Dolan et al. ( 2008 ) contend that innovation catalyzes social and cultural advancement. Innovations spanning education, art, and culture can enrich societies, fostering a more vibrant and fulfilling way of life. Such steps have the potential to reinforce a sense of community and belonging, thus contributing to overall happiness levels. Innovation can precipitate technological breakthroughs that make everyday life more convenient and pleasant. For instance, advancements in communication technology have facilitated easier connections among individuals, cultivating social bonds and, consequently, augmenting happiness. In the realm of environmental sustainability, innovative solutions have the promise of addressing environmental predicaments, thereby nurturing a healthier and cleaner environment. This, in turn, can produce improved health outcomes and an increased sense of well-being for both individuals and communities (Aldieri et al. 2019 ). Even at the individual level, creative pursuits have been correlated with elevated personal competence and individual growth, fundamental components of a profound sense of well-being (Ryan et al. 2008 ). Elevated innovation performance can engender augmented personal competence, thus constituting a foundation for happiness (McManus and Carvalho 2022 ).

In an exploration of the effects of innovation on happiness and social welfare, Castellacci ( 2022 ) identifies four spheres of life significantly impacted by innovation: (i) the realm of work, (ii) consumption, (iii) leisure and personal life, and (iv) capabilities and functionings. Specifically: (i) Regarding the sphere of work, innovation influences individual happiness through various avenues: wage level (absolute income), relative income and social comparisons, and the quality of the workplace environment. (ii) Consumption implies increased utility and satisfaction for individuals. Innovation increases happiness by affecting consumption dynamics, ensuring preference fulfillment, time savings, and information provision. (iii) The domains of leisure and personal life experience innovation’s effects through aspects like social interaction and communication, physical environment enhancements (e.g., cleaner production), and the socio-institutional milieu. (iv) Finally, innovation impacts happiness by improving capabilities and functionings, achieved through improved education and health systems.

Recent empirical studies have produced conflicting results. Su and Muhammad ( 2023 ) documented a positive impact of innovation on the level of human happiness within Chinese society. They devised the metric ‘Innovation and development’ and estimated its influence on the dependent variable ‘Life satisfaction and happiness’. Using patents as an estimator of innovation, Derclaye ( 2014 ) found a robust correlation between innovation and happiness in developed countries, although without measuring specific effects. On the contrary, Aldieri et al. ( 2021 ) noted that innovation had a negative impact on subjective well-being in eight Western European countries during the period 1980–2014. This adverse effect was primarily ascribed to inequality, as a positive correlation between income and happiness was observed in the investigated nations.

The relationship between innovation and happiness at the country level has also recently been explored in conjunction with several other variables. Among these variables, one can discern: GDP, unemployment, inequality gauged by the Gini index (Aldieri et al. 2021 ), GDP per capita, consumer price index (CPI), taxes as a proportion of GDP, unemployment rate (Derclaye 2014 ), governmental control, and the degree of behavioral social constraints (Chua et al. 2019 ), freedom to make life choices, GDP growth, social contribution, employment rate, social support, life expectancy, coverage of social safety nets and high qualification (Su and Muhammad 2023 ).

On the other hand, an alternate body of research has found evidence suggesting that happiness contributes to increased innovation performance , implying that happier environments are more conducive to innovation. Happiness nurtures innovation capital and entrepreneurial initiative (Usai et al. 2020 ), while contented individuals are more likely to display traits of creativity, innovation, and productivity (Isen 2008 ; Diener 2012 ), as well as increased self-control, optimism, trust, and sociability (Huntsinger and Raoul 2019 ).

In the context of industrial England, Huntsinger and Raoul ( 2019 ) posited that higher living standards led to increased happiness, which in turn spurred a surge in innovation and economic growth. At the city level, elevated happiness stimulates investment behavior and research and development (R&D) efforts of local enterprises, particularly those of younger firms and R&D investments (Chuluun and Graham 2016 ; Kamguia et al. 2023 ). Furthermore, the role of local happiness is amplified in regions where happiness is more evenly distributed. Given its link to increased trust and social capital (Layous et al. 2017 ; Guven 2011 ), happiness stimulates social networking undertakings that facilitate the acquisition for innovation. At the regional level, happiness was also identified to play an important role in corporate green innovation (Li and Shen 2022 ). Using the quality of the local environment as a proxy for happiness, Ji and Wang ( 2022 ) provided evidence that happiness contributes positively and significantly to the efficiency of high-tech industries.

Exploring the potential pathways through which happiness might enhance innovation performance, we have identified prior research that underscores happiness’s influence on individuals’ motivation, creativity, health, well-being, collaboration, social cohesion, education, learning, and entrepreneurial initiative (e.g., Usai et al. 2020 ), as follows. Happy individuals are more prone to being motivated, productive, and inventive, as has been previously suggested (e.g., Ceci and Kumar 2016 ; Armenta et al. 2020 ; Rego et al. 2009 ). When individuals possess a sense of life satisfaction and an optimistic perspective, they are more inclined to engage in innovative thinking and problem-solving, producing fresh ideas, inventions, and advancements in diverse industries. Furthermore, happiness is closely related to physical and mental well-being (Trabelsi 2023 ). When people enjoy good health and well-being, they are more likely to actively participate in both the workforce and society. Strong social bonds and a sense of community enhance the propensity for collaboration, knowledge sharing, and collective involvement in innovative projects. Individuals who are both happy and healthy are better positioned to contribute to innovative and research-oriented behaviors, while a positive and unified social environment can foster an innovative culture (Mutonyi et al. 2020 ; Espasandín-Bustelo et al. 2021 ). In addition, happy and fulfilled individuals are more predisposed to value education and continuous learning. Education plays an essential role in nurturing innovation, as it equips individuals with the knowledge and skills requisite to contribute to scientific, technological, and cultural progress. Happiness can exert an influence on individuals’ inclination to explore entrepreneurial ventures (Bao and Dou 2021 ; Sweida and Sherman 2020 ). Consequently, individuals who experience happiness may exhibit greater openness to exploring novel opportunities and ideas, thereby driving innovation across business and technology domains.

Overall, the theoretical framework presented offers a comprehensive overview of the literature at the intersection of happiness and innovation. Three main theoretical strands regarding the relationship between happiness and innovation are integrated into this study’s conceptual framework. First, happiness as subjective well-being has been acknowledged within the economics literature. The perspective of subjective well-being centers on individuals’ subjective perceptions and assessments of their own lives. Previous studies within this domain have explored dimensions such as life satisfaction, happiness, and overall well-being, confirming the reliability and validity of these subjective measures as reliable indicators (Diener et al. 2002 ; Frey and Stutzer 2009 ; Veenhoven 2012 ). Second, innovation has been seen as a catalyst for economic growth, echoing the seminal contributions of Schumpeter ( 1934 ). It emphasizes how innovation acts as a catalyst for enhanced productivity growth and improvements in various macroeconomic dimensions. This perspective underscores the importance of innovation in fostering economic progress and lays the groundwork for exploring its implications for happiness. Third, the economic growth theory explores the factors and mechanisms that drive sustained growth with prioritization of well-being. Along these lines, this study considers happiness as a crucial social goal alongside economic prosperity.

On examination of recent pertinent research, we found contradictory findings in empirical studies exploring the relationship between happiness and innovation. The disparity in the findings arises from the application of varying measurements, analytical scales, and national contexts across previous studies. Furthermore, happiness is frequently assessed as a variable with subjective attributes, and emotional states tend to exhibit transience. This temporal aspect can lead to inconsistencies in happiness assessment over time, even when utilizing a consistent methodology. Common metrics employed to measure happiness include the Cantril ladder derived from the World Happiness Index (Ionescu-Feleagă et al. 2022 ; Carlsen 2018 ; Araújo et al. 2022 ), happiness indicators sourced from alternative references (e.g., European Social Survey, European Value Survey, Chinese General Social Survey (CGSS), and China Family Panel Studies (CFPS) surveys) (Plepytė-Davidavičienė 2020 ; Wang et al. 2022a ; Derclaye 2014 ), and even author-constructed happiness indices for both happiness and subjective well-being (Ross et al. 2005 ; Li and Shen 2022 ), along with life satisfaction measurements (Diener and Diener 1995 ). Less frequently employed happiness metrics encompass affect balance (Tsurumi et al. 2018 ; Yoon et al. 2022 ), quality of the living environment (Ji and Wang 2022 ), people’s livelihood, happiness, and shared development (Wang et al. 2022b ). In contrast, diverse metrics have been used for innovation, with the most commonplace including research and development (R&D) expenditure, patent counts, and innovation indices computed by international organizations (Popescu 2020 ).

Consequently, earlier studies addressing the direction of the relationship between happiness and innovation remain inconclusive, highlighting the idea that the connection between human happiness and a country’s innovation performance is complex and multifaceted, thus requiring further exploration. As recently highlighted by Aldieri et al. ( 2021 , p. 1300), a research gap persists in the study of the relationship between innovation and happiness.

Methodology

This study aims to bridge this gap by undertaking a series of estimations encompassing both directions of potential dependency, as derived from previous academic research. The primary objective is to determine the directional interdependence of the relationship between happiness and innovation performance on a country level, along with its associated effects. Therefore, this study aims to address the following research question: ‘ Do happier environments breed greater innovation or do more innovative environments tend to be happier?’

For happiness assessment, we have chosen to utilize the World Happiness Index (WHI), sourced from the World Happiness Reports (United Nations) (Helliwell et al. 2023 ), covering all available years (2011–2022). The World Happiness Report (WHR) constitutes an openly accessible online publication under the aegis of the United Nations’ global initiative, the Sustainable Development Solutions Network, predominantly drawing data from the Gallup World Poll. Currently, the WHR includes 156 countries and is progressively receiving acknowledgment from international entities and governments as a framework for shaping policies by employing happiness indicators (Stiglitz et al. 2018 ; Jaswal et al. 2020 ). The WHI measures the degree of happiness and contentment among a nation’s populace through the application of the Cantril ladder, a scale ranging from 0 (representing the lowest value) to 10 (indicating the highest value), with respondents utilizing it to assess their contentment across diverse facets of life. Several studies have agreed on the reliability of WHI, further confirming its suitability in previous research studies (Ionescu-Feleagă et al. 2022 ; Carlsen 2018 ; Araújo et al. 2022 ). The principal benefits inherent in employing this WHI encompass the canvassing of nationally representative samples, the use of weighting mechanisms to render estimates representative of the population, and the cross-national comparability of the data. To quantify innovation performance on a country level, we will opt, in this work, to exhibit the outcomes considering the Global Innovation Index, as the variable related to innovation. The rationale is that this variable encompasses other indicators for innovation (namely, Research & Development as a percentage of GDP, information technology exports as a percentage of total goods exports, and High-tech exports as percentage of manufactured exports, among others). Data for GDP per capita, in current US dollars, were collected from The World Bank (World Bank 2024 ).

Our database comprises a maximum of 1560 observations conducted across 130 countries spanning the period from 2011 to 2022. Descriptive statistics for our dataset are outlined in Table 1 .

The discussion surrounding the concept of causality, as well as the empirical tools to scrutinize hypotheses such as ‘cause X precedes effect Y ,’ is a longstanding and complex discourse within economics and other social sciences.

We will begin by offering a concise overview of the different models under examination, followed by a summary of empirical investigations based on the inherent nature of the data.

The term ‘cause’ involves one dimension preceding another dimension, called ‘effect.’ However, it is crucial for there to exist a substantiated rationale within the literature supporting this directional linkage. The mere observation that alterations in variable X , for instance, appear to precede alterations in variable Y is inadequate to establish a causal relationship, as this observation could be deemed ’spurious.’ In addition to this, temporal consistency must be maintained. The relationship established between X (the cause) and Y (the effect) should not depend on the specific time frame being considered. If the causal link between X and Y is only valid during certain periods, it is plausible that seasonal influences or longer-term cycles could contribute to this phenomenon. Beyond temporal consistency, the examination of individual consistency is essential. This involves assessing whether the influence on Y holds true for most of the observed individuals. It should be noted that, as we explore further, particularly during our discussion of cointegrated panel data, several tests analyze the adequacy of X being the cause of Y for a minimal number of individuals, positing it as a hypothesis of causality.

Finally, X is indeed the cause of Y when the impact of X persists over Y in the same direction within an observed trajectory. If the elevation leads to a corresponding increase in Y , this incremental effect tends to last for a certain duration. If, however, the consequence of the elevation on Y is inconsistent, such as an increment in one period followed by a decrement in the immediate subsequent period, then the observed periodicity becomes a critical determinant. In this scenario, we might be confronted with either a spurious relationship or cyclical causality effects, albeit with a periodicity different from the one being studied.

The discussion of causality can also be categorized based on the type of data under observation. Primarily, within time-series analysis, the concept of ‘Granger’ causality constitutes a pivotal element in the current scientific discourse. There is a substantial body of literature on this topic (Maziarz 2015 ; Radu 2013 ). It is noteworthy to acknowledge that the advent of ‘Granger’ causality triggered a profound revolution within the realm of time-series econometrics (Zaman 2008 ). In the context of ‘Granger’ causality tests for time-series data, we recommend referring to Grosche ( 2014 ).

Subsequently, this concept of causality was extended to dynamic panel data. Works such as those authored by Lopez and Weber ( 2017 ), Lu et al. ( 2017 ), or Juodis and Karavias ( 2019 ) contribute to this discourse. The fundamental premise lies in the notion that lagged observations of X (such as X t-1 , X t-2 , …, X t-n ) elucidate current observations of Y t . In addition, this causality framework has been expanded to include a broader array of individuals under observation. While time-series observations often focus on a single entity (e.g., a country) across years, panel data facilitate observations of multiple entities over diverse periods. For testing the causality of Y over X in panel data, techniques such as joint significance tests of the estimated coefficients for time lags of Y within the estimated regressions are employed, among other methodologies.

When the temporal horizon is extensive and a multitude of individuals are observed, the concept of cointegrated panel data arises (Herzer and Strulik 2017 ; Jalles 2015 ; Law et al. 2014 ). This approach seeks confirmation not only of the existence of a long-term relationship but also of estimated significant relationships between the dependent variable (effect variable) and the independent variables (cause variables) in the short term. Tests such as Kao ( 1999 ), Pedroni ( 1999 , 2004 ), and Westerlund ( 2005 ) are employed in this context.

The Kao ( 1999 ) test presupposes a cointegration vector uniform across all panels, estimating means for each panel (as fixed effects) and precludes the inclusion of a time trend. The alternative hypothesis in this test posits that the series exhibits cointegration across all panels with the same cointegration vector. In contrast, the Pedroni test (1999, 2004) diverges from the Kao test in two aspects: It assumes distinct cointegration vectors and specific autocorrelation terms for each panel. Consequently, the alternative hypothesis posits cointegration across all panels with panel-specific cointegration vectors. The Westerlund test (Westerlund 2005 ) encompasses a statistical examination of the variance ratio, obtained through testing for the existence of a unit root within the estimated residuals of the Dickey-Fuller regression. This test assumes uniform autocorrelation terms for all panels. The alternative hypothesis in this case stipulates cointegration across all panels.

At this juncture, it is vital to acknowledge that both dimensions X and Y in our study, happiness, and innovation, might be influenced by a shared ‘hidden/latent’ dimension, each deriving positive influences from this latent dimension. For example, we can posit that robust societal institutions (e.g., efficient courts, low crime rates, and equitable income distribution) foster happy residents and a conducive environment for innovation. However, even in such a scenario, one of the dimensions under scrutiny (innovation or happiness) could preclude the absorption of certain positive influences from this shared source, channeling these forces toward the other dimension. This generates causal processes between the initially affected and the resultant effects observed in the receiving dimension.

In empirical terms, due to the lack of consensus in the literature on whether ‘happier’ spaces are more innovative or if more innovative spaces are ‘happier’, we conducted a series of estimates. The study takes two main approaches to explore this relationship. First, using dynamic panel data analysis, it investigates how changes in happiness levels, measured by the Happiness indicator from the World Happiness Report, influence innovation outcomes. The Global Innovation Index serves as the dependent variable in this analysis. Second, in response to criticisms about the consistency of results when happiness is treated as an independent variable, the study reverses the analysis. It examines how levels of innovation, as measured by the Global Innovation Index, affect happiness levels, using the same Happiness indicator as the dependent variable. This dual approach aims to provide a complete understanding of how happiness and innovation interact, addressing methodological challenges such as omitted variable bias through robust panel data techniques.

Innovation as dependent variable

As we built a dynamic panel data, we chose to highlight throughout this section the results of the estimations carried out using the System-GMM (Roodman 2009 ), without prejudice to being able to show the estimations made with fixed effects, random effects or Pooled-OLS that turned out to be of lower statistical quality. Thus, Table 2 shows the results of the estimation that considered the Innovation indicator as the dependent variable and the Happiness indicator as the main independent variable. We also emphasize that we used several control variables whose estimated coefficients and respective significance values will be shown if requested. Finally, even regarding the issue of omitted variables, we based our rationale on Bond ( 2002 ), who clearly stated that dynamic panel data models are better able to address the omitted variable problems and endogeneity issues than static models.

Table 2 also shows the p -values of the Arellano-Bond tests for autocorrelation in first differences as well as the Sargan and Hansen tests for overidentified restrictions. Difference-in-Hansen tests of exogeneity values are available for consultation upon request. However, the various tests did not identify problems that would prevent an inference from the results in Table 2 .

The results in Table 2 show that there is a long persistence of the values observed for Innovation. The estimated coefficient for the Innovation lag (0.709) reveals that countries with higher values in a given year tend to maintain high values in the following year (Costa and Tashakori 2023 ; Bianchini and Pellegrino 2019 ). A country having a one-point higher innovation score will tend to have for the next year an expected increase of 0.709 in the same variable. The effect of happiness is positive for the year under observation – higher values of happiness in a given year in a country are associated with higher values of the Innovation indicator in that country and in that year (estimated coefficient of 4.242, statistically significant at 5%). Once again, we interpret the estimated coefficient as follows: A country happier than another in 1 point will tend to have an expected score of innovation increased by 4.242 points. However, the effect arising from the happiness first lag on Innovation is negative (statistically significant at 10%). Therefore, innovation increases in ‘less happy’ countries in the previous year and in ‘happier’ countries in the same year.

This type of result should be seen in the face of criticism in Baraldi et al. ( 2013 ) or Musick and Meier ( 2012 ). Cycles of influence between two variables (related in non-spurious terms) must be consistent. This implies that if the variable X is the cause of the variable Y, which generates a contemporary positive effect on Y, then the same positive effect should be noticed in the estimated coefficients for the first lags observed in X in the regression that has Y as the dependent variable.

Happiness as dependent variable

In view of this criticism of the inconsistency observed in the estimated results of the first lags of happiness over Innovation, we estimate the reverse equation. Thus, we also estimated Innovation as an explanatory variable for happiness (now the dependent variable). These results are in Table 3 .

The results in Table 3 show another level of consistency. In fact, we observe in Table 3 the following: (i) There is persistence in the observations related to happiness. The effect arising from the variable observed in the previous year is positive and statistically significant; (ii) There is consistency in the (positive) effect arising from Innovation on Happiness. Countries with higher values in the Innovation indicator are countries with higher values on the Happiness indicator. This effect is contemporary but also comes from the previous period.

Therefore, we favor the hypothesis that “Innovation causes happiness’ in our study. Therefore, more innovative countries tend to be associated with higher values for the Happiness indicator as well. Although innovation processes are processes that, ultimately, will favor all countries and all economies that, in the following years, adopt the objects resulting from innovation, there is a statistical association here that cannot be neglected.

We aimed to further investigate this empirical evidence. To achieve this, we used a partitioning approach within our shared sample. Specifically, we divided the sample into two segments based on whether the observations fell below or above the median value. This was applied to both the GDP per capita variable and the Gini coefficient variable. This strategy follows empirical studies like Plepytė-Davidavičienė ( 2020 ) or Schumpeter ( 1934 ). The rationale is that economies with higher levels of real GDP per capita tend to exhibit particular patterns of happiness metrics and innovation scores. Related to the Gini indicator, a popular construction for debating income inequality, it is expected that populations with higher levels of economic inequality will tend to express particular responses in terms of assumed happiness. Table 4 presents the results corresponding to observations below and above the median values for GDP per capita.

The results in Table 4 show the following: (i) the persistence of the variable related to Happiness is greater in countries and periods with higher real GDP per capita; (ii) in a way that raises several challenges to further investigation, we found that the effects arising from Innovation are not associated with estimated coefficients that are statistically significant in countries with lower real GDP per capita; (iii) On the other hand, in countries and periods with higher values of real GDP per capita, the positive effect of Innovation tends to only be noticed contemporaneously.

Thus, when synthetically interpreting the potential implications of Table 3 , we discern that Innovation primarily impacts Happiness in instances characterized by higher real GDP per capita. This observation introduces additional challenges for further investigation, prompting exploration of the mechanisms that operate within contexts of elevated real GDP per capita, as well as those that may not be as streamlined in scenarios falling below the median of real GDP per capita.

Finally, Table 5 allows for additional interpretations, which generally converge with the interpretations in Table 3 . The separation of our database considering the pattern of income inequality, measured by the Gini coefficient, shows that Innovation values have a positive contemporary effect on Happiness. However, by performing a coefficient equality test, we do not reject the null hypothesis that the estimated coefficient for Innovation in countries with less inequality is equivalent to the estimated coefficient for Innovation in cases of greater inequality. This evidence can be further supported by the argument that the variability observed in the database in the Gini coefficient variable is relatively small (for example, in comparison).

The results derived from our analysis on both directions of dependence within the relationship between happiness and innovation offer valuable insights for discussion. As our review of the literature affirms, there remains a lack of consensus regarding the correlation between innovation and happiness (Dolan and Metcalfe 2012 ). The dimensions identified in the literature as contributors to community or country-level happiness are multifaceted. Parameters such as per capita income, low unemployment, minimized income inequality or access to quality healthcare have been recognized as pertinent aspects. However, the quality of innovation tied to a particular region or space should not be disregarded (Mourao and Popescu 2023 ). On the one hand, regions marked by higher innovation levels tend to reap the benefits of early exposure to externalities generated by innovation. These regions may enjoy improved healthcare access due to increased innovation in pharmaceuticals, for example, or they may access more efficient production methods by incorporating innovative inputs.

Working with panel data (consisting of 1560 observations across 130 countries for the period 2011–2022), our approach to causality analysis diverged from that employed for time-series data - as seen in works like Lopez and Weber ( 2017 ), Lu et al. ( 2017 ), or Juodis and Karavias ( 2019 ). Our methodology necessitated not only assessing the statistical significance of contemporaneous estimates of the primary independent variable, but also evaluating the significance of estimates from lagged observations of the same variable. Furthermore, to establish the causality direction, we examined the persistence of the causal effect, scrutinizing whether estimates for the independent variable consistently aligned in the same direction across different time points.

Previous research shows that performance on global competitiveness pillars of innovation and institutions is positively relate to performances on happiness and life satisfaction (Canatay et al. 2023 ). Based on our observations, we draw the conclusion that the hypothesis most substantiated in terms of causality is that innovation acts as a catalyst for the well-being of surrounding communities (in line with previous results obtained by Su and Muhammad 2023 ). We have systematically examined this hypothesis by scrutinizing subsamples. These subsamples include evaluations of real GDP per capita and the Gini index. Utilizing these subsamples has allowed us to deduce that this relationship particularly comes to the forefront in observations marked by higher real income per capita. This finding highlights the existence of persistent barriers within regions with lower real per capita income, which hinder the full extension of innovation’s positive impacts on the presumed level of happiness. Addressing the effectiveness of these barriers poses a significant challenge, important for enhancing the potential of innovation to improve the well-being of the communities involved.

The findings of this study are in line with those of Dolan et al. ( 2008 ), who argued that innovation acts as a catalyst for social and cultural progress. Innovations have the potential to enrich societies and promote a more dynamic and fulfilling quality of life. While research findings support the hypothesis that innovation causes happiness, it is important to acknowledge the divergent perspectives highlighted in previous studies and explore possible reasons for this divergence. For example, Aldieri et al. ( 2021 ) noted a negative impact of innovation on subjective well-being in certain Western European countries, primarily attributed to issues of inequality. In the context of industrial England, Huntsinger and Raoul ( 2019 ) suggested that higher living standards are associated with greater happiness, thereby fostering a surge in innovation and economic growth. It is essential to consider the contextual nuances that may underlie these divergent findings. For example, the socioeconomic conditions, cultural norms, and policy environments of the studied countries could influence the observed relationship between innovation and happiness. Furthermore, variations in the level of analysis and the research methodologies, such as sample selection criteria and measurement approaches, can contribute to differing conclusions between studies. The opposing views suggest that happiness nurtures innovation capital, fosters creativity and collaboration, and enhances individuals’ motivation and entrepreneurial initiative (Usai et al. 2020 ; Rego et al. 2009 ; Ceci and Kumar 2016 ; Armenta et al. 2020 ). This discrepancy highlights the complexity of the relationship between innovation and happiness, suggesting that contextual factors and social dynamics may influence the observed effects.

This research study analyzed the causality relationship between happiness and innovation with data collected at national level. Our findings support for the hypothesis that innovation causes happiness within our dataset for 130 countries.

Empirical evidence highlights a compelling degree of consistency. The analysis reveals the following key patterns: (i) A noticeable persistence effect within happiness observations, with a positive and statistically significant influence from the previous year; (ii) Consistency in the positive impact of innovation on happiness, showcasing a contemporary effect alongside the influence from the previous period. Consequently, countries that exhibit higher levels of innovation are closely associated with elevated levels of the Happiness indicator. Although innovation processes inherently benefit all nations and economies that adopt innovation-driven outcomes in subsequent years, the observed statistical correlation underpins the significance of this association. With the methodological resources available, we favor this hypothesis that more innovative spaces become happier spaces. Further avenues for research can use other methods such as PLS-SEM (Partial Least Squares Structural Equations Modelling) to confirm or complement this analysis, including the possibility of studying latent dimensions that intervene in the constructs measured by innovation or happiness.

We further partitioned our sample into two segments based on GDP per capita and Gini coefficient variables. Our findings show: (i) Enhanced persistence within the happiness variable across countries and periods characterized by higher real GDP per capita; (ii) a nuanced scenario where Innovation’s effects are not statistically significant in countries with lower real GDP per capita; (iii) Conversely, the positive impact of Innovation is primarily concurrent in countries and periods with elevated real GDP per capita. This interpretation underscores that Innovation’s influence on happiness predominantly resonates in observations marked by higher real GDP per capita. This observation requires further inquiries into the channels at play within these contexts, contrasting them with cases below the median of real GDP per capita. The division of our dataset based on the pattern of income inequality, measured by the Gini coefficient, shows that innovation has a positive immediate impact on happiness.

Our findings support the idea that innovation acts as a catalyst for well-being. This outcome led us to recognize that innovation is just one of several factors contributing to overall happiness. These results suggest some implications for policies. First, when designing policies to improve happiness and well-being in a comprehensive way, it is important to recognize that several policies should be aligned to foster innovation to further spur happiness. The main policy goal is to create environments and societies where individuals have the opportunity to lead fulfilling lives that go beyond mere innovation and economic success. Additionally, policymakers must develop policies that foster innovation and promote happiness to create an environment where individuals are empowered to be creative, solve problems, and contribute positively to society, through, for instance, the development of educational systems that focus not only on academic achievement but also on nurturing creativity, critical thinking, emotional intelligence, and social skills; development of flexible employment policies that benefit from technological advancements and workplace innovations; provision of funding and incentives for research and innovation in various sectors (including technology, healthcare, and sustainability); development and support of entrepreneurial ecosystems, digital infrastructure, workplace innovation, community engagement and diversity, and inclusion initiatives.

Second, the positive impacts of innovation on well-being are more pronounced in regions with higher real income per capita. Policymakers should address regional disparities by implementing targeted initiatives to support innovation in areas with lower income levels. This could involve providing incentives for companies to establish operations in these regions or investing in education and infrastructure to boost innovation capacity. Third, income inequality may play a role in hindering the full extension of innovation’s positive impacts on happiness. National policies should therefore focus on promoting inclusive growth to ensure that the benefits of innovation are shared more equitably among different segments of the population. National policies should prioritize capacity-building initiatives to improve the ability of regions, especially those with lower income levels, to take advantage of innovation. This may involve targeted training programs, infrastructure development, and other forms of support.

Efforts to integrate happiness and innovation into national policies should be made. Countries that recognize the importance of these factors are more likely to implement policies that prioritize the well-being of their citizens and foster an environment conducive to innovation. As global perspectives on success and development continue to evolve, it is possible that more nations will consider these broader indicators in shaping their policies. Several countries have shown that it is possible to pursue policies that foster innovation and promote well-being simultaneously, recognizing the interdependence between economic growth, innovation, and the quality of life of their citizens. Finland is renowned for its comprehensive approach to education and innovation while prioritizing citizen well-being. It invests significantly in education and research to foster innovation and economic growth while also focusing on social welfare programs, healthcare, and environmental sustainability to ensure the well-being of its citizens (Prime Minister’s Office, Finland 2020 ). Similarly, Danish public policies aim to support innovation through initiatives such as investment in research and development, fostering entrepreneurship, and promoting sustainable practices. At the same time, Denmark places a strong emphasis on social equality, healthcare, education, and work-life balance, contributing to the overall well-being of its population (Denmark Ministry of Foreign Affairs 2021 ).

Future research could focus on elucidating the specific mechanisms through which innovation impacts societal happiness. This could involve exploring the role of factors such as job creation, income inequality, access to education and healthcare, and social capital in mediating the relationship between innovation and well-being. Understanding these mechanisms is important to designing targeted interventions and policies aimed at maximizing the positive effects of innovation on happiness. Future research could investigate further into categorizing countries based on their development status or Human Development Index (HDI). This approach would allow a more nuanced understanding of how the relationship between innovation and happiness varies between different levels of human development. Additionally, examining how socioeconomic factors interact with innovation to influence happiness levels within each category could provide valuable information for policymakers.

Data availability

The data used are publicly available, and the data sources are mentioned in the Methodology section.

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Popescu, I.A., Reis Mourão, P.J. Exploring the nexus between national innovation performance and happiness. Humanit Soc Sci Commun 11 , 960 (2024). https://doi.org/10.1057/s41599-024-03491-7

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Perception of AI and Human Collaboration

Description.

Research Hypothesis The study hypothesizes that design students' perceptions of authorship in AI-assisted design vary depending on the degree of influence their original image prompts have on the final AI-generated outcomes. It aims to understand at what point students consider AI-generated images their own creation and how comfortable they are in collaborating with AI tools, giving credit to the AI where due. Data Collection &Analysis Data was gathered through a mixed-methods approach involving an AI-aided design workshop followed by a survey. Participants included second-year industrial design (ID) and interior architecture (IA) students. The workshop introduced the Vizcom AI tool, which students used to generate AI-assisted designs based on their studio project outcomes. The survey assessed students' familiarity with AI tools, perceptions of authorship, reasons for their perceptions, and comfort levels in co-designing with AI. The sample size was 30 students (12 ID, 18 IA). difference in familiarity level with AI tools (Q1), perception of authorship (Q2), reasons of perception of the puthorship (Q3), and comfort level of collaboration with ai (Q4) between ID and IA students. A Spearman's rank correlation coefficient can be calculated to assess the relationship between students' familiarity with AI tools (Q1) and their comfort levels in co-designing with AI (Q4). Textual analysis can be conducted to thematically analyze the responses from the open-ended question, Q5. Notable Findings T-Test: The T-test results indicate that there is no statistically significant difference between ID and IA students in terms of their familiarity with AI tools, perception of authorship, reasons for their perception of authorship, and comfort level with collaborating with AI. Perception of Authorship: 33.3% of students considered AI-generated images as their own creation up to a 50% image prompt influence level. Significant thresholds for authorship were identified between 40% and 70% image prompt influence, with most students feeling a sense of ownership within this range. Comfort with AI Collaboration: 46.4% of participants were comfortable or very comfortable collaborating with AI and might give credit to AI. A moderate positive correlation (rs=0.48) was found between familiarity with AI tools and comfort in co-designing with AI. Reasons for Perceived Authorship: The primary reason cited was that the design was still based on the students' original research or findings (60%). Implications for Future Research The study's findings suggest a need for further research with a larger and more diverse sample. Exploring perceptions of more experienced designers and different design fields could provide a broader understanding of authorship in AI-assisted design. Future studies could also delve deeper into the reasons behind neutral attitudes towards AI collaboration and explore the impact of storytelling in enhancing AI-human collaboration.

Steps to reproduce

Study Design -The study used a mixed-methods approach, combining an AI-aided design workshop with a survey to collect both quantitative and qualitative data. Participants -The study involved 30 second-year students: 12 from Industrial Design (ID) and 18 from Interior Architecture (IA). Workshop Protocol -The 50-minute workshop introduced students to the Vizcom AI tool. -First 20 minutes: Introduction to the tool's features and use. -Next 20 minutes: Practice session where students used their project outcomes as prompts to generate AI-assisted designs. They created 11 images by adjusting the image prompt influence from 100% to 0% in 10% decrements. Suggested prompts were "modern design of a salt and pepper grinder" for ID and "a modern and sleek house exterior/interior" for IA. Survey Protocol -After the workshop, students completed a 10-minute survey. Survey Questions: -Familiarity with AI tools (Likert scale: 1-5). -Perception of authorship at different AI contribution levels (percentage-based scale: 0%-100%). -Reasons for authorship perception (categorical with open-ended option). -Comfort in co-designing with AI and willingness to give credit (Likert scale: 1-5). -Open-ended question on overall thoughts about using Vizcom AI. Instruments and Software -Vizcom AI Tool: Used in the workshop. -Survey Software: For administering and collecting responses. -Statistical Software: Excel/SPSS/R for t-tests and correlation analysis. -Qualitative Analysis Software: Qualtrics for thematic analysis. Data Analysis Workflow Quantitative Data Analysis -Descriptive statistics summarized frequencies and percentages. -Independent samples t-tests compared ID and IA student responses. -Spearman's rank correlation coefficient assessed the relationship between AI familiarity and comfort in co-designing. Qualitative Data Analysis -Thematic analysis of open-ended responses involved coding, categorizing, and interpreting themes. Reproducibility To reproduce the study: -Recruit second-year ID and IA students. -Conduct a 50-minute workshop introducing the Vizcom AI tool. -Administer a post-workshop survey assessing AI familiarity, authorship perceptions, comfort levels in co-designing with AI, and overall thoughts. -Use electronic survey platforms and ensure data anonymity. -Analyze data with statistical and qualitative software, following the outlined workflows. -By following these protocols, researchers can replicate the study to explore design students' perceptions of authorship in AI-assisted design.