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Hypothesis Testing | A Step-by-Step Guide with Easy Examples
Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.
There are 5 main steps in hypothesis testing:
- State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a or H 1 ).
- Collect data in a way designed to test the hypothesis.
- Perform an appropriate statistical test .
- Decide whether to reject or fail to reject your null hypothesis.
- Present the findings in your results and discussion section.
Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.
Table of contents
Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.
After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.
The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.
- H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.
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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.
There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).
If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.
Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.
Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .
- an estimate of the difference in average height between the two groups.
- a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.
Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.
In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.
In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).
The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .
In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.
In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.
However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.
If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”
These are superficial differences; you can see that they mean the same thing.
You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.
If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
- Normal distribution
- Descriptive statistics
- Measures of central tendency
- Correlation coefficient
- Cluster sampling
- Stratified sampling
- Types of interviews
- Cohort study
- Thematic analysis
- Implicit bias
- Cognitive bias
- Survivorship bias
- Availability heuristic
- Nonresponse bias
- Regression to the mean
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
A hypothesis 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).
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.
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Statistics Made Easy
How to Write Hypothesis Test Conclusions (With Examples)
A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.
To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:
- Null Hypothesis (H 0 ): The sample data occurs purely from chance.
- Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.
If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .
Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .
When writing the conclusion of a hypothesis test, we typically include:
- Whether we reject or fail to reject the null hypothesis.
- The significance level.
- A short explanation in the context of the hypothesis test.
For example, we would write:
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…
Or, we would write:
We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…
The following examples show how to write a hypothesis test conclusion in both scenarios.
Example 1: Reject the Null Hypothesis Conclusion
Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
She then performs a hypothesis test at a 5% significance level using the following hypotheses:
- H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
- H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)
Suppose the p-value of the test turns out to be 0.002.
Here is how she would report the results of the hypothesis test:
We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.
Example 2: Fail to Reject the Null Hypothesis Conclusion
Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.
He performs a hypothesis test at a 10% significance level using the following hypotheses:
- H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
- H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)
Suppose the p-value of the test turns out to be 0.27.
Here is how he would report the results of the hypothesis test:
We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.
The following tutorials provide additional information about hypothesis testing:
Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis
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Course: biology library > unit 1, the scientific method.
- Controlled experiments
- The scientific method and experimental design
- Make an observation.
- Ask a question.
- Form a hypothesis , or testable explanation.
- Make a prediction based on the hypothesis.
- Test the prediction.
- Iterate: use the results to make new hypotheses or predictions.
Scientific method example: Failure to toast
1. make an observation..
- Observation: the toaster won't toast.
2. Ask a question.
- Question: Why won't my toaster toast?
3. Propose a hypothesis.
- Hypothesis: Maybe the outlet is broken.
4. Make predictions.
- Prediction: If I plug the toaster into a different outlet, then it will toast the bread.
5. Test the predictions.
- Test of prediction: Plug the toaster into a different outlet and try again.
- If the toaster does toast, then the hypothesis is supported—likely correct.
- If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.
- Iteration time!
- If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
- If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.
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The Scientific Method by Science Made Simple
Understanding and using the scientific method.
The Scientific Method is a process used to design and perform experiments. It's important to minimize experimental errors and bias, and increase confidence in the accuracy of your results.
In the previous sections, we talked about how to pick a good topic and specific question to investigate. Now we will discuss how to carry out your investigation.
Steps of the Scientific Method
Now that you have settled on the question you want to ask, it's time to use the Scientific Method to design an experiment to answer that question.
If your experiment isn't designed well, you may not get the correct answer. You may not even get any definitive answer at all!
The Scientific Method is a logical and rational order of steps by which scientists come to conclusions about the world around them. The Scientific Method helps to organize thoughts and procedures so that scientists can be confident in the answers they find.
OBSERVATION is first step, so that you know how you want to go about your research.
HYPOTHESIS is the answer you think you'll find.
PREDICTION is your specific belief about the scientific idea: If my hypothesis is true, then I predict we will discover this.
EXPERIMENT is the tool that you invent to answer the question, and
CONCLUSION is the answer that the experiment gives.
Don't worry, it isn't that complicated. Let's take a closer look at each one of these steps. Then you can understand the tools scientists use for their science experiments, and use them for your own.
This step could also be called "research." It is the first stage in understanding the problem.
After you decide on topic, and narrow it down to a specific question, you will need to research everything that you can find about it. You can collect information from your own experiences, books, the internet, or even smaller "unofficial" experiments.
Let's continue the example of a science fair idea about tomatoes in the garden. You like to garden, and notice that some tomatoes are bigger than others and wonder why.
Because of this personal experience and an interest in the problem, you decide to learn more about what makes plants grow.
For this stage of the Scientific Method, it's important to use as many sources as you can find. The more information you have on your science fair topic, the better the design of your experiment is going to be, and the better your science fair project is going to be overall.
Also try to get information from your teachers or librarians, or professionals who know something about your science fair project. They can help to guide you to a solid experimental setup.
The next stage of the Scientific Method is known as the "hypothesis." This word basically means "a possible solution to a problem, based on knowledge and research."
The hypothesis is a simple statement that defines what you think the outcome of your experiment will be.
All of the first stage of the Scientific Method -- the observation, or research stage -- is designed to help you express a problem in a single question ("Does the amount of sunlight in a garden affect tomato size?") and propose an answer to the question based on what you know. The experiment that you will design is done to test the hypothesis.
Using the example of the tomato experiment, here is an example of a hypothesis:
TOPIC: "Does the amount of sunlight a tomato plant receives affect the size of the tomatoes?"
HYPOTHESIS: "I believe that the more sunlight a tomato plant receives, the larger the tomatoes will grow.
This hypothesis is based on:
(1) Tomato plants need sunshine to make food through photosynthesis, and logically, more sun means more food, and;
(2) Through informal, exploratory observations of plants in a garden, those with more sunlight appear to grow bigger.
The hypothesis is your general statement of how you think the scientific phenomenon in question works.
Your prediction lets you get specific -- how will you demonstrate that your hypothesis is true? The experiment that you will design is done to test the prediction.
An important thing to remember during this stage of the scientific method is that once you develop a hypothesis and a prediction, you shouldn't change it, even if the results of your experiment show that you were wrong.
An incorrect prediction does NOT mean that you "failed." It just means that the experiment brought some new facts to light that maybe you hadn't thought about before.
Continuing our tomato plant example, a good prediction would be: Increasing the amount of sunlight tomato plants in my experiment receive will cause an increase in their size compared to identical plants that received the same care but less light.
This is the part of the scientific method that tests your hypothesis. An experiment is a tool that you design to find out if your ideas about your topic are right or wrong.
It is absolutely necessary to design a science fair experiment that will accurately test your hypothesis. The experiment is the most important part of the scientific method. It's the logical process that lets scientists learn about the world.
On the next page, we'll discuss the ways that you can go about designing a science fair experiment idea.
The final step in the scientific method is the conclusion. This is a summary of the experiment's results, and how those results match up to your hypothesis.
You have two options for your conclusions: based on your results, either:
(1) YOU CAN REJECT the hypothesis, or
(2) YOU CAN NOT REJECT the hypothesis.
This is an important point!
You can not PROVE the hypothesis with a single experiment, because there is a chance that you made an error somewhere along the way.
What you can say is that your results SUPPORT the original hypothesis.
If your original hypothesis didn't match up with the final results of your experiment, don't change the hypothesis.
Instead, try to explain what might have been wrong with your original hypothesis. What information were you missing when you made your prediction? What are the possible reasons the hypothesis and experimental results didn't match up?
Remember, a science fair experiment isn't a failure simply because does not agree with your hypothesis. No one will take points off if your prediction wasn't accurate. Many important scientific discoveries were made as a result of experiments gone wrong!
A science fair experiment is only a failure if its design is flawed. A flawed experiment is one that (1) doesn't keep its variables under control, and (2) doesn't sufficiently answer the question that you asked of it.
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How to Write an APA Results Section
Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.
Verywell / Nusha Ashjaee
What to Include in an APA Results Section
- Justify Claims
- Summarize Results
Report All Relevant Results
- Report Statistical Findings
Include Tables and Figures
What not to include in an apa results section.
Psychology papers generally follow a specific structure. One important section of a paper is known as the results section. An APA results section of a psychology paper summarizes the data that was collected and the statistical analyses that were performed. The goal of this section is to report the results of your study or experiment without any type of subjective interpretation.
At a Glance
The results section is a vital part of an APA paper that summarizes a study's findings and statistical analysis. This section often includes descriptive text, tables, and figures to help summarize the findings. The focus is purely on summarizing and presenting the findings and should not include any interpretation, since you'll cover that in the subsequent discussion section.
This article covers how to write an APA results section, including what to include and what to avoid.
The results section is the third section of a psychology paper. It will appear after the introduction and methods sections and before the discussion section.
The results section should include:
- A summary of the research findings.
- Information about participant flow, recruitment, retention, and attrition. If some participants started the study and later left or failed to complete the study, then this should be described.
- Information about any reasons why some data might have been excluded from the study.
- Statistical information including samples sizes and statistical tests that were used. It should report standard deviations, p-values, and other measures of interest.
Results Should Justify Your Claims
Report data in order to sufficiently justify your conclusions. Since you'll be talking about your own interpretation of the results in the discussion section, you need to be sure that the information reported in the results section justifies your claims.
When you start writing your discussion section, you can then look back on your results to ensure that all the data you need are there to fully support your conclusions. Be sure not to make claims in your discussion section that are not supported by the findings described in your results section.
Summarize Your Results
Remember, you are summarizing the results of your psychological study, not reporting them in full detail. The results section should be a relatively brief overview of your findings, not a complete presentation of every single number and calculation.
If you choose, you can create a supplemental online archive where other researchers can access the raw data if they choose.
How long should a results section be?
The length of your results section will vary depending on the nature of your paper and the complexity of your research. In most cases, this will be the shortest section of your paper.
Just as the results section of your psychology paper should sufficiently justify your claims, it should also provide an accurate look at what you found in your study. Be sure to mention all relevant information.
Don't omit findings simply because they failed to support your predictions.
Your hypothesis may have expected more statistically significant results or your study didn't support your hypothesis , but that doesn't mean that the conclusions you reach are not useful. Provide data about what you found in your results section, then save your interpretation for what the results might mean in the discussion section.
While your study might not have supported your original predictions, your finding can provide important inspiration for future explorations into a topic.
How is the results section different from the discussion section?
The results section provides the results of your study or experiment. The goal of the section is to report what happened and the statistical analyses you performed. The discussion section is where you will examine what these results mean and whether they support or fail to support your hypothesis.
Report Your Statistical Findings
Always assume that your readers have a solid understanding of statistical concepts. There's no need to explain what a t-test is or how a one-way ANOVA works. Your responsibility is to report the results of your study, not to teach your readers how to analyze or interpret statistics.
Include Effect Sizes
The Publication Manual of the American Psychological Association recommends including effect sizes in your results section so that readers can appreciate the importance of your study's findings.
Your results section should include both text and illustrations. Presenting data in this way makes it easier for readers to quickly look at your results.
Structure your results section around tables or figures that summarize the results of your statistical analysis. In many cases, the easiest way to accomplish this is to first create your tables and figures and then organize them in a logical way. Next, write the summary text to support your illustrative materials.
Only include tables and figures if you are going to talk about them in the body text of your results section.
In addition to knowing what you should include in the results section of your psychology paper, it's also important to be aware of things that you should avoid putting in this section:
Don't draw cause-effect conclusions. Avoid making any claims suggesting that your result "proves" that something is true.
Present the data without editorializing it. Save your comments and interpretations for the discussion section of your paper.
Statistics Without Context
Don't include statistics without narration. The results section should not be a numbers dump. Instead, you should sequentially narrate what these numbers mean.
Don't include the raw data in the results section. The results section should be a concise presentation of the results. If there is raw data that would be useful, include it in the appendix .
Don't only rely on descriptive text. Use tables and figures to present these findings when appropriate. This makes the results section easier to read and can convey a great deal of information quickly.
Don't present the same data twice in your illustrative materials. If you have already presented some data in a table, don't present it again in a figure. If you have presented data in a figure, don't present it again in a table.
All of Your Findings
Don't feel like you have to include everything. If data is irrelevant to the research question, don't include it in the results section.
But Don't Skip Relevant Data
Don't leave out results because they don't support your claims. Even if your data does not support your hypothesis, including it in your findings is essential if it's relevant.
More Tips for Writing a Results Section
If you are struggling, there are a few things to remember that might help:
- Use the past tense . The results section should be written in the past tense.
- Be concise and objective . You will have the opportunity to give your own interpretations of the results in the discussion section.
- Use APA format . As you are writing your results section, keep a style guide on hand. The Publication Manual of the American Psychological Association is the official source for APA style.
- Visit your library . Read some journal articles that are on your topic. Pay attention to how the authors present the results of their research.
- Get a second opinion . If possible, take your paper to your school's writing lab for additional assistance.
What This Means For You
Remember, the results section of your paper is all about providing the data from your study. This section is often the shortest part of your paper, and in most cases, the most clinical.
Be sure not to include any subjective interpretation of the results. Simply relay the data in the most objective and straightforward way possible. You can then provide your own analysis of what these results mean in the discussion section of your paper.
Bavdekar SB, Chandak S. Results: Unraveling the findings . J Assoc Physicians India . 2015 Sep;63(9):44-6. PMID:27608866.
Snyder N, Foltz C, Lendner M, Vaccaro AR. How to write an effective results section . Clin Spine Surg . 2019;32(7):295-296. doi:10.1097/BSD.0000000000000845
American Psychological Association. Publication Manual of the American Psychological Association (7th ed.). Washington DC: The American Psychological Association; 2019.
Purdue Online Writing Lab. APA sample paper: Experimental psychology .
Berkeley University. Reviewing test results .
Tuncel A, Atan A. How to clearly articulate results and construct tables and figures in a scientific paper ? Turk J Urol . 2013;39(Suppl 1):16-19. doi:10.5152/tud.2013.048
By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Home » What is a Hypothesis – Types, Examples and Writing Guide
What is a Hypothesis – Types, Examples and Writing Guide
Table of Contents
Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.
Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.
Types of Hypothesis
Types of Hypothesis are as follows:
A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.
The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.
An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.
A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.
A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.
A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.
A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.
An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.
A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.
A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.
Applications of Hypothesis
Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:
- Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
- Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
- Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
- Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
- Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
- Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.
How to write a Hypothesis
Here are the steps to follow when writing a hypothesis:
Identify the Research Question
The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.
Conduct a Literature Review
Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.
Determine the Variables
The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.
Formulate the Hypothesis
Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.
Write the Null Hypothesis
The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.
Refine the Hypothesis
After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.
Examples of Hypothesis
Here are a few examples of hypotheses in different fields:
- Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
- Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
- Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
- Education : “Implementing a new teaching method will result in higher student achievement scores.”
- Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
- Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
- Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”
Purpose of Hypothesis
The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.
The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.
In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.
When to use Hypothesis
Here are some common situations in which hypotheses are used:
- In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
- In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
- I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.
Characteristics of Hypothesis
Here are some common characteristics of a hypothesis:
- Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
- Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
- Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
- Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
- Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
- Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
- Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.
Advantages of Hypothesis
Hypotheses have several advantages in scientific research and experimentation:
- Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
- Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
- Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
- Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
- Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
- Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.
Limitations of Hypothesis
Some Limitations of the Hypothesis are as follows:
- Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
- May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
- May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
- Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
- Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
- May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.
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11.6: Reporting the Results of a Hypothesis Test
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- Page ID 4012
- Danielle Navarro
- University of New South Wales
When writing up the results of a hypothesis test, there’s usually several pieces of information that you need to report, but it varies a fair bit from test to test. Throughout the rest of the book I’ll spend a little time talking about how to report the results of different tests (see Section 12.1.9 for a particularly detailed example), so that you can get a feel for how it’s usually done. However, regardless of what test you’re doing, the one thing that you always have to do is say something about the p value, and whether or not the outcome was significant.
The fact that you have to do this is unsurprising; it’s the whole point of doing the test. What might be surprising is the fact that there is some contention over exactly how you’re supposed to do it. Leaving aside those people who completely disagree with the entire framework underpinning null hypothesis testing, there’s a certain amount of tension that exists regarding whether or not to report the exact p value that you obtained, or if you should state only that p<α for a significance level that you chose in advance (e.g., p<.05).
To see why this is an issue, the key thing to recognise is that p values are terribly convenient. In practice, the fact that we can compute a p value means that we don’t actually have to specify any α level at all in order to run the test. Instead, what you can do is calculate your p value and interpret it directly: if you get p=.062, then it means that you’d have to be willing to tolerate a Type I error rate of 6.2% to justify rejecting the null. If you personally find 6.2% intolerable, then you retain the null. Therefore, the argument goes, why don’t we just report the actual p value and let the reader make up their own minds about what an acceptable Type I error rate is? This approach has the big advantage of “softening” the decision making process – in fact, if you accept the Neyman definition of the p value, that’s the whole point of the p value. We no longer have a fixed significance level of α=.05 as a bright line separating “accept” from “reject” decisions; and this removes the rather pathological problem of being forced to treat p=.051 in a fundamentally different way to p=.049.
This flexibility is both the advantage and the disadvantage to the p value. The reason why a lot of people don’t like the idea of reporting an exact p value is that it gives the researcher a bit too much freedom. In particular, it lets you change your mind about what error tolerance you’re willing to put up with after you look at the data. For instance, consider my ESP experiment. Suppose I ran my test, and ended up with a p value of .09. Should I accept or reject? Now, to be honest, I haven’t yet bothered to think about what level of Type I error I’m “really” willing to accept. I don’t have an opinion on that topic. But I do have an opinion about whether or not ESP exists, and I definitely have an opinion about whether my research should be published in a reputable scientific journal. And amazingly, now that I’ve looked at the data I’m starting to think that a 9% error rate isn’t so bad, especially when compared to how annoying it would be to have to admit to the world that my experiment has failed. So, to avoid looking like I just made it up after the fact, I now say that my α is .1: a 10% type I error rate isn’t too bad, and at that level my test is significant! I win.
In other words, the worry here is that I might have the best of intentions, and be the most honest of people, but the temptation to just “shade” things a little bit here and there is really, really strong. As anyone who has ever run an experiment can attest, it’s a long and difficult process, and you often get very attached to your hypotheses. It’s hard to let go and admit the experiment didn’t find what you wanted it to find. And that’s the danger here. If we use the “raw” p-value, people will start interpreting the data in terms of what they want to believe, not what the data are actually saying… and if we allow that, well, why are we bothering to do science at all? Why not let everyone believe whatever they like about anything, regardless of what the facts are? Okay, that’s a bit extreme, but that’s where the worry comes from. According to this view, you really must specify your α value in advance, and then only report whether the test was significant or not. It’s the only way to keep ourselves honest.
In practice, it’s pretty rare for a researcher to specify a single α level ahead of time. Instead, the convention is that scientists rely on three standard significance levels: .05, .01 and .001. When reporting your results, you indicate which (if any) of these significance levels allow you to reject the null hypothesis. This is summarised in Table 11.1. This allows us to soften the decision rule a little bit, since p<.01 implies that the data meet a stronger evidentiary standard than p<.05 would. Nevertheless, since these levels are fixed in advance by convention, it does prevent people choosing their α level after looking at the data.
Table 11.1: A commonly adopted convention for reporting p values: in many places it is conventional to report one of four different things (e.g., p<.05) as shown below. I’ve included the “significance stars” notation (i.e., a * indicates p<.05) because you sometimes see this notation produced by statistical software. It’s also worth noting that some people will write n.s. (not significant) rather than p>.05.
Nevertheless, quite a lot of people still prefer to report exact p values. To many people, the advantage of allowing the reader to make up their own mind about how to interpret p=.06 outweighs any disadvantages. In practice, however, even among those researchers who prefer exact p values it is quite common to just write p<.001 instead of reporting an exact value for small p. This is in part because a lot of software doesn’t actually print out the p value when it’s that small (e.g., SPSS just writes p=.000 whenever p<.001), and in part because a very small p value can be kind of misleading. The human mind sees a number like .0000000001 and it’s hard to suppress the gut feeling that the evidence in favour of the alternative hypothesis is a near certainty. In practice however, this is usually wrong. Life is a big, messy, complicated thing: and every statistical test ever invented relies on simplifications, approximations and assumptions. As a consequence, it’s probably not reasonable to walk away from any statistical analysis with a feeling of confidence stronger than p<.001 implies. In other words, p<.001 is really code for “as far as this test is concerned, the evidence is overwhelming.”
In light of all this, you might be wondering exactly what you should do. There’s a fair bit of contradictory advice on the topic, with some people arguing that you should report the exact p value, and other people arguing that you should use the tiered approach illustrated in Table 11.1. As a result, the best advice I can give is to suggest that you look at papers/reports written in your field and see what the convention seems to be. If there doesn’t seem to be any consistent pattern, then use whichever method you prefer.
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S.3 hypothesis testing.
In reviewing hypothesis tests, we start first with the general idea. Then, we keep returning to the basic procedures of hypothesis testing, each time adding a little more detail.
The general idea of hypothesis testing involves:
- Making an initial assumption.
- Collecting evidence (data).
- Based on the available evidence (data), deciding whether to reject or not reject the initial assumption.
Every hypothesis test — regardless of the population parameter involved — requires the above three steps.
Is normal body temperature really 98.6 degrees f section .
Consider the population of many, many adults. A researcher hypothesized that the average adult body temperature is lower than the often-advertised 98.6 degrees F. That is, the researcher wants an answer to the question: "Is the average adult body temperature 98.6 degrees? Or is it lower?" To answer his research question, the researcher starts by assuming that the average adult body temperature was 98.6 degrees F.
Then, the researcher went out and tried to find evidence that refutes his initial assumption. In doing so, he selects a random sample of 130 adults. The average body temperature of the 130 sampled adults is 98.25 degrees.
Then, the researcher uses the data he collected to make a decision about his initial assumption. It is either likely or unlikely that the researcher would collect the evidence he did given his initial assumption that the average adult body temperature is 98.6 degrees:
- If it is likely , then the researcher does not reject his initial assumption that the average adult body temperature is 98.6 degrees. There is not enough evidence to do otherwise.
- either the researcher's initial assumption is correct and he experienced a very unusual event;
- or the researcher's initial assumption is incorrect.
In statistics, we generally don't make claims that require us to believe that a very unusual event happened. That is, in the practice of statistics, if the evidence (data) we collected is unlikely in light of the initial assumption, then we reject our initial assumption.
Criminal trial analogy section .
One place where you can consistently see the general idea of hypothesis testing in action is in criminal trials held in the United States. Our criminal justice system assumes "the defendant is innocent until proven guilty." That is, our initial assumption is that the defendant is innocent.
In the practice of statistics, we make our initial assumption when we state our two competing hypotheses -- the null hypothesis ( H 0 ) and the alternative hypothesis ( H A ). Here, our hypotheses are:
- H 0 : Defendant is not guilty (innocent)
- H A : Defendant is guilty
In statistics, we always assume the null hypothesis is true . That is, the null hypothesis is always our initial assumption.
The prosecution team then collects evidence — such as finger prints, blood spots, hair samples, carpet fibers, shoe prints, ransom notes, and handwriting samples — with the hopes of finding "sufficient evidence" to make the assumption of innocence refutable.
In statistics, the data are the evidence.
The jury then makes a decision based on the available evidence:
- If the jury finds sufficient evidence — beyond a reasonable doubt — to make the assumption of innocence refutable, the jury rejects the null hypothesis and deems the defendant guilty. We behave as if the defendant is guilty.
- If there is insufficient evidence, then the jury does not reject the null hypothesis . We behave as if the defendant is innocent.
In statistics, we always make one of two decisions. We either "reject the null hypothesis" or we "fail to reject the null hypothesis."
Errors in Hypothesis Testing Section
Did you notice the use of the phrase "behave as if" in the previous discussion? We "behave as if" the defendant is guilty; we do not "prove" that the defendant is guilty. And, we "behave as if" the defendant is innocent; we do not "prove" that the defendant is innocent.
This is a very important distinction! We make our decision based on evidence not on 100% guaranteed proof. Again:
- If we reject the null hypothesis, we do not prove that the alternative hypothesis is true.
- If we do not reject the null hypothesis, we do not prove that the null hypothesis is true.
We merely state that there is enough evidence to behave one way or the other. This is always true in statistics! Because of this, whatever the decision, there is always a chance that we made an error .
Let's review the two types of errors that can be made in criminal trials:
Table S.3.2 shows how this corresponds to the two types of errors in hypothesis testing.
Note that, in statistics, we call the two types of errors by two different names -- one is called a "Type I error," and the other is called a "Type II error." Here are the formal definitions of the two types of errors:
There is always a chance of making one of these errors. But, a good scientific study will minimize the chance of doing so!
Making the Decision Section
Recall that it is either likely or unlikely that we would observe the evidence we did given our initial assumption. If it is likely , we do not reject the null hypothesis. If it is unlikely , then we reject the null hypothesis in favor of the alternative hypothesis. Effectively, then, making the decision reduces to determining "likely" or "unlikely."
In statistics, there are two ways to determine whether the evidence is likely or unlikely given the initial assumption:
- We could take the " critical value approach " (favored in many of the older textbooks).
- Or, we could take the " P -value approach " (what is used most often in research, journal articles, and statistical software).
In the next two sections, we review the procedures behind each of these two approaches. To make our review concrete, let's imagine that μ is the average grade point average of all American students who major in mathematics. We first review the critical value approach for conducting each of the following three hypothesis tests about the population mean $\mu$:
- We would want to conduct the first hypothesis test if we were interested in concluding that the average grade point average of the group is more than 3.
- We would want to conduct the second hypothesis test if we were interested in concluding that the average grade point average of the group is less than 3.
- And, we would want to conduct the third hypothesis test if we were only interested in concluding that the average grade point average of the group differs from 3 (without caring whether it is more or less than 3).
Upon completing the review of the critical value approach, we review the P -value approach for conducting each of the above three hypothesis tests about the population mean \(\mu\). The procedures that we review here for both approaches easily extend to hypothesis tests about any other population parameter.
6 Steps to Evaluate the Effectiveness of Statistical Hypothesis Testing
You know what is tragic? Having the potential to complete the research study but not doing the correct hypothesis testing. Quite often, researchers think the most challenging aspect of research is standardization of experiments, data analysis or writing the thesis! But in all honesty, creating an effective research hypothesis is the most crucial step in designing and executing a research study. An effective research hypothesis will provide researchers the correct basic structure for building the research question and objectives.
In this article, we will discuss how to formulate and identify an effective research hypothesis testing to benefit researchers in designing their research work.
Table of Contents
What Is Research Hypothesis Testing?
Hypothesis testing is a systematic procedure derived from the research question and decides if the results of a research study support a certain theory which can be applicable to the population. Moreover, it is a statistical test used to determine whether the hypothesis assumed by the sample data stands true to the entire population.
The purpose of testing the hypothesis is to make an inference about the population of interest on the basis of random sample taken from that population. Furthermore, it is the assumption which is tested to determine the relationship between two data sets.
Types of Statistical Hypothesis Testing
1. there are two types of hypothesis in statistics, a. null hypothesis.
This is the assumption that the event will not occur or there is no relation between the compared variables. A null hypothesis has no relation with the study’s outcome unless it is rejected. Null hypothesis uses H0 as its symbol.
b. Alternate Hypothesis
The alternate hypothesis is the logical opposite of the null hypothesis. Furthermore, the acceptance of the alternative hypothesis follows the rejection of the null hypothesis. It uses H1 or Ha as its symbol
Hypothesis Testing Example: A sanitizer manufacturer company claims that its product kills 98% of germs on average. To put this company’s claim to test, create null and alternate hypothesis H0 (Null Hypothesis): Average = 98% H1/Ha (Alternate Hypothesis): The average is less than 98%
2. Depending on the population distribution, you can categorize the statistical hypothesis into two types.
A. simple hypothesis.
A simple hypothesis specifies an exact value for the parameter.
b. Composite Hypothesis
A composite hypothesis specifies a range of values.
Hypothesis Testing Example: A company claims to have achieved 1000 units as their average sales for this quarter. (Simple Hypothesis) The company claims to achieve the sales in the range of 900 to 100o units. (Composite Hypothesis).
3. Based on the type of statistical testing, the hypothesis in statistics is of two types.
One-Tailed test or directional test considers a critical region of data which would result in rejection of the null hypothesis if the test sample falls in that data region. Therefore, accepting the alternate hypothesis. Furthermore, the critical distribution area in this test is one-sided which means the test sample is either greater or lesser than a specific value.
Two-Tailed test or nondirectional test is designed to show if the sample mean is significantly greater than and significantly less than the mean population. Here, the critical distribution area is two-sided. If the sample falls within the range, the alternate hypothesis is accepted and the null hypothesis is rejected.
Statistical Hypothesis Testing Example: Suppose H0: mean = 100 and H1: mean is not equal to 100 According to the H1, the mean can be greater than or less than 100. (Two-Tailed test) Similarly, if H0: mean >= 100, then H1: mean < 100 Here the mean is less than 100. (One-Tailed test)
Steps in Statistical Hypothesis Testing
Step 1: develop initial research hypothesis.
Research hypothesis is developed from research question. It is the prediction that you want to investigate. Moreover, an initial research hypothesis is important for restating the null and alternate hypothesis, to test the research question mathematically.
Step 2: State the null and alternate hypothesis based on your research hypothesis
Usually, the alternate hypothesis is your initial hypothesis that predicts relationship between variables. However, the null hypothesis is a prediction of no relationship between the variables you are interested in.
Step 3: Perform sampling and collection of data for statistical testing
It is important to perform sampling and collect data in way that assists the formulated research hypothesis. You will have to perform a statistical testing to validate your data and make statistical inferences about the population of your interest.
Step 4: Perform statistical testing based on the type of data you collected
There are various statistical tests available. Based on the comparison of within group variance and between group variance, you can carry out the statistical tests for the research study. If the between group variance is large enough and there is little or no overlap between groups, then the statistical test will show low p-value. (Difference between the groups is not a chance event).
Alternatively, if the within group variance is high compared to between group variance, then the statistical test shows a high p-value. (Difference between the groups is a chance event).
Step 5: Based on the statistical outcome, reject or fail to reject your null hypothesis
In most cases, you will use p-value generated from your statistical test to guide your decision. You will consider a predetermined level of significance of 0.05 for rejecting your null hypothesis , i.e. there is less than 5% chance of getting the results wherein the null hypothesis is true.
Step 6: Present your final results of hypothesis testing
You will present the results of your hypothesis in the results and discussion section of the research paper . In results section, you provide a brief summary of the data and a summary of the results of your statistical test. Meanwhile, in discussion, you can mention whether your results support your initial hypothesis.
Note that we never reject or fail to reject the alternate hypothesis. This is because the testing of hypothesis is not designed to prove or disprove anything. However, it is designed to test if a result is spuriously occurred, or by chance. Thus, statistical hypothesis testing becomes a crucial statistical tool to mathematically define the outcome of a research question.
Have you ever used hypothesis testing as a means of statistically analyzing your research data? How was your experience? Do write to us or comment below.
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P-Value And Statistical Significance: What It Is & Why It Matters
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On This Page:
The p-value in statistics quantifies the evidence against a null hypothesis. A low p-value suggests data is inconsistent with the null, potentially favoring an alternative hypothesis. Common significance thresholds are 0.05 or 0.01.
When you perform a statistical test, a p-value helps you determine the significance of your results in relation to the null hypothesis.
The null hypothesis (H0) states no relationship exists between the two variables being studied (one variable does not affect the other). It states the results are due to chance and are not significant in supporting the idea being investigated. Thus, the null hypothesis assumes that whatever you try to prove did not happen.
The alternative hypothesis (Ha or H1) is the one you would believe if the null hypothesis is concluded to be untrue.
The alternative hypothesis states that the independent variable affected the dependent variable, and the results are significant in supporting the theory being investigated (i.e., the results are not due to random chance).
What a p-value tells you
A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e., that the null hypothesis is true).
The level of statistical significance is often expressed as a p-value between 0 and 1.
The smaller the p -value, the less likely the results occurred by random chance, and the stronger the evidence that you should reject the null hypothesis.
Remember, a p-value doesn’t tell you if the null hypothesis is true or false. It just tells you how likely you’d see the data you observed (or more extreme data) if the null hypothesis was true. It’s a piece of evidence, not a definitive proof.
Example: Test Statistic and p-Value
Suppose you’re conducting a study to determine whether a new drug has an effect on pain relief compared to a placebo. If the new drug has no impact, your test statistic will be close to the one predicted by the null hypothesis (no difference between the drug and placebo groups), and the resulting p-value will be close to 1. It may not be precisely 1 because real-world variations may exist. Conversely, if the new drug indeed reduces pain significantly, your test statistic will diverge further from what’s expected under the null hypothesis, and the p-value will decrease. The p-value will never reach zero because there’s always a slim possibility, though highly improbable, that the observed results occurred by random chance.
The significance level (alpha) is a set probability threshold (often 0.05), while the p-value is the probability you calculate based on your study or analysis.
A p-value less than or equal to your significance level (typically ≤ 0.05) is statistically significant.
A p-value less than or equal to a predetermined significance level (often 0.05 or 0.01) indicates a statistically significant result, meaning the observed data provide strong evidence against the null hypothesis.
This suggests the effect under study likely represents a real relationship rather than just random chance.
For instance, if you set α = 0.05, you would reject the null hypothesis if your p -value ≤ 0.05.
It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random).
Therefore, we reject the null hypothesis and accept the alternative hypothesis.
Example: Statistical Significance
Upon analyzing the pain relief effects of the new drug compared to the placebo, the computed p-value is less than 0.01, which falls well below the predetermined alpha value of 0.05. Consequently, you conclude that there is a statistically significant difference in pain relief between the new drug and the placebo.
What does a p-value of 0.001 mean?
A p-value of 0.001 is highly statistically significant beyond the commonly used 0.05 threshold. It indicates strong evidence of a real effect or difference, rather than just random variation.
Specifically, a p-value of 0.001 means there is only a 0.1% chance of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is correct.
Such a small p-value provides strong evidence against the null hypothesis, leading to rejecting the null in favor of the alternative hypothesis.
A p-value more than the significance level (typically p > 0.05) is not statistically significant and indicates strong evidence for the null hypothesis.
This means we retain the null hypothesis and reject the alternative hypothesis. You should note that you cannot accept the null hypothesis; we can only reject it or fail to reject it.
Note : when the p-value is above your threshold of significance, it does not mean that there is a 95% probability that the alternative hypothesis is true.
How do you calculate the p-value ?
Most statistical software packages like R, SPSS, and others automatically calculate your p-value. This is the easiest and most common way.
Online resources and tables are available to estimate the p-value based on your test statistic and degrees of freedom.
These tables help you understand how often you would expect to see your test statistic under the null hypothesis.
Understanding the Statistical Test:
Different statistical tests are designed to answer specific research questions or hypotheses. Each test has its own underlying assumptions and characteristics.
For example, you might use a t-test to compare means, a chi-squared test for categorical data, or a correlation test to measure the strength of a relationship between variables.
Be aware that the number of independent variables you include in your analysis can influence the magnitude of the test statistic needed to produce the same p-value.
This factor is particularly important to consider when comparing results across different analyses.
Example: Choosing a Statistical Test
If you’re comparing the effectiveness of just two different drugs in pain relief, a two-sample t-test is a suitable choice for comparing these two groups. However, when you’re examining the impact of three or more drugs, it’s more appropriate to employ an Analysis of Variance ( ANOVA) . Utilizing multiple pairwise comparisons in such cases can lead to artificially low p-values and an overestimation of the significance of differences between the drug groups.
How to report
A statistically significant result cannot prove that a research hypothesis is correct (which implies 100% certainty).
Instead, we may state our results “provide support for” or “give evidence for” our research hypothesis (as there is still a slight probability that the results occurred by chance and the null hypothesis was correct – e.g., less than 5%).
Example: Reporting the results
In our comparison of the pain relief effects of the new drug and the placebo, we observed that participants in the drug group experienced a significant reduction in pain ( M = 3.5; SD = 0.8) compared to those in the placebo group ( M = 5.2; SD = 0.7), resulting in an average difference of 1.7 points on the pain scale (t(98) = -9.36; p < 0.001).
The 6th edition of the APA style manual (American Psychological Association, 2010) states the following on the topic of reporting p-values:
“When reporting p values, report exact p values (e.g., p = .031) to two or three decimal places. However, report p values less than .001 as p < .001.
The tradition of reporting p values in the form p < .10, p < .05, p < .01, and so forth, was appropriate in a time when only limited tables of critical values were available.” (p. 114)
- Do not use 0 before the decimal point for the statistical value p as it cannot equal 1. In other words, write p = .001 instead of p = 0.001.
- Please pay attention to issues of italics ( p is always italicized) and spacing (either side of the = sign).
- p = .000 (as outputted by some statistical packages such as SPSS) is impossible and should be written as p < .001.
- The opposite of significant is “nonsignificant,” not “insignificant.”
Why is the p -value not enough?
A lower p-value is sometimes interpreted as meaning there is a stronger relationship between two variables.
However, statistical significance means that it is unlikely that the null hypothesis is true (less than 5%).
To understand the strength of the difference between the two groups (control vs. experimental) a researcher needs to calculate the effect size .
When do you reject the null hypothesis?
In statistical hypothesis testing, you reject the null hypothesis when the p-value is less than or equal to the significance level (α) you set before conducting your test. The significance level is the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.01, 0.05, and 0.10.
Remember, rejecting the null hypothesis doesn’t prove the alternative hypothesis; it just suggests that the alternative hypothesis may be plausible given the observed data.
The p -value is conditional upon the null hypothesis being true but is unrelated to the truth or falsity of the alternative hypothesis.
What does p-value of 0.05 mean?
If your p-value is less than or equal to 0.05 (the significance level), you would conclude that your result is statistically significant. This means the evidence is strong enough to reject the null hypothesis in favor of the alternative hypothesis.
Are all p-values below 0.05 considered statistically significant?
No, not all p-values below 0.05 are considered statistically significant. The threshold of 0.05 is commonly used, but it’s just a convention. Statistical significance depends on factors like the study design, sample size, and the magnitude of the observed effect.
A p-value below 0.05 means there is evidence against the null hypothesis, suggesting a real effect. However, it’s essential to consider the context and other factors when interpreting results.
Researchers also look at effect size and confidence intervals to determine the practical significance and reliability of findings.
How does sample size affect the interpretation of p-values?
Sample size can impact the interpretation of p-values. A larger sample size provides more reliable and precise estimates of the population, leading to narrower confidence intervals.
With a larger sample, even small differences between groups or effects can become statistically significant, yielding lower p-values. In contrast, smaller sample sizes may not have enough statistical power to detect smaller effects, resulting in higher p-values.
Therefore, a larger sample size increases the chances of finding statistically significant results when there is a genuine effect, making the findings more trustworthy and robust.
Can a non-significant p-value indicate that there is no effect or difference in the data?
No, a non-significant p-value does not necessarily indicate that there is no effect or difference in the data. It means that the observed data do not provide strong enough evidence to reject the null hypothesis.
There could still be a real effect or difference, but it might be smaller or more variable than the study was able to detect.
Other factors like sample size, study design, and measurement precision can influence the p-value. It’s important to consider the entire body of evidence and not rely solely on p-values when interpreting research findings.
Can P values be exactly zero?
While a p-value can be extremely small, it cannot technically be absolute zero. When a p-value is reported as p = 0.000, the actual p-value is too small for the software to display. This is often interpreted as strong evidence against the null hypothesis. For p values less than 0.001, report as p < .001