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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 ).

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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

Methodology

- Cluster sampling
- Stratified sampling
- Types of interviews
- Cohort study
- Thematic analysis

Research bias

- 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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Hypothesis testing, or significance test-ing, a method of testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likeli hood that a sample statistic could have been selected, if the hypothesis regarding the popu lation parameter were true.

Harold's Statistics Hypothesis Testing Cheat Sheet Hypothesis Terms Definitions. g Cheat Sheet23 June 2022Hypothesis TermsDefinitions. Significance Level ( )Defines the strength of evidence in probabilistic terms. Specifically, alpha represents the probability that tests w. l produce statistically significant results w.

The major purpose of hypothesis testing is to choose between two competing hypotheses about the value of a population parameter. For example, one hypothesis might claim that the wages of men and women are equal, while the alternative might claim that men make more than women.

23.1 How Hypothesis Tests Are Reported in the News Determine the null hypothesis and the alternative hypothesis. Collect and summarize the data into a test statistic. Use the test statistic to determine the p-value. The result is statistically significant if the p-value is less than or equal to the level of significance.

In hypothesis testing, we quantify our uncertainty by asking whether it is likely that data came from a particular distribution. We will focus on the following common type of hypothesis testing scenario:

1a. Hypothesis test about mean (one mean value) - the test is called hypothesis test about a population mean - we're interested if the population mean is equal to a specific value which is known (a constant) - notation (H0): µ=µ0. o if the population parameters are known ( µ,σ2,σ) we use the formula (1) to calculate the test statistic ...

9 Hypothesis Tests. (Ch 9.1-9.3, 9.5-9.9) Statistical hypothesis: a claim about the value of a parameter or population characteristic. Examples: H: μ = 75 cents, where μ is the true population average of daily per-student candy+soda expenses in US high schools. H: p < .10, where p is the population proportion of defective helmets for a given ...

4 Hypothesis Testing Rather than looking at con dence intervals associated with model parameters, we might formulate a question associated with the data in terms of a hypothesis. In particular, we have a so-called null hypothesis which refers to some basic premise which to we will adhere unless evidence from the data causes us to abandon it.

Hypothesis testing is formulated in terms of two hypotheses: H0: the null hypothesis; H1: the alternate hypothesis. The hypothesis we want to test is if H1 is \likely" true. So, there are two possible outcomes: Reject H0 and accept H1 because of su the sample in favor or H1; cient evidence in.

In this module, we review the basics of hypothesis testing. We shall develop the binomial distribution formulas, show how they lead to some important sampling distributions, and then investigate the key principles of hypothesis testing. binomial process is characterized by the following: binomial process is characterized by the following:

Using a confidence interval for hypothesis testing might be insufficient in some cases since it gives a yes/no (reject/don't reject) answer, as opposed to quantifying our decision with a probability. Formal hypothesis testing allows us to report a probability along with our decision. Confidence intervals. Hypothesis testing.

Hypothesis Testing. The intent of hypothesis testing is formally examine two opposing conjectures (hypotheses), H0 and HA. These two hypotheses are mutually exclusive and exhaustive so that one is true to the exclusion of the other. We accumulate evidence - collect and analyze sample information - for the purpose of determining which of the two ...

Hypothesis Testing and Confidence Intervals Learning Objectives Test a hypothesis about a regression coefficient Form a confidence interval around a regression coefficient Show how the central limit theorem allows econometricians to ignore assumption CR4 in large samples Present results from a regression model

Steps in Hypothesis testing. Statement of hypothesis. Identification of the test statistic and its distribution. Specification of the significance level. Statement of the decision rule. Collection of the data and performance of the calculations. Making the statistical decision. Drawing a conclusion.

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.

Statistics: Hypothesis Testing A hypothesis is a claim made about a population. A hypothesis test uses sample data to test the validity of the claim. This handout will define the basic elements of hypothesis testing and provide the steps to perform hypothesis tests using the P-value method and the critical value

Why do hypothesis testing? Sample mean may be di↵erent from the population mean.

Motivation . . . The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about a parameter. Examples: Is there statistical evidence, from a random sample of potential customers, to support the hypothesis that more than 10% of the potential customers will pur ...

Hypothesis testing will rely extensively on the idea that, having a pdf, one can compute the probability of all the corresponding events. Make sure you understand this point before going ahead. We have seen that the pdf of a random variable synthesizes all the probabilities of realization of the underlying events.

All expected counts > 0. and. no more than 20% are 5 or less. df = n-1 for Goodness of. Fit test. df = (r-1)(c-1) for Test of Association. *. Note that it is common to all tests that we require the sample to be an SRS. Definition of Symbols Used.

Hypothesis Testing One type of statistical inference, estimation, was discussed in Chapter 5.

Summary of hypothesis tests page 30 This gives, in chart form, a layout of the commonly-used statistical hypothesis tests.

How Does Hypothesis Testing Improve Products & Processes? Hypothesis testing can be used in business operations as well. Tests can help identify diferences between machines, formulas, raw materials, medications, etc. Without such testing, employees may change the product or process causing more variation.