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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

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 Examples

Related Papers

Hedyan Poetra

Siddharth Agrawal

8-1 We must deal with uncertainty in our decisions because we rarely know the values for population characteristics. In addition, there are other circumstances unknown to us in any given situation. Statistical analysis can reduce uncertainty, but not eliminate it entirely. 8-2 Theoretically, one could toss a coin a large number of times and see if the proportion of heads was very different from 5. Similarly by recording the outcomes of many dice rolls, one could see if the proportion of each side was very different from 1/6. You would need a large number of trials for each of these samples. 8-3 Yes, it is possible that a false hypothesis will be accepted. If the observed value does not differ enough from the hypothesized one, the hypothesis will be accepted. Acceptance of a hypothesis is based on probability and therefore we can never be absolutely certain that our decision is correct. 8-4 a) Assume hypothesis about population b) Collect sample data c) Calculate a sample statistic d) Use sample statistic (c) to evaluate hypothesis (a) e) Take decision. 8-5 There is always a statistical possibility that a sample does not accurately represent the population from which it has been drawn. 8-6 We mean that we would not have reasonably expected to find that particular sample if in fact the hypothesis had been true. 8-7 The level of probability, or certainty, depends upon how accurate our answer needs to be. 8-8 P(z 1.75) = 2(.5-.4599) =.0802 8-9 The z value which leaves (100-98)% = 2% in the tails is ± 2.33, so the interval should be the hypothesized value ± 2.33 standard errors.

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We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. The focus will be on conditions for using each test, the hypothesis tested by each test, and the appropriate (and inappropriate) ways of using each test. We conclude by summarizing the different tests (what conditions must be met to use them, what the test statistic is, and what the critical region is).

BOHR Publishers

BOHR International Journal of Operations Management Research and Practices (BIJOMRP)

Many researchers and beginners in social research have several dilemmas and confusion in their mind about hypothesis statement and statistical testing of hypotheses. A distinction between the research hypothesis and statistical hypotheses, and understanding the limitations of the historically used null hypothesis statistical testing, is useful in clarifying these doubts. This article presents some data from the published research articles to support the view that the is format as well as the will format is appropriate to stating hypotheses. The article presents a social research framework to present the research hypothesis and statistical hypotheses is proper perspective.

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In this paper problem of testing of hypothesis is discussed when the samples have been drawn from normal distribution. The study of hypothesis testing is also extended to Baye’s set up.

ForsChem Research Reports

Hugo Hernandez

There are two very important steps in hypothesis testing that are commonly undervalued: Selecting the sample size and choosing the significance level. A minimum sample size can be obtained based on power analysis, but this method requires previously choosing the significance level. The significance level has been classically considered to be 5% (following the initial suggestion provided by Ronald Fisher) and while other typical values are sometimes employed (e.g. 10%, 1%, 0.1%) many practitioners of hypothesis testing do not have a clear, objective criterion for choosing this value. Considering that the significance level has a direct influence on the conclusion of the test, it should not be chosen using subjective methods. In this direction, a new approach for determining the optimal sample size and optimal significance level during hypothesis testing is presented. The focus in the first of a series of reports about this topic is discussing the tests of means: The Z-test and Student’s T-test. The optimization of the tests is done considering a desired Cohen resolution, which can be obtained from the particular problem conditions or by using default values based on the minimum viability of each test. The optimal sample size can be found by solving an economical optimization problem, involving the ratio between the cost of an erroneous decision and the cost of an individual observation. When this cost ratio is not available, a maximum tolerable test error can be used for optimizing the sample size. Once the sample size has been defined, the optimal significance level is found by minimizing the total test error, including both type I and type II errors. The hypothesis tests are then performed as usual. In order to simplify the interpretation of the tests, a decision value (D-value) is proposed. Positive D-values represent a positive decision (rejecting the null hypothesis), and negative D-values represent a negative decision (not rejecting the null hypothesis). D-values within a critical threshold around zero are considered inconclusive. Decisions based on D-values are shown to be less fluctuating than those based on P-values, and therefore, the former can lead to more reliable conclusions.

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