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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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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.
HYPOTHESIS TESTING. STEPS IN HYPOTHESIS TESTING. Step 1: State the Hypotheses. Null Hypothesis (H. 0. in the general population there is no change, no difference, or no relationship; the independent variable will have no effect on the dependent variable. o Example.
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.
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.
Chapter 5 Hypothesis Testing. Chapter 5Hypothesis TestingA second type of statistical inf. rence is hypothesis testing. Here, rather than use ei-ther a point (or interval) estimate from a random sample to approximate a population parameter, hypothesis testing uses point estimate to decide which of two hypotheses (guesses.
Steps to Hypothesis Testing Identify Population and Sample Example: Population: All GVSU students who enrolled in STA215 during WINTER 2018 Sample: 50 randomly selected students who enrolled in STA215 during WINTER 2018 State the Hypotheses in terms of population parameters Null hypothesis, usually is the opposite of our research hypothesis.
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.
The hypothesis testing framework Start with two hypotheses about the population: the null hypothesis and the alternative hypothesis Choose a sample, collect data, and analyze the data Figure out how likely it is to see data like what we got/observed, IF the null hypothesis were true
Effect size. Significance tests inform us about the likelihood of a meaningful difference between groups, but they don't always tell us the magnitude of that difference. Because any difference will become "significant" with an arbitrarily large sample, it's important to quantify the effect size that you observe.
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:
What is Hypothesis Testing? ... the use of statistical procedures to answer research questions Typical research question (generic): For hypothesis testing, research questions are statements: This is the null hypothesis (assumption of "no difference") Statistical procedures seek to reject or accept the null hypothesis (details to follow)
8-2 Basics of hypothesis testing In this section, 1st we introduce the language of hypothesis testing, then we discuss the formal process of testing a hypothesis.
Hypothesis Testing. Is also called significance testing. Tests a claim about a parameter using evidence (data in a sample. The technique is introduced by considering a one-sample z test. The procedure is broken into four steps.
Why do hypothesis testing? Sample mean may be di↵erent from the population mean.
Null hypothesis tested . H0: It is the hypothesis to be Alternative hypothesis HA : It is a statement of what we believe is true if our sample data cause us to reject the null hypothesis 7.2 Testing a hypothesis about the mean a population have the following steps:
8.1 Hypothesis Testing Logic Hypothesis testing is one of the most commonly used inferential procedures Definition: a statistical method that uses sample data to evaluate the validity of a hypothesis about a population parameter
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 method.
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.
Thepurposeofhypothesistestingistodeterminewhether 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- chase a new product?
Hypothesis Tests: Single-Sample tTests. Hypothesis test in which we compare data from one sample to a population for which we know the mean but not the standard deviation. Degrees of Freedom: The number of scores that are free to vary when estimating a population parameter from a sample df = N. 1 (for a Single-Sample.
By increasing sample size, one can increase the value of the test statistic, thus increasing probability of finding a significant effect Example: Psychology GRE scores
The logic of hypothesis testing, as compared to jury trials page 3 This simple layout shows an excellent correspondence between hypothesis testing and jury decision-making.