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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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Example 3: Public Opinion About President Step 1. Determine the null and alternative hypotheses. Null hypothesis: There is no clear winning opinion on this issue; the proportions who would answer yes or no are each 0.50. Alternative hypothesis: Fewer than 0.50, or 50%, of the population would answer yes to this question.
Hypothesis testing or significance testing is a method for 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 likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true.
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.
Case1: Population is normally or approximately normally distributed with known or unknown variance (sample size n may be small or large), Case 2: Population is not normal with known or unknown variance (n is large i.e. n≥30). 3.Hypothesis: we have three cases. Case I : H0: μ=μ0 HA: μ μ0. e.g. we want to test that the population mean is ...
3 Components*of*a*Hypothesis*Test 1. Formulatethe*hypothesistobetested. 2. Determine*the*appropriate*test*statistic*and* calculateit using*the*sample*data. 3 ...
hypothesis if the computed test statistic is less than -1.96 or more than 1.96 P(Z # a) = α, i.e., F(a) = α for a one-tailed alternative that involves a < sign. Note that a is a negative number. H0: p = .5 HA: p < .5 Reject the null hypothesis if the computed test statistic is less than -1.65 Introduction to Hypothesis Testing - Page 5
March 24, 2013. In this lecture note, we discuss the fundamentals of statistical hypothesis tests. Any statistical hypothesis test, no matter how complex it is, is based on the following logic of stochastic proof by contradiction. In mathematics, proof by contradiction is a proof technique where we begin by assuming the validity of a hypothesis ...
Instead, hypothesis testing concerns on how to use a random sample to judge if it is evidence that supports or not the hypothesis. 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:
A second type of statistical inference 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) about parameter is correct. We will look at hypothesis tests for proportion,
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 hypotheses is true ...
STEPS IN HYPOTHESIS TESTING. Step 1: State the Hypotheses. Null Hypothesis (H0) in the general population there is no change, no difference, or no relationship; the independent variable will have no effect on the dependent variable. Example.
Calculating SSR. Population mean: y. Independent variable (x) The Sum of Squares Regression (SSR) is the sum of the squared differences between the prediction for each observation and the population mean. Regression Formulas. The Total Sum of Squares (SST) is equal to SSR + SSE. Mathematically,
Hypothesis testing (or test of significance) is a procedure, based on a sample evidence and probability, used to test claims regarding a characteristic of one or ... Example 6: The p-value for a hypothesis test is P-value = 0.0237. What is your decision if the level of significance is a) = 0.05 and b) = 0.01?
Hypothesis Testing Steps Objectives In this chapter, you learn: (Slide 9) ⚫ The basic principles of hypothesis testing ⚫ How to use hypothesis testing to test a mean or proportion ⚫ The assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are seriously violated ⚫ Define Type I and Type II ...
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.
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. t test examples page 4 Here are some examples of the very widely used t test. The t test through Minitab page 8 This shows an example of a two-sample problem, as performed ...
Understand the nature of a hypothesis test, the difference between one-tailed and two-tailed tests, and the terms null hypothesis, alternative hypothesis, signi cance level, rejection region (or critical region), ... and he examines the records of a random sample of 95 of these students. The number of drop-outs was found to be 20. Test the Dean ...
Chapter 8 Stat 4570/5570. Material from Devore's book (Ed 8), and Cengage. A statistical hypothesis: a claim about the value of a parameter, population characteristic (could be a combination of parameters), or about the form of an entire probability distribution. Examples:
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.
1. INTRODUCTION. This review highlights many current approaches to hypothesis testing in the econometrics literature. We consider the general problem of testing in the classical Neyman-Pearson framework, reviewing the key concepts in Section 2. As such, optimality is defined via the power function.
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: I The data Y come from some distribution f(Yj ), with parameter . I There are two possibilities for : either = 0, or 6= 0.
A sample of 100 private sector workers reveals an average output of 74.3 parts per hour with a sample standard deviation of 16 parts per hour. A sample of 100 state ... This question is asking for a hypothesis test of the equality of two means in the setting of paired data. The data are paired because each participant was measured on two ...