Steps in Statistical Hypothesis Testing
Step 1: State the null hypothesis, H0, and the alternative hypothesis, Ha. The alternative hypothesis represents what the researcher is trying to prove. The null hypothesis represents the negation of what the researcher is trying to prove. (In a criminal trial in the American justice system, the null hypothesis is that the defendant is innocent; the alternative is that the defendant is guilty; either the jury rejects the null hypothesis if they find that the prosecution has presented convincing evidence, or the jury fails to reject the null hypothesis if they find that the prosecution has not presented convincing evidence).
Step 2: State the size(s) of the sample(s). This represents the amount of evidence that is being used to make a decision. State the significance level, , for the test. The significance level is the probability of making a Type I error. A Type I error is a decision in favor of the alternative hypothesis when, in fact, the null hypothesis is true. A Type II error is a decision to fail to reject the null hypothesis when, in fact, the null hypothesis is false.
Step 3: State the test statistic that will be used to conduct the hypothesis test (the appropriate test statistics for the different kinds of hypothesis tests are given in the tables on the reverse side of this handout). The following statement must appear in this step: “The test statistic is ______, which under H0 has a ______probability distribution (with _____ degrees of freedom).”
Step 4: Find the rejection region of the test, using the form of the alternative hypothesis from Step 1, the value of from Step 2, and the distribution of the test statistic from Step 3.
Step 5: Choose the random sample(s) from the population(s). Calculate the value of the test statistic, and the p-value for the test, using the gathered data.
Step 6:
Compare the calculated p-value to the chosen level of significance. If the p-value is less than , then the null hypothesis will be rejected, and the alternative hypothesis will be affirmed. If the p-value is greater than , the null hypothesis will not be rejected.
If the decision is to reject H0, the statement of the conclusion should read as follows: “We reject H0 at the _____ level of significance. There is sufficient evidence to conclude that (statement of the alternative hypothesis).”
If the decision is to fail to reject H0, the statement of the conclusion should read as follows: “We fail to reject H0 at the_____ level of significance. There is not sufficient evidence to conclude that (statement of the alternative hypothesis).”1
1 Note: It is not correct to say that we accept the null hypothesis, or that we conclude that the null hypothesis is true. We never attempt to prove a null hypothesis. We either disprove it, or we fail to disprove it.