Hypothesis Testing in Multiple Comparisons
A researcher is investigating the effectiveness of three different teaching methods on student performance. The study involves comparing the mean test scores across these methods using hypothesis tests (t-tests or z-tests, as appropriate). (a) Formulate at least three pairs of hypotheses (null and alternative) that could be used to compare these methods. Include a brief […]
Controlling Type I Error Inflation with Multiple Comparisons
A clinical trial is conducted to evaluate the effectiveness of four different drugs compared to a placebo using independent two-sample t-tests. Since four comparisons are performed, the overall Type I error rate is inflated beyond the nominal level of 0.05. Answer the following questions: (a) Explain how performing multiple comparisons in this trial inflates the […]
Evaluating Familywise Error Inflation
Consider an experiment conducting 10 independent T or Z tests, each at a significance level of 0.05. Explain why the overall probability of making at least one type I error (the familywise error rate) increases with the number of tests. Additionally, describe one method to control this error inflation.