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Based on the case context, explain why the psychologist must use a modified procedure like the Bonferroni procedure instead of running three separate standard -tests, and describe how this choice protects the validity of their conclusions.
Case context: A psychologist conducts a study comparing memory recall scores across three different groups: a control group, a group that practiced meditation, and a group that listened to white noise. A one-way ANOVA reveals a statistically significant main effect of the group on memory recall. The psychologist now wants to determine which specific groups differ from one another and decides to use the Bonferroni procedure.
Question: Based on the case context, explain why the psychologist must use a modified procedure like the Bonferroni procedure instead of running three separate standard -tests, and describe how this choice protects the validity of their conclusions.
Sample answer: The psychologist must use the Bonferroni procedure because running multiple standard -tests would inflate the overall probability of making a Type I error. The Bonferroni procedure is a modified -test technique designed to safely compare pairs of group means. By using it, the psychologist keeps the overall risk of mistakenly rejecting a true null hypothesis to an acceptable level, typically close to , across all three pairwise comparisons, thereby protecting the validity of their statistical conclusions.
Key points:
- Explains that running multiple standard -tests would inflate the overall probability of committing a Type I error.
- Recognizes that the Bonferroni procedure is a post hoc method used to compare pairs of group means after a significant one-way ANOVA.
- Describes how the procedure keeps the overall risk of a Type I error to an acceptable level, typically close to , across all comparisons.
Rubric: The response must explain that running multiple standard t-tests increases the overall Type I error rate. It must clarify that the Bonferroni procedure is a modified t-test that controls this overall risk, keeping the familywise Type I error rate close to 5% across all pairwise comparisons.
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Research Methods in Psychology - 4th American Edition @ KPU
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