Question

4. Assume a researcher wishes to compare student mathematics performance on a standardized test among three 6th grade teachers: Ms. White, Ms. Jones, and Ms. Griffin. The researcher will use ANOVA to first determine if there are differences in mean mathematics scores among the three teachers, and if there are significant differences, then the researcher will perform multiple comparisons to examine the following pairwise comparisons:
Pairwise comparisons of Mean Mathematics Scores
i. Ms. White vs. Ms. Jones
ii. Ms. White vs. Ms. Griffin
iii. Ms. Jones vs. Ms. Griffin
a. Suppose the ANOVA results indicated significant mean differences in mathematics scores among the three teachers. Next the researcher must conduct pairwise comparisons. The researcher sets the overall Type 1 error rate to α = .10 due to the small sample sizes of students within each class. Using the Type 1 error rate of α = .10 for each pairwise comparison, what would be the inflated familywise error rate for the three pairwise comparisons for this unadjusted α of .10? That is, what would be probability of committing at least one Type 1 error across the family of tests for these pairwise comparisons if the per comparison α is .10? (2 points)
b. Lastly, suppose the researcher finds the familywise error rate calculated in “a” above to be too large for comfort and decides to use the Bonferroni correction for the pairwise comparisons. If the overall familywise α = .10, what would be the per comparison Bonferroni corrected α for each pairwise comparison? (2 points)

Answer 1

a.

There would be ³C₂ = 3 possible pairwise comparisons of Mean Mathematics Scores

Probability of committing at least one Type 1 error = 1 - Probability of committing no Type 1 error in three comparisons

= 1 - (1 - 0.1)³

= 0.271

b.

Using Bonferroni correction for the three pairwise comparisons,  Bonferroni corrected α for each pairwise comparison

= 0.10 / 3

= 0.0333