Question

When an ANOVA comparing the means of 3 groups indicates that at least one group is different from the others, a common follow-up analysis to determine which group(s) is (are) different is pairwise two-sample t-tests each assessed using

a. a pooled standard deviation based on the ANOVA MSE when calculating the standard error for the differences in means.
b. a Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5%

Is this true?

Answer 1

a. True.

b. True.

Explanation:

(a) A pooled standard deviation based on the ANOVA MSE when calculating the standard error for the differences in means - True.

The pooled standard deviation is used to compute the standard error of the difference used to compute multiple comparison tests.

(b) A Bonferonni-corrected alpha level of 0.0167 to control the type I error rate for the overall inference to 5% - True.

In statistics, one of the several methods used to counteract the problem of multiple comparisons is the Bonferroni correction.

Bonferroni correction = α/m

Where α = significance level

m = number of groups (here, it is 3) .

So,

Bonferroni correction = 0.05 /29100 = 0.0167.