I run an ANOVA with two factors A & B and repeated measurements. Now, I'm mostly interested in the interaction effect of the two factors A*B and would like to do some post-hoc tests in the form of pairwise comparisons.

In particular, factor A has two and factor B has six levels and I would like to check for each level of factor B whether a switch in A is statistically significant.

Using the typical formula for contrasts i would compute the following:

$t= \frac{\bar{y}_{A_1B_1\bullet} -\bar{y}_{A_2B_1\bullet}}{\sqrt{\frac{{2*MS_{error}}}{n}}} $

Here are my questions:

1.) What is n? If I have 5 subjects in both cells A1*B1 and A2*B2 and 6 measurements, n should be 30. Is this reasoning correct?

2) What is $MS_{error}$? ANOVA reports two error terms. Which one should I use? Should I pool them.

3) Ive read that it is possible to use the Holm-Bonferroni correction in such a setting. Which method would you recommend?


1 Answer 1


The Holm-Bonferroni correction is not as conservative (read harsh) as the straight up Bonferroni correction. With Bonferroni and 6 tests you'll end up needing a p value of 0.008 if you want to set your alpha at 0.05. That's pretty low depending on what type of experiment you ran. @ Henrik has an excellent and easy to understand post here about the Holm-Bonferroni correction: https://stats.stackexchange.com/a/760/49037


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