Question

10) If we have homogeneity of variances and equal group sizes, why might we decide to use a R-E-G-W-Q post hoc instead of a Bonferroni post hoc? (Note: Think Type I/Type II error)

Answer 1

1. R-E-G-W-Q post hoc- is used because of good power and tight control over the type-I error rate.

Bonferroni-adjusted multiple t-tests(Dunn)- lacks power due to the fact that it assumes null hypothesis is true for all the tests in consideration

regwq is used if all pair wise comparisons of the means are to be tested, but confidence intervals are not required. When all pairs of means are compared, this procedure is probably best . This method is used for unplanned multiple comparisons.

2.  it appears to be the most powerful test generally available that still keeps the familywise error rate at alpha.

3.  if you are going to run only a few pair-wise comparisons, the critical values for the Holm-modified Bonferroni test may be smaller than the critical values for the REGWQ. In that case, go with the modified Bonferroni.

On the other hand, you may discover that even though you do not wish to make all possible pairwise comparisons, the REGWQ (or the Tukey) gives smaller critical values than the modified Bonferroni, in which case you would waste power to go with the Bonferroni. The important point is that these decisions have to be based on a consideration of the critical values, and not the final results.

4.