I've tried to compare both approaches in the do-file below using the dataset
that Alan cited. The -mtest(bonferroni)- approach yields far more null
hypothesis rejections than the corresponding Bonferroni-adjusted separate
t-test approach. Such a discrepancy is surprising.
This happens in a oneway between-subjects design too. The reason the
contrast is more powerful than the independent ttest is that the contrast
uses information for MSw from all groups and is therefore more accurate.
Of course this is true only if the homogeneity of variances assumption
holds. Perhaps along the same vein, the contrasts reject the null more
than the dependent ttests because more information is used for the
estimate of error, and in this case homogeneity of differences variances
holds? The dependent ttest is sometimes preferred because you can use
information from only those means tested, which is useful when sphericity
is violated.
