When doing ANCOVAs, software usually gives both unadjusted means as well as adjusted means. However, the post hoc tests for most statistical programs are limited to unadjusted means. Yet, sometimes, if one is doing an ANCOVA, post hoc comparisons of adjusted means is what is desired, not the unadjusted comparisons. Or am I mistaken – should post hoc tests of adjusted means be avoided for some reason?
Post hoc tests for adjusted means have been around for quite some time, such as the GT2 method of Hochberg (1974). A modified version of the GT2 test appears in Sokal and Rohlf's Biometry (1981 2nd edition, and presumably in newer versions) specifically for adjusted means. There is also the T-method (Spjotvoll and Stoline 1973), also modified in Sokal and Rohlf (1981) for comparing adjusted means.
Why then do statistical programs not give post hoc tests for adjusted means, if one wants to know which treatment (A vs B, A vs C, etc) differ, after removing some of the variance of the covariate?
Hochberg, Y. 1974. Some Conservative Generalizations of the T-Method in Simultaneous Inference. Journal of Multivariate Analysis, 4:224 -234.
Spjotvoll, E, Stoline, MR. 1973. An extension of the T-method of multiple comparison to include the cases with unequal sample sizes. J Am Stat Assoc. 68:976-978.