Yesterday, I ran a repeated-measures ANCOVA. The purpose was to determine the usability of two computer systems, call them 1 and 2. Each subject completed three (conceptually different) tasks, call them A B and C, on each system. (The covariate was whether the subject had prior experience with the current system, system 1). The dependent variable was time taken to complete each task.

A GLM in SPSS prints out both the standard and multivariate results. The standard, within-subjects results indicated a main effect of system and an interaction of system*task. Now why would I need to use the multivariate results? They were significant as well, and I've heard multivariate tests have more power. But this seems to provide too much wiggle room for researchers-- if the within subjects test isn't significant, they can just look to see if the multivariate results are significant.

Also, since there was an interaction system*task, I ran simple main effects on each task. Turned out, A and B were significant in one direction, C was significant in the other. This seems to suggest to me that doing a MANOVA is a bad idea here. But how would I even know that if I was only looking at the multivariate results?

In short, I guess I just don't understand when to use MANOVA vs ANOVA if I have more than one DV.