Let's assume one has an analysis in which there are multiple correlated DVs (average correlation .46) being examined in separate univariate analyses (e.g. t-tests; insufficient df and frustration tolerance to restructure the data fro a MANOVA) in relation to a single IV. All except one of these DVs is not significantly affected by an IV manipulation.
I was thinking that in general, dependence between DVs would tend to globally trend analyses to be significant or non-significant. However, when a DV with a legitimate effect is correlated with a variable which has no effect, wouldn't that correlation represent an association between them which is a source of error variance in the DV with the legitimate effect? Thus, if anything, the presence of significance in a DV associated with non-significant DVs should be taken as a sign of a true effect on that DV?
- What, if anything, do the non-significant tests tells us about the one that is significant?
- Is there a relationship between this question and the notion of suppressor variables in regression?