I have run a psychology experiment where participants received one of three sets of instructions (between-subjects). Either they were told to approach the experiment a certain way, told to approach it a different way or it was not specified how they should approach the task (it turned out that some in this group did it one way and some the other, about 60/40).
My ANOVA on performance in the experiment is nonsignificant, but my comparison between the 2 groups which received specified instructions were significant either as a planned comparison or in an independent t-test (the effect size between the two is pretty good, Cohen's d = ~0.45). I've been taught not to interpret ANOVA comparisons unless the overall effect is significant, but it seems to me that including this middle group (the means of which tend to be between the two groups) is underpowering the ANOVA. Is it "cheating" to just compare the two groups with a t-test? It certainly doesn't seem right to conclude there is no difference between groups when the ANOVA only breaks with inclusion of this middle group.