# What if an overall ANOVA is not significant, but specific contrasts are?

Study Design: I have a 2x3 factorial design, 2 levels of Time (2050 or 2100) by 3 levels of information (None/Control, Moderate, Extreme).

I set up some very specific contrasts when analyzing this design, in particular Control vs. Other, Moderate vs. Extreme, and 2050 vs. 2100. For one DV, the overall ANOVA was not significant but the Control vs. Other contrast was.

Question: What is the best way to interpret a nonsignificant ANOVA but a significant contrast?

I know that ANOVA is used to lower familywise error rates, and I wouldn't want to fall into the trap of ignoring the overall ANOVA for pairwise comparisons. However, this is one of a select few contrasts that I planned ahead of time. Does that make a difference in interpretation, or should I simply consider the manipulation not significant?

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There are a lot of posts on this site that ask, essentially, this same question. Here is one example: possible duplicate of How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure? –  Macro Jun 8 '12 at 1:59
Good catch, Macro. The present question, however, appears to focus on a different aspect of this issue: interpretation. Given that the replies to the duplicate do not appear to address this at all, I am reluctant to vote to close. –  whuber Jun 8 '12 at 12:51
Also, the question you suggest as a duplicate is something of an "opposite" -- it asks what to do when ANOVA is significant but post-hocs are not. In this case I was asking how to interpret it when the ANOVA is non-significant but the post-hocs are. –  Lee Jun 15 '12 at 20:59

Yes you need to adjust alpha, especially if you do planned comparisons that are non-orthogonal. If you have set the contrasts in an ANOVA and tested the orthogonality between them, you can descompose the SC and df of the ANOVA. The planned comparison are always more powerful than traditional post hoc test, but in cases where the contrast are non.orthogonal you have inflated the experimentwise error. you can check for orthogonality among contrast in many textboxs. However i don´t undestand if you have set that time was factor with two levels, why are you performing a contrast between those times?

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