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I perfomed a 2 (groups) x 5 (emotion) repeated measures anova in SPSS. The interaction between groups x emotion is not significant, but Bonferroni post hoc comparisons of this interaction reported a significant difference (p<.0005) between the two groups for each emotion. Is it possible the case in which the interaction is not significant, while post hoc comparisons are significant? There is a mistake?

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  • $\begingroup$ So your design is within subjects regarding the emotions but between subjects regarding the groups? Are you sure these posthoc tests actually test the interaction effect? Perhaps describe in details what you are comparing in those post hoc tests. $\endgroup$ – David Ernst Nov 19 '16 at 14:05
  • $\begingroup$ Thanks for the answer. I have two groups (experimental and control group). I admenestered the same set of emotional stimuli (5 kind of emotions) for both groups. I want to know if exist a difference between the two groups in the recognition of a specific emotion. For this reason I looked the post of interaction. The post hoc comparisons are significant, but the F of fischer of the interaction emotions x groups is not significant. $\endgroup$ – Filomena S Jan 13 '17 at 10:46
  • $\begingroup$ That's not an interaction. You are only interested in 1 of the five emotions. Ignore the data from the other four. Now you have 2 groups and one output variable, that corresponds to one single t-test. $\endgroup$ – David Ernst Jan 13 '17 at 11:04
  • $\begingroup$ thanks. If I want know differences in all five emotions is the repeated anova correct? In this case, is there a mistake if F of Fisher of emotions x groups interaction isn't significant, while post hocs are significant? $\endgroup$ – Filomena S Jan 16 '17 at 7:06
  • $\begingroup$ That's still not an interaction. Interaction means that the difference between control and the other group are different depending on the 5 emotions. $\endgroup$ – David Ernst Jan 16 '17 at 15:40
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There is no mistake. Have a look at this explanation:

ANOVA tests the "exploratory value" of a predictor in a model (typically a factor with more than two levels). It answers the questions how likely we can expect a reduction in the residual variance when there was no association of the presumed predictor with the response.

Posthoc tests are apriori unspecified tests, so to say tests after seeing the data and deciding then which comparisons might be interesting. They use pooled variance estimates and control the FWER or the FDR for the family of tests. There are few special cases of posthoc tests that do not efficiently control the FWER. They need a kind of "protection" by a "significant" ANOVA. Most famous example is Fisher's LSD, but this is restricted to 3 groups. Tukey does not require any protection and it keeps the FWER.

In general, ANOVA and posthoc tests answer considerably different questions.

As a rule of thumb, if you are into NHST (null hypothesis significance testing) and didn't have prior expectations (specific contrasts set) you most likely should stop exploring the interaction after discovering it's insignificant.

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