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JOURNAL OF CONSUMER PSYCHOLOGY 10 1 2 5 35 Copyright 2001 Lawrence Erlbaum Associates Inc ANALYS IS OF VARIANC E Analysis of Variance I A CAN I TEST FOR SIMPLE EFFECTS IN THE PRESENCE OF AN INSIGNIFICANT INTERACTION On more than a few occasions I have encountered the situation in which a hypothesized two way interaction was not significant according to the analysis of variance ANOVA and yet simple effects tests yielded results consistent with the expected interaction e g a significant simple effect in one condition but an insignificant simple effect in the other condition What can account for this apparent inconsistency Moreover if an interaction is hypothesized is it appropriate to proceed with the simple effects tests even though the interaction term fails to achieve significance in the ANOVA I have seen this done in published articles and believe that it is appropriate when a priori expectations exist but I have also heard others including reviewers argue that simple effects tests are appropriate only if the ANOVA interaction term is significant Editor I see two elements in this question namely a Why might a simple effect be significant when the overall interaction was not and b Must the overall interaction be significant to conduct tests of the simple effects To answer to the first question consider the apparent interaction depicted in Figure 1 One s MSerror term may be large enough that the interaction would not be significant The simple effect of Factor A at Level b 1 may also be insignificant However a test of the simple effect of Factor A at Level b 2 could be significant In the assessment of the overall interaction which is after all an aggregate of these components the significant simple effect may be washed out by the insignificant one It would be a superiorly clean result if both simple effects were significant for example either a qualitative difference in that the slopes were going in opposite directions or a quantitative difference with both slopes

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