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I want to interpret an interaction. Usually a conditional regression analysis is done with 1 SD below/above the mean (see Aiken & West, 1993, p. 18). My result is a contrast with $p=.068$ if I take 1.5 SDs $p=.044$. with 2 SDs $p=.033$.

It seems that contrasts get stronger by increasing values the number of SDs. Thus, is it appropriate to report contrasts for 2 SDs in a paper? Why does it have to be 1 SDs?

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I think this post reveals that you are a bit too focused on the p-values involved in your interaction. I recommend focusing more on the values of your focal regression coefficient (and the coefficient's interpretation) at the levels you choose (e.g., plus or minus 1 SD) of the other. There are many reasons why focusing too narrowly on p-values can be misleading, especially when it comes to the interpretations of simple effects. – Patrick S. Forscher Sep 19 '12 at 2:19

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The interaction term in a moderated regression is either significant or it's not. When it comes to simple slopes, however, you can test whether each single simple slope differs significantly from zero. These significance tests are dependent on which value of the moderator you probe the slope.

Using +/- 1 SD simply is just a convention - but it makes sense. It shows the slopes of two hypothetical groups, one 1 SD below the mean (which equals a percentage rank of 16% under the assumption of normality) and one 1 SD above the mean (PR = 84%). If you take 2 SD it would characterize groups at PR = 2% and 98% - these are rather extreme values and do not characterize a typical member of the sample.

So I would say it is not OK to use 2 SD, unless you have a good argument why you want to show simple slopes for very extreme groups.

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Good point, the fact that it would concern a very small proportion of the population. And indeed, if ± 2 SD yields smaller p-values than ± 1 SD, why stop there... – Patrick Coulombe May 17 at 2:18

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