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I want to conduct a statictical analysis on reation times(dependent) between two groups of people.

suppose the factors are: A, B, group

Is it possible for me to conducting a posthoc test(by using emmeans() function with Tukey adjustments) eventhough there is no significant interactions between each levels of factors?

and is it meaningful to test pairwise comparisons for each participant group(using the emmeans() function with Tukey adjustments)?


e.g. (only interactions specified below)

A x B p>o.5

B x group p>o.5

A x group p>o.5

A x B x group p>o.5


Thanks in advance!!

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1 Answer 1

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First, when a model has interaction terms, the "significance" of the difference from 0 of an individual-predictor coefficient or of a lower-level interaction coefficient (in your case with a 3-way interaction, any 2-way interaction coefficient) depends on how the interacting predictors are coded or centered. See this page, for example. You thus shouldn't worry about their "significance" at all.

Second, you don't even need a significant overall model to do valid pairwise comparisons, provided that you correct for the multiple comparisons. See this page, for example.

So it's certainly OK to do pairwise comparisons of scenarios in your model. The danger with multiple interactions, however, is that you end up needing to correct for a lot of multiple comparisons and thus lose power for detecting truly significant differences. Think carefully whether you want to test all pairwise differences, or if there are a few specific comparisons that are of primary interest.

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