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Interaction, no main effect

I am reviewing a scenario where I have two factors (insecticide, herbicide) each with two levels (absent, present). There is no main effect for insecticide or herbicide, but there is a cross-over interaction.

Let say I'm using Tukeys-HSD post-hoc test - with 4 means this would normally result in 6 pairwise comparisons with the corresponding p-value adjustment. In the case that I've outlined where there is no main effect but a significant cross-over interaction, should or would the number of post-hoc tests be reduced as only 4 comparisons have any potential significance?

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    $\begingroup$ Would you in reality ever know for sure that there can't be a main effect (in a situation in which there may well be interaction)? I doubt that, but you need to assume such knowledge (rather than just finding main effects insignificant) in order to reduce the number of comparisons. $\endgroup$ Commented Nov 30, 2024 at 12:26

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