My current experimental design involves several factors (e.g. Treatment, Enclosure, Night and Round), and involving all of them in a multi-factorial ANOVA would result in a large number of interactions. Should I conduct some one-way ANOVA first to drop some unsignificant factors prior to the multi-factorial ANOVA? Is it reasonable to restrict the interactions to two-ways? Many thanks for your attention.
Hi Ling-Ying Shuai
The trouble with dropping factors with 1-way ANOVAs is that these factors may not be relevant by themselves but may become relevant when combined with other variables in a multi-way ANOVA. If such is the case, this is a an important result in itself.
My suggestion is to fit a multi-way ANOVA, make sure its assumptions are satisfied, test for significance, remove all the non-significant factors and the non-significant interactions, create interaction plots for the remaining significant interactions (examples here: https://statisticsbyjim.com/regression/interaction-effects/), and finally apply pair-wise tests without p-value adjustment (justification here: Article No Adjustments Are Needed for Multiple Comparisons
).
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