*some*statisticians recommend that in 3-way interactions p equal to or less than .05 is acceptable but in the simple main effects and the simple simple effects it is recommended that Bonferroni correction be made such that a p value of greater than .025 is unacceptable in omnibus output. I expect that the reason for the reduction in acceptable p-value at the simple main effect and simple simple effect is to reduce the chance of a Type I error. But this would also increase the chance of Type II error.

The book did not provide specific references for this. Most texts only discuss 1-way or 2-way ANOVA, so I find this difficult to follow up. (I do report Bonferroni corrections simple simple pairwise comparisons).

I have tried a Google Scholar search on the topic without any luck. I would appreciate any leads (paper titles, authors, or alternative key words) that I could follow-up on the p-value at the level simple main effect and simple simple effects in a 3-way ANOVA analysis.

Thank you in advance.