(This article was first published on The 20% Statistician, and kindly contributed to R-bloggers) In a 2X2X2 design, there are three main effects, three two-way interactions, and one three-way interaction to test. That’s 7 statistical tests.The probability of making at least one Type 1 error in a single ANOVA is 1-(0.95)^7=30%. There are earlier blog posts on this, but...