Results of 5000 simulations of two-ways Anova with different number of levels (2x2, 2x3, and 3x3), number of subjects per group (N = 5, 10, 20, 30, 50, or 100), and average difference between means (0, 0.1, 0.25, or 0.5).

The null hypothesis was posed as true by looking at differences between observations which have comparable true means, and a standard deviation of 1. The false positive risk represents the relative frequency (%) of either (in orange) Bonferroni-corrected pairwise comparisons based on observed means and errors were statistically significant (p<0.05) or (in green) 95% confidence intervals of the estimated marginal means overlapping for less than 25% of the full CI length.