I recently read the article "Is It Really Robust?" (Schmider, E., Ziegler M., Danay, E., Beyer, L. & Bühner M., 2010)
The authors of the article come to the conclusion that an ANOVA is quite robust against violations of the normality assumption.
However the study focusses on one-way ANOVAs. I would like to know if these findings can be generalized on a two-way repeated measures ANOVA?
References to peer-reviewed articles are highly appreciated!
Schmider, E., Ziegler M., Danay, E., Beyer, L. & Bühner M. (2010). Is It Really Robust?.Methodology, 6 (4), 147 – 151.
Unfortunately, the methodology used by the Schmidler et al paper is seriously flawed*, so their results are questionable even for the one-way, fixed-effect design they studied.
*Specifically, to simulate Type I or Type II error using a Monte Carlo simulation, one needs to use all samples that were generated by the Monte Carlo process. Just using the 10% selected by some nonrandom selection method does not give a simulation of the sampling distribution for the test statistic; however, it is this sampling distribution that needs to be simulated.