I have several dependant variables that are non normal in distribution: Kolmogorov-Smirnov test is significant, skewness ranges up to 8 for some variable, and kurtosis is generally about 2 but in a couple of cases raises to 12! It is a repeated-measures (RM) ANOVA model for the normally distributed variables.
A couple of questions:
- How robust is RM ANOVA to violations of normality, when there is an equal number of observations per group?
- If I use non-parametric tests, do I need to correct for multiple testing that impacts type 1 error?