Non-parametric alternative to Two-way repeated measures ANOVA

Hi everyone,

I have searched extensively on the forum and online for an answer to my issue but I've struggled to get a definitive answer.

My study consists of 10 subjects and is a repeated measures design. There are three conditions (high intensity exercise, low intensity exercise and control [no exercise]). I measured the concentration (continuous data) of a protein in the blood over time in each condition (pre-exercise, 0h, 1h, 2h, 4h and 7h post-exercise). Therefore, I planned to use a 3 x 6 (condition x time) repeated measures ANOVA for the statistical analysis.

However, the data are massively skewed i.e. not normally distributed so I have been looking into non-parametric alternatives. The only solution I have found being suggested is Friedman's test, however this appears to be an alternative for a one-way repeated measures ANOVA. Can anyone provide some knowledge on what test should be used?

Many thanks


Global Moderator
First of all the "data" don't need to be normally distributed. The residuals of the fitted ANOVA should be. This is a very common misconception; (Williams et al 2013). So if the RESIDUALS are skewed, only then do you have a problem.

Other than that you can see if a PERMOVA method fits your problem: Anderson 2005 -->
(which is included in the "randomization test" suggested by katxt.

More refers on this;
Pesarin, Salmaso. Permutation Tests for Complex Data (2010) and Bonnini, Corain, Marozzi, Salmaso. Nonparametric Hypothesis Testing - Rank and Permutation Methods with Applications in R (2014)
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TS Contributor
Have you tried transforming the concentration, say by logging it?
Agreed. One should not use transformations mindlessly, just to achieve normality.
But as is the case in many biological studies, maybe the outcome of interest is best
described (and interpreted) on a logarithmic scale?

With kind regards