sure, there is a method published in:

Noguchi, K., Gel, Y., Brunner, E. , Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software 50, Iss. 12.

The theory is described in:

Brunner, E. and Puri, M.L. (2001). Nonparametric Methods in Factorial Designs. Statistical Papers 42, 1-52.

If you send me an e-mail then I can send you the papers.

e-mail:  [email protected]

Data distribution is not necessarily to be normal. Do you have ordinal or discrete data? RM-ANOVA is a very restricted analysis which depends on sphericity which is hardly satisfied. Instead, I recommend mixed effects models.

The Friedman test is the equivalent of rm-ANOVA when the assumption of normality is not met.

This question is asked here very frequently; if you search the forums here, or Google, you will find lots of responses.

Since Friedman test is often criticized, you can also follow below approach. However, it still depends on the answer to question: if your data is seriously violating assumptions? You can find a lot of useful informations on this kind of models in:

Zuur et al. 2009. Mixed effects models and extensions in ecology with R.

https://www.r-bloggers.com/beware-the-friedman-test/

The Friedman test (and Quade) is not in general the equivalent of repeated measures anova.

It handles only unreplicated complete block design.

It this case, if you have multiple rats, multiple groups, and multiple times, there's no way to get the data into the Friedman test.

*     *      *

To reiterate points made by Mehmet:

One consideration:  Is the dependent variable really a continuous measurement variable?   That is, if it's really count, ordinal, proportion, etc., there are more appropriate models to use, that may get you out of the non-normal residuals problem.

Also: You want to be looking at the distribution of the residuals of the analysis, not the raw data.

sure, there is a method published in:

Noguchi, K., Gel, Y., Brunner, E. , Konietschke, F. (2012). nparLD: An R Software Package for the Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Journal of Statistical Software 50, Iss. 12.

The theory is described in:

Brunner, E. and Puri, M.L. (2001). Nonparametric Methods in Factorial Designs. Statistical Papers 42, 1-52.

If you send me an e-mail then I can send you the papers.

e-mail:  [email protected]

Thanks for your suggestion Edgar Brunner,

Fast, easy and really useful R package.