Is there a non-parametric alternative for a multi-factorial repeated measures ANOVA (between AND within subject design) ?

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Jos Feys

There are indeed nonparametric alternatives. The nparLD R package and SAS macro (sse attachments).

You could also use the ARTool: http://depts.washington.edu/madlab/proj/art/ The authors claim it can be used with repeated measures, but I am not sure they are wright.

Mehmet Sinan Iyisoy

GLMM is also applicable.

Bear in mind that you have a mixed ANOVA case, so your proposed method might not be applicable because it seems applicable to a factorial ANOVA.

Try nparLD package Jos proposed.

Martin Schmettow

When data is non-normal that does not mean you have to resort to a crappy nonparametric procedure. The familiy of Generalized Linear (Multilevel) Models offers all you need for basically any type of response variable. Read more about it in my book (chapter 7):

https://www.researchgate.net/project/Book-New-statistics-for-the-design-researcher