Hi everyone!
With 3 different intervention groups (control, treatment1, treatment2) and measures of stress taken at the continuous level at 3 time points (baseline, 3months, 6month) how can I analyse this data using a non-parametric test?
I was going to run a mixed ANOVA but there is a violation of the normality of distribution on the DV.
Thanks in advance, Natalie
First of all: it is not the data that has to be normally distributed, but the errors of the model and/or the sampling distribution (where you can't test the latter directly). So you should check the distribution of your residuals for normality. For the sampling distribution you can make a reasonable guess that if the data is normally distributed that this is also true for the sampling distribution, BUT this does not guarantee it (and vice versa). Additionally, if you want to check it, you have to do it for each group/condition separately, not overall.
If you really doubt the normality assumption, I would check the data for possible reasons (e.g. outliers) and look for an appropriate remedy instead of directly switching to 'non-parametric' alternatives, there are a lot of parametric alternatives availabe (e.g. trimmed means). But have a look at the phantastic books by Rand R. Wilcox (e.g. 'Introduction to robust estimation and hypothesis testing'), who provides R codes in his WRS2 package for all topics covered in his books.
Another way to tackle it is the GLMM as proposed by Salvatore to account for other distributions (other as normal) of the residuals.
A non-parametric approach is aligned-ranks. See ARTool, which can be used as an R package or as a stand-alone program (http://depts.washington.edu/madlab/proj/art/). (I have no experience with either).
You might also consider a generalized mixed model (GLMM).
First of all: it is not the data that has to be normally distributed, but the errors of the model and/or the sampling distribution (where you can't test the latter directly). So you should check the distribution of your residuals for normality. For the sampling distribution you can make a reasonable guess that if the data is normally distributed that this is also true for the sampling distribution, BUT this does not guarantee it (and vice versa). Additionally, if you want to check it, you have to do it for each group/condition separately, not overall.
If you really doubt the normality assumption, I would check the data for possible reasons (e.g. outliers) and look for an appropriate remedy instead of directly switching to 'non-parametric' alternatives, there are a lot of parametric alternatives availabe (e.g. trimmed means). But have a look at the phantastic books by Rand R. Wilcox (e.g. 'Introduction to robust estimation and hypothesis testing'), who provides R codes in his WRS2 package for all topics covered in his books.
Another way to tackle it is the GLMM as proposed by Salvatore to account for other distributions (other as normal) of the residuals.
My Dear , when I read your question not see any problem, you can run repeated mesurement design with 3 treatent and 3 responses time points (baseline, 3months, 6month) by GLM...
With Best Regards
Thank you very much for your advice! This is all very helpful and I will definitely purchase the Rand R. Wilcox book.
Best wishes from Nat
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