Hello,
I have a question regarding non-parametric alternatives for a RM-ANOVA.
In my study I had two groups that were measured on two timepoints (pre-post measurements only). I was planning to conduct a repeated-measures ANOVA instead of mixed models, since I only have a pre-post test. However the data is not-normally distributed so I'm looking for a non-parametric alternative. It's suggested to use Friedman ANOVA, however this only works if you have > 2 groups. Therefore I wonder if I'm even allowed to do a RM-ANOVA.
Is it then recommended to perform mixed models instead, or is there a recommendation for a non-parametric alternative of a RM-ANOVA for 2 groups with 2 timepoints?
Thank you in advance for the suggestions!
Babak Jamshidi I think that's not possible since I only have 2 groups, right?
There are non-parametric alternatives for 2-way factorial repeated measures designs.
There is the ARTool
https://depts.washington.edu/acelab/proj/art/index.html
Brunner and his collagues offer an number of test in the npaLD SAS and R packages or procedures.
In the R script 'between_within_2x2.R at the bottom there are non-parametric tests
I think the key question is why do want to do that? How do you know how your data is distributed. Whach variables? David Booth
Hello Joëlle Janssen
I recommend the query from David Booth. How do you know your data violate assumptions for ANOVA? It is widely believed, but not true, that we check this before analysis. The assumptions for ANOVA apply to the residuals -- that they are homogeneous, normal, and independent. See for example Sokal and Rohlf 2011, 4th Edition. We have to obtain the residuals in order to evaluate the assumptions.
The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools to evaluate the residuals (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). See also (Chatfield 1998; Gelman, Pasarica & Dodhia 2002). La¨a¨ ra¨ (2009) gives several reasons for not applying preliminary tests for normality, including: most statistical techniques based on normal errors are robust against violation; for larger data sets the central limit theory implies approximate normality; for small samples the power of the tests is low; and for larger data sets the tests are sensitive to small deviations (contradicting the central limit theory).
Have a look at your residuals (residual vs fit plots, QQ plots, histograms) before giving up and using a non-parametric test, which tells us nothing about means, medians, or any other measure of central tendency.
It is unfortunate that answers contrary to the publications listed below show up as popular here on ResearchGate. When frequent testimony online conflicts with consistent advice in the refereed literature, what are we to believe? I leave the decision to you.
Suum quique,
David S.
Chatfield, C. (1998) Problem Solving: A Statistician’s Guide. Chapman & Hall, Boca Raton, FL
Draper, N.R. & Smith, H. (1998) Applied Regression Analysis, 3rd edn. John Wiley and Sons, New York
Gelman, A., Pasarica, C. & Dodhia, R. (2002) Let’s practice what we preach: turning tables into graphs in statistic research. The American Statistician, 56, 121–130.
La¨a¨ra¨, E. (2009) Statistics: reasoning on uncertainty, and the insignificance of testing null. Annales Zoologici Fennici, 46, 138–157.
Montgomery, D.C. & Peck, E.A. (1992) Introduction to Linear Regression Analysis. Wiley, New York.
Quinn, G.P. & Keough, M.J. (2002) Experimental Design and Data Analysis for Biologists. Cambridge University Press, Cambridge, UK
Zuur et al 2010 Methods in Ecology & Evolution 1: 3–14
You also might consider running an RANCOVA, i.e. a regression on the ranks of pre and post variables:
ranked_post = ranked_pre + Treatment Group (in that order)
The critical assumption for an ANCOVA is the homogeneity of slopes, i.e. that there is no interaction between the covariate 'ranked_pre' and the between factor 'Group'.
see:
https://www.discoveringstatistics.com/repository/ancova.pdf
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