I have a pre-post dataset with 2 observations per subject (propotion data -bounded between 0 and 1-).

I have analyzed the data with a classical dependent t-test under the NHST paradigm. However, as data does not follow normality and I have a relatively small sample size (i.e., 10 subjects), the p-value may be unreliable. In the NHST framework it is typical conducting a Wilcoxon test afterwards in order to compare both distributions.

However, I want to conduct the analysis with Bayesian statistics due to its simple interpretation (i.e., in probability terms). Is there any equivalent to the Wilcoxon test (or in general non-parametric statistical tests) in Bayesian statistics?

  • $\begingroup$ Is this "before and after" data? $\endgroup$ – Dave Harris Feb 15 '18 at 17:36
  • $\begingroup$ Yes it is a within subjects experiment $\endgroup$ – Adrian Santos Feb 15 '18 at 18:09
  • $\begingroup$ Is there a reason you do not believe it to be normal? With such a small sample size, you shouldn't be able to tell from the data. $\endgroup$ – Dave Harris Feb 15 '18 at 22:03
  • $\begingroup$ There is such a thing. See Ferguson (1973) "A Bayesian analysis of some nonparametric problems" in The Annals of Statistics. He introduces the Dirichlet Process. If you're not familiar with this stuff, it probably won't be helpful. Unfortunately I don't have time right now to provide an answer that would illustrate what to do. $\endgroup$ – mef Feb 16 '18 at 1:21
  • $\begingroup$ proceedings.mlr.press/v32/benavoli14.pdf $\endgroup$ – kjetil b halvorsen Apr 25 '18 at 17:58

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