On Thu, Sep 20, 2012 at 5:46 AM, Mohamed Radhouane Aniba <arad...@gmail.com> wrote: > Hello All, > > I am writing to ask your opinion on how to interpret this case. I have two > vectors "a" and "b" that I am trying to compare. > > The wilcoxon test is giving me a pvalue of 5.139217e-303 of a over b with the > alternative "greater". Now if I make a summary on each of them I have the > following > >> summary(a) > Min. 1st Qu. Median Mean 3rd Qu. Max. > 0.0000000 0.0001411 0.0002381 0.0002671 0.0003623 0.0012910 >> summary(c) > Min. 1st Qu. Median Mean 3rd Qu. Max. > 0.0000000 0.0000000 0.0000000 0.0004947 0.0002972 1.0000000 > > The mean ratio is then around 0.5399031 which naively goes in opposite > direction of the wilcoxon test ( I was expecting to find a ratio >> 1) >
There's nothing conceptually strange about the Wilcoxon test showing a difference in the opposite direction to the difference in means. It's probably easiest to think about this in terms of the Mann-Whitney version of the same test, which is based on the proportion of pairs of one observation from each group where the `a' observation is higher. Your 'c' vector has a lot more zeros, so a randomly chosen observation from 'c' is likely to be smaller than one from 'a', but the non-zero observations seem to be larger, so the mean of 'c' is higher. The Wilcoxon test probably isn't very useful in a setting like this, since its results really make sense only under 'stochastic ordering', where the shift is in the same direction across the whole distribution. -thomas -- Thomas Lumley Professor of Biostatistics University of Auckland ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
