No, it is not distribution free. Independent random sampling is assumed. That is a non-trivial assumption, and one that is very often not true or not strictly true.
John Maindonald email: john.maindon...@anu.edu.au<mailto:john.maindon...@anu.edu.au> On 21/03/2021, at 00:00, r-help-requ...@r-project.org<mailto:r-help-requ...@r-project.org> wrote: From: Jiefei Wang <szwj...@gmail.com<mailto:szwj...@gmail.com>> Subject: Re: [R] about a p-value < 2.2e-16 Date: 20 March 2021 at 04:41:33 NZDT To: Spencer Graves <spencer.gra...@effectivedefense.org<mailto:spencer.gra...@effectivedefense.org>> Cc: Bogdan Tanasa <tan...@gmail.com<mailto:tan...@gmail.com>>, Vivek Das <vd4mm...@gmail.com<mailto:vd4mm...@gmail.com>>, r-help <r-help@r-project.org<mailto:r-help@r-project.org>> Hi Spencer, Thanks for your test results, I do not know the answer as I haven't used wilcox.test for many years. I do not know if it is possible to compute the exact distribution of the Wilcoxon rank sum statistic, but I think it is very likely, as the document of `Wilcoxon` says: This distribution is obtained as follows. Let x and y be two random, independent samples of size m and n. Then the Wilcoxon rank sum statistic is the number of all pairs (x[i], y[j]) for which y[j] is not greater than x[i]. This statistic takes values between 0 and m * n, and its mean and variance are m * n / 2 and m * n * (m + n + 1) / 12, respectively. As a nice feature of the non-parametric statistic, it is usually distribution-free so you can pick any distribution you like to compute the same statistic. I wonder if this is the case, but I might be wrong. Cheers, Jiefei [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
