X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fm%2Fstatistics%2Ftests%2Fwilcoxon_test.m;fp=octave_packages%2Fm%2Fstatistics%2Ftests%2Fwilcoxon_test.m;h=5e1f10cce4b6686f992faaef386cf49d452b8d7d;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/tests/wilcoxon_test.m b/octave_packages/m/statistics/tests/wilcoxon_test.m new file mode 100644 index 0000000..5e1f10c --- /dev/null +++ b/octave_packages/m/statistics/tests/wilcoxon_test.m @@ -0,0 +1,91 @@ +## Copyright (C) 1995-2012 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{pval}, @var{z}] =} wilcoxon_test (@var{x}, @var{y}, @var{alt}) +## For two matched-pair sample vectors @var{x} and @var{y}, perform a +## Wilcoxon signed-rank test of the null hypothesis PROB (@var{x} > +## @var{y}) == 1/2. Under the null, the test statistic @var{z} +## approximately follows a standard normal distribution when @var{n} > 25. +## +## @strong{Caution:} This function assumes a normal distribution for @var{z} +## and thus is invalid for @var{n} @leq{} 25. +## +## With the optional argument string @var{alt}, the alternative of +## interest can be selected. If @var{alt} is @code{"!="} or +## @code{"<>"}, the null is tested against the two-sided alternative +## PROB (@var{x} > @var{y}) != 1/2. If alt is @code{">"}, the one-sided +## alternative PROB (@var{x} > @var{y}) > 1/2 is considered. Similarly +## for @code{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < +## 1/2 is considered. The default is the two-sided case. +## +## The p-value of the test is returned in @var{pval}. +## +## If no output argument is given, the p-value of the test is displayed. +## @end deftypefn + +## Author: KH +## Description: Wilcoxon signed-rank test + +function [pval, z] = wilcoxon_test (x, y, alt) + + if (nargin < 2 || nargin > 3) + print_usage (); + endif + + if (! (isvector (x) && isvector (y) && (length (x) == length (y)))) + error ("wilcoxon_test: X and Y must be vectors of the same length"); + endif + + n = length (x); + x = reshape (x, 1, n); + y = reshape (y, 1, n); + d = x - y; + d = d (find (d != 0)); + n = length (d); + if (n > 25) + r = ranks (abs (d)); + z = sum (r (find (d > 0))); + z = ((z - n * (n + 1) / 4) / sqrt (n * (n + 1) * (2 * n + 1) / 24)); + else + error ("wilcoxon_test: implementation requires more than 25 different pairs"); + endif + + cdf = stdnormal_cdf (z); + + if (nargin == 2) + alt = "!="; + endif + + if (! ischar (alt)) + error("wilcoxon_test: ALT must be a string"); + elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) + pval = 2 * min (cdf, 1 - cdf); + elseif (strcmp (alt, ">")) + pval = 1 - cdf; + elseif (strcmp (alt, "<")) + pval = cdf; + else + error ("wilcoxon_test: option %s not recognized", alt); + endif + + if (nargout == 0) + printf (" pval: %g\n", pval); + endif + +endfunction