## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This program 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 2, or (at your option) ## any later version. ## ## This program 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 this file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: [pval, z] = wilcoxon_test (x, y [, alt]) ## ## For two matched-pair sample vectors x and y, perform a Wilcoxon ## signed-rank test of the null hypothesis PROB(x > y) == 1/2. ## Under the null, the test statistic z approximately follows a ## standard normal distribution. ## ## With the optional argument string alt, the alternative of interest ## can be selected. ## If alt is "!=" or "<>", the null is tested against the two-sided ## alternative PROB(x > y) != 1/2. ## If alt is ">", the one-sided alternative PROB(x > y) > 1/2 is ## considered, similarly for "<". ## The default is the two-sided case. ## ## pval is the p-value of the test. ## ## If no output argument is given, the p-value of the test is displayed. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Wilcoxon signed-rank test function [pval, z] = wilcoxon_test (x, y, alt) if ((nargin < 2) || (nargin > 3)) usage ("[pval, z] = wilcoxon_test (x, y [, alt])"); endif if (! (is_vector (x) && is_vector (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 > 0) 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 z = 0; endif cdf = stdnormal_cdf (z); if (nargin == 2) alt = "!="; endif if (! isstr (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 (sprintf ("wilcoxon_test: option %s not recognized", alt)); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction

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