update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / wilcoxon_test.m

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+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- 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 <Kurt.Hornik@wu-wien.ac.at>
+## 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