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scripts/statistics/tests/wilcoxon_test.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (62 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007

     2##               Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {[@var{pval}, @var{z}] =} wilcoxon_test (@var{x}, @var{y}, @var{alt})

    22## For two matched-pair sample vectors @var{x} and @var{y}, perform a

    23## Wilcoxon signed-rank test of the null hypothesis PROB (@var{x} >

    24## @var{y}) == 1/2.  Under the null, the test statistic @var{z}

    25## approximately follows a standard normal distribution when @var{n} > 25.

    26##

    27## @strong{Warning}: This function assumes a normal distribution for @var{z}

    28## and thus is invalid for @var{n} <= 25.

    29##

    30## With the optional argument string @var{alt}, the alternative of

    31## interest can be selected.  If @var{alt} is @code{"!="} or

    32## @code{"<>"}, the null is tested against the two-sided alternative

    33## PROB (@var{x} > @var{y}) != 1/2.  If alt is @code{">"}, the one-sided

    34## alternative PROB (@var{x} > @var{y}) > 1/2 is considered.  Similarly

    35## for @code{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) <

    36## 1/2 is considered.  The default is the two-sided case.

    37##

    38## The p-value of the test is returned in @var{pval}.

    39##

    40## If no output argument is given, the p-value of the test is displayed.

    41## @end deftypefn

    42

    43## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    44## Description: Wilcoxon signed-rank test

    45

    46function [pval, z] = wilcoxon_test (x, y, alt)

    47

    48  if (nargin < 2 || nargin > 3)

    49    print_usage ();

    50  endif

    51

    52  if (! (isvector (x) && isvector (y) && (length (x) == length (y))))

    53    error ("wilcoxon_test: x and y must be vectors of the same length");

    54  endif

    55

    56  n = length (x);

    57  x = reshape (x, 1, n);

    58  y = reshape (y, 1, n);

    59  d = x - y;

    60  d = d (find (d != 0));

    61  n = length (d);

    62  if (n > 25)

    63    r = ranks (abs (d));

    64    z = sum (r (find (d > 0)));

    65    z = ((z - n * (n + 1) / 4) / sqrt (n * (n + 1) * (2 * n + 1) / 24));

    66  else

    67    error ("wilcoxon_test: implementation requires more than 25 different pairs");

    68  endif

    69

    70  cdf = stdnormal_cdf (z);

    71

    72  if (nargin == 2)

    73    alt = "!=";

    74  endif

    75

    76  if (! ischar (alt))

    77    error("wilcoxon_test: alt must be a string");

    78  elseif (strcmp (alt, "!=") || strcmp (alt, "<>"))

    79    pval = 2 * min (cdf, 1 - cdf);

    80  elseif (strcmp (alt, ">"))

    81    pval = 1 - cdf;

    82  elseif (strcmp (alt, "<"))

    83    pval = cdf;

    84  else

    85    error ("wilcoxon_test: option %s not recognized", alt);

    86  endif

    87

    88  if (nargout == 0)

    89    printf ("  pval: %g\n", pval);

    90  endif

    91

    92endfunction