changelog shortlog tags changeset files revisions annotate raw

scripts/statistics/tests/u_test.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (35 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2006,

     2##               2007 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}] =} u_test (@var{x}, @var{y}, @var{alt})

    22## For two samples @var{x} and @var{y}, perform a Mann-Whitney U-test of

    23## the null hypothesis PROB (@var{x} > @var{y}) == 1/2 == PROB (@var{x}

    24## < @var{y}).  Under the null, the test statistic @var{z} approximately

    25## follows a standard normal distribution.  Note that this test is

    26## equivalent to the Wilcoxon rank-sum test.

    27##

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

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

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

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

    32## one-sided alternative PROB (@var{x} > @var{y}) > 1/2 is considered.

    33## Similarly for @code{"<"}, the one-sided alternative PROB (@var{x} >

    34## @var{y}) < 1/2 is considered.  The default is the two-sided case.

    35##

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

    37##

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

    39## @end deftypefn

    40

    41## This implementation is still incomplete---for small sample sizes,

    42## the normal approximation is rather bad ...

    43

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

    45## Description: Mann-Whitney U-test

    46

    47function [pval, z] = u_test (x, y, alt)

    48

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

    50    print_usage ();

    51  endif

    52

    53  if (! (isvector (x) && isvector (y)))

    54    error ("u_test: both x and y must be vectors");

    55  endif

    56

    57  n_x  = length (x);

    58  n_y  = length (y);

    59  r    = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]);

    60  z    = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ...

    61           / sqrt (n_x * n_y * (n_x + n_y + 1) / 12);

    62

    63  cdf  = stdnormal_cdf (z);

    64

    65  if (nargin == 2)

    66    alt  = "!=";

    67  endif

    68

    69  if (! ischar (alt))

    70    error("u_test: alt must be a string");

    71  endif

    72  if (strcmp (alt, "!=") || strcmp (alt, "<>"))

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

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

    75    pval = cdf;

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

    77    pval = 1 - cdf;

    78  else

    79    error ("u_test: option %s not recognized", alt);

    80  endif

    81

    82  if (nargout == 0)

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

    84  endif

    85

    86endfunction