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scripts/statistics/tests/sign_test.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (70 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{b}, @var{n}] =} sign_test (@var{x}, @var{y}, @var{alt})

    22## For two matched-pair samples @var{x} and @var{y}, perform a sign test

    23## of the null hypothesis PROB (@var{x} > @var{y}) == PROB (@var{x} <

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

    25## follows a binomial distribution with parameters @code{@var{n} = sum

    26## (@var{x} != @var{y})} and @var{p} = 1/2.

    27##

    28## With the optional argument @code{alt}, the alternative of interest

    29## can be selected.  If @var{alt} is @code{"!="} or @code{"<>"}, the

    30## null hypothesis is tested against the two-sided alternative PROB

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

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

    33## stochastically greater than y") is considered.  Similarly for

    34## @code{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < 1/2

    35## ("x is stochastically less than y") is considered.  The default is

    36## 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: Sign test

    45

    46function [pval, b, n] = sign_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 ("sign_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  n   = sum (x != y);

    60  b   = sum (x > y);

    61  cdf = binomial_cdf (b, n, 1/2);

    62

    63  if (nargin == 2)

    64    alt  = "!=";

    65  endif

    66

    67  if (! ischar (alt))

    68    error ("sign_test: alt must be a string");

    69  endif

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

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

    72  elseif strcmp (alt, ">")

    73    pval = 1 - cdf;

    74  elseif strcmp (alt, "<")

    75    pval = cdf;

    76  else

    77    error ("sign_test: option %s not recognized", alt);

    78  endif

    79

    80  if (nargout == 0)

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

    82  endif

    83

    84endfunction