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## Copyright (C) 1995-2013 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{b}, @var{n}] =} sign_test (@var{x}, @var{y}, @var{alt})
## For two matched-pair samples @var{x} and @var{y}, perform a sign test
## of the null hypothesis PROB (@var{x} > @var{y}) == PROB (@var{x} <
## @var{y}) == 1/2. Under the null, the test statistic @var{b} roughly
## follows a binomial distribution with parameters @code{@var{n} = sum
## (@var{x} != @var{y})} and @var{p} = 1/2.
##
## With the optional argument @code{alt}, the alternative of interest
## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the
## null hypothesis is tested against the two-sided alternative PROB
## (@var{x} < @var{y}) != 1/2. If @var{alt} is @qcode{">"}, the
## one-sided alternative PROB (@var{x} > @var{y}) > 1/2 ("x is
## stochastically greater than y") is considered. Similarly for
## @qcode{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < 1/2
## ("x is stochastically less than y") 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: Sign test
function [pval, b, n] = sign_test (x, y, alt)
if ((nargin < 2) || (nargin > 3))
print_usage ();
endif
if (! (isvector (x) && isvector (y) && (length (x) == length (y))))
error ("sign_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);
n = sum (x != y);
b = sum (x > y);
cdf = binocdf (b, n, 1/2);
if (nargin == 2)
alt = "!=";
endif
if (! ischar (alt))
error ("sign_test: ALT must be a string");
endif
if (strcmp (alt, "!=") || strcmp (alt, "<>"))
pval = 2 * min (cdf, 1 - cdf);
elseif (strcmp (alt, ">"))
pval = 1 - cdf;
elseif (strcmp (alt, "<"))
pval = cdf;
else
error ("sign_test: option %s not recognized", alt);
endif
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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