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## Copyright (C) 1996-2015 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{chisq}, @var{df}] =} mcnemar_test (@var{x})
## For a square contingency table @var{x} of data cross-classified on the row
## and column variables, @nospell{McNemar's} test can be used for testing the
## null hypothesis of symmetry of the classification probabilities.
##
## Under the null, @var{chisq} is approximately distributed as chisquare with
## @var{df} degrees of freedom.
##
## The p-value (1 minus the CDF of this distribution at @var{chisq}) 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: McNemar's test for symmetry
function [pval, chisq, df] = mcnemar_test (x)
if (nargin != 1)
print_usage ();
endif
if (! (min (size (x)) > 1) && issquare (x))
error ("mcnemar_test: X must be a square matrix of size > 1");
elseif (! (all ((x(:) >= 0)) && all (x(:) == fix (x(:)))))
error ("mcnemar_test: all entries of X must be non-negative integers");
endif
r = rows (x);
df = r * (r - 1) / 2;
if (r == 2)
num = max (abs (x - x') - 1, 0) .^ 2;
else
num = abs (x - x') .^ 2;
endif
chisq = sum (sum (triu (num ./ (x + x'), 1)));
pval = 1 - chi2cdf (chisq, df);
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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