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## Copyright (C) 1996, 1997 Kurt Hornik
##
## This program 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 2, or (at your option)
## any later version.
##
## This program 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 this file. If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
## usage: [pval, z] = prop_test_2 (x1, n1, x2, n2 [, alt])
##
## If x1 and n1 are the counts of successes and trials in one sample,
## and x2 and n2 those in a second one, test the null hypothesis that
## the success probabilities p1 and p2 are the same.
## Under the null, the test statistic z approximately follows a
## standard normal distribution.
##
## With the optional argument string alt, the alternative of interest
## can be selected.
## If alt is "!=" or "<>", the null is tested against the two-sided
## alternative p1 != p2.
## If alt is ">", the one-sided alternative p1 > p2 is used, similarly
## for "<".
## The default is the two-sided case.
##
## pval is the p-value of the test.
##
## If no output argument is given, the p-value of the test is displayed.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Compare two proportions
function [pval, z] = prop_test_2 (x1, n1, x2, n2, alt)
if ((nargin < 4) || (nargin > 5))
usage ("[pval, z] = prop_test_2 (x1, n1, x2, n2 [, alt])");
endif
## Could do sanity checking on x1, n1, x2, n2 here
p1 = x1 / n1;
p2 = x2 / n2;
pc = (x1 + x2) / (n1 + n2);
z = (p1 - p2) / sqrt (pc * (1 - pc) * (1/n1 + 1/n2));
cdf = stdnormal_cdf (z);
if (nargin == 4)
alt = "!=";
endif
if !isstr (alt)
error ("prop_test_2: 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 (sprintf ("prop_test_2: option %s not recognized", alt));
endif
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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