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## Copyright (C) 1995, 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] = u_test (x, y [, alt])
##
## For two samples x and y, perform a Mann-Whitney U-test of the null
## hypothesis PROB(x > y) == 1/2 == PROB(x < y). Under the null, the
## test statistic z approximately follows a standard normal
## distribution. Note that this test is equivalent to the Wilcoxon
## rank-sum test.
##
## 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 PROB(x > y) != 1/2.
## If alt is ">", the one-sided alternative PROB(x > y) > 1/2 is
## considered, 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.
## This implementation is still incomplete---for small sample sizes,
## the normal approximation is rather bad ...
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Mann-Whitney U-test
function [pval, z] = u_test (x, y, alt)
if ((nargin < 2) || (nargin > 3))
usage ("[pval, z] = u_test (x, y [, alt])");
endif
if (! (is_vector (x) && is_vector (y)))
error ("u_test: both x and y must be vectors");
endif
n_x = length (x);
n_y = length (y);
r = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]);
z = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ...
/ sqrt (n_x * n_y * (n_x + n_y + 1) / 12);
cdf = stdnormal_cdf (z);
if (nargin == 2)
alt = "!=";
endif
if (! isstr (alt))
error("u_test: alt must be a string");
endif
if (strcmp (alt, "!=") || strcmp (alt, "<>"))
pval = 2 * min (cdf, 1 - cdf);
elseif (strcmp (alt, ">"))
pval = cdf;
elseif (strcmp (alt, "<"))
pval = 1 - cdf;
else
error (sprintf ("u_test: option %s not recognized", alt));
endif
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction
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