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hotelling_test_2.m
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1997-02-26
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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, Tsq] = hotelling_test_2 (x, y)
##
## For two samples x from multivariate normal distributions with the
## same number of variables (columns), unknown means and unknown equal
## covariance matrices, test the null hypothesis mean (x) == mean (y).
##
## Tsq is Hotelling's two-sample T^2. Under the null,
## (n_x+n_y-p-1) T^2 / (p(n_x+n_y-2))
## has an F distribution with p and n_x+n_y-p-1 degrees of freedom,
## where n_x and n_y are the sample sizes and p is the number of
## variables.
##
## 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 means of two multivariate normals
function [pval, Tsq] = hotelling_test_2 (x, y)
if (nargin != 2)
usage ("hotelling_test_2 (x, y)");
endif
if (is_vector (x))
n_x = length (x);
if (! is_vector (y))
error ("hotelling_test_2: If x is a vector, y must be too.");
else
n_y = length (y);
p = 1;
endif
elseif (is_matrix (x))
[n_x, p] = size (x);
[n_y, q] = size (y);
if (p != q)
error (strcat ("hotelling_test_2: ",
"x and y must have the same number of columns"));
endif
else
error ("hotelling_test_2: x and y must be matrices (or vectors)");
endif
d = mean (x) - mean (y);
S = ((n_x - 1) * cov (x) + (n_y - 1) * cov (y)) / (n_x + n_y - 2);
Tsq = (n_x * n_y / (n_x + n_y)) * d * (S \ d');
pval = 1 - f_cdf ((n_x + n_y - p - 1) * Tsq / (p * (n_x + n_y - 2)),
p, n_x + n_y - p - 1);
if (nargout == 0)
printf (" pval: %g\n", pval);
endif
endfunction