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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 (x, m)
- ##
- ## For a sample x from a multivariate normal distribution with unknown
- ## mean and covariance matrix, test the null hypothesis that mean (x) ==
- ## m.
- ##
- ## Tsq is Hotelling's T^2. Under the null, (n-p) T^2 / (p(n-1)) has an
- ## F distribution with p and n-p degrees of freedom, where n and p are
- ## the numbers of samples and variables, respectively.
- ##
- ## 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: Test for mean of a multivariate normal
-
- function [pval, Tsq] = hotelling_test (x, m)
-
- if (nargin != 2)
- usage ("hotelling_test (x, m)");
- endif
-
- if (is_vector (x))
- if (! is_scalar (m))
- error ("hotelling_test: If x is a vector, m must be a scalar.");
- endif
- n = length (x);
- p = 1;
- elseif (is_matrix (x))
- [n, p] = size (x);
- if (n <= p)
- error ("hotelling_test: x must have more rows than columns.");
- endif
- if (is_vector (m) && length (m) == p)
- m = reshape (m, 1, p);
- else
- error (strcat ("hotelling_test: ",
- "If x is a matrix, m must be a vector\n",
- "\tof length columns (x)"));
- endif
- else
- error ("hotelling_test: x must be a matrix or vector");
- endif
-
- d = mean (x) - m;
- Tsq = n * d * (cov (x) \ d');
- pval = 1 - f_cdf ((n-p) * Tsq / (p * (n-1)), p, n-p);
-
- if (nargout == 0)
- printf (" pval: %g\n", pval);
- endif
-
- endfunction
-