## 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

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