## 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, t, df] = t_test_2 (x, y [, alt]) ## ## For two samples x and y from normal distributions with unknown means ## and unknown equal variances, perform a two-sample t-test of the null ## hypothesis of equal means. ## Under the null, the test statistic t follows a Student distribution ## with df degrees of freedom. ## ## 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 mean(x) != mean(y). ## If alt is ">", the one-sided alternative mean(x) > mean(y) 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: Student's two-sample t test function [pval, t, df] = t_test_2 (x, y, alt) if ((nargin < 2) || (nargin > 3)) usage ("[pval, t, df] = t_test_2 (x, y [, alt])"); endif if (! (is_vector (x) && is_vector (y))) error ("t_test_2: both x and y must be vectors"); endif n_x = length (x); n_y = length (y); df = n_x + n_y - 2; mu_x = sum (x) / n_x; mu_y = sum (y) / n_y; v = sumsq (x - mu_x) + sumsq (y - mu_y); t = (mu_x - mu_y) * sqrt ( (n_x * n_y * df) / (v * (n_x + n_y)) ); cdf = t_cdf (t, df); if (nargin == 2) alt = "!="; endif if (! isstr (alt)) error ("t_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 ("t_test_2: option %s not recognized", alt)); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction

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