## 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] = welch_test (x, y [, alt]) ## ## For two samples x and y from normal distributions with unknown means ## and unknown and not necessarily equal variances, perform a Welch test ## of the null hypothesis of equal means. ## Under the null, the test statistic t approximately 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) != m. ## If alt is ">", the one-sided alternative mean(x) > m 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. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Welch two-sample t test function [pval, t, df] = welch_test (x, y, alt) if ((nargin < 2) || (nargin > 3)) usage ("[pval, t, df] = welch_test (x, y [, alt])"); endif if (! (is_vector (x) && is_vector (y))) error ("welch_test: both x and y must be vectors"); endif n_x = length (x); n_y = length (y); mu_x = sum (x) / n_x; mu_y = sum (y) / n_y; v_x = sumsq (x - mu_x) / (n_x * (n_x - 1)); v_y = sumsq (x - mu_y) / (n_y * (n_y - 1)); c = v_x / (v_x + v_y); df = 1 / ( c^2 / (n_x - 1) + (1 - c)^2 / (n_y - 1)); t = (mu_x - mu_y) / sqrt (v_x + v_y); cdf = t_cdf (t, df); if (nargin == 2) alt = "!="; endif if (! isstr (alt)) error ("welch_test: 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 ("welch_test: option %s not recognized", alt)); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction

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