## 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, z] = z_test_2 (x, y, v_x, v_y [, alt]) ## ## For two samples x and y from normal distributions with unknown ## means and known variances v_x and v_y, perform a Z-test of the ## hypothesis of equal means. ## Under the null, the test statistic z follows a standard normal ## distribution. ## ## 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 ## along with some information. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Compare means of two normal samples with known variances function [pval, z] = z_test_2 (x, y, v_x, v_y, alt) if ((nargin < 4) || (nargin > 5)) usage ("[pval, z] = z_test_2 (x, y, v_x, v_y [, alt])"); endif if (! (is_vector (x) && is_vector (y))) error("z_test_2: both x and y must be vectors"); elseif (! (is_scalar (v_x) && (v_x > 0) && is_scalar (v_y) && (v_y > 0))) error ("z_test_2: both v_x and v_y must be positive scalars."); endif n_x = length (x); n_y = length (y); mu_x = sum (x) / n_x; mu_y = sum (y) / n_y; z = (mu_x - mu_y) / sqrt (v_x / n_x + v_y / n_y); cdf = stdnormal_cdf (z); if (nargin == 4) alt = "!="; endif if (! isstr (alt)) error ("z_test_2: alt must be a string"); elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) pval = 2 * min (cdf, 1 - cdf); elseif (strcmp (alt, ">")) pval = 1 - cdf; elseif (strcmp (alt, "<")) pval = cdf; else error (sprintf ("z_test_2: option %s not recognized", alt)); endif if (nargout == 0) s = strcat ("Two-sample Z-test of mean(x) == mean(y) against ", "mean(x) %s mean(y),\n", "with known var(x) == %g and var(y) == %g:\n", " pval = %g\n"); printf (s, alt, v_x, v_y, pval); endif endfunction

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