## 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 (x, m, v [, alt]) ## ## Perform a Z-test of the null hypothesis mean(x) == m for a sample x ## from a normal distribution with unknown mean and known variance v. ## 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) != 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 ## along with some information. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Test for mean of a normal sample with known variance function [pval, z] = z_test (x, m, v, alt) if ((nargin < 3) || (nargin > 4)) usage ("[pval, z] = z_test (x, m, v [, alt])"); endif if (! is_vector (x)) error ("z_test: x must be a vector."); endif if (! is_scalar (m)) error ("z_test: m must be a scalar."); endif if (! (is_scalar (v) && (v > 0))) error ("z_test: v must be a positive scalar."); endif n = length (x); z = sqrt (n/v) * (sum (x) / n - m); cdf = stdnormal_cdf (z); if (nargin == 3) alt = "!="; endif if (! isstr (alt)) error ("z_test: 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: option %s not recognized", alt)); endif if (nargout == 0) s = strcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n", "with known var(x) == %g:\n", " pval = %g\n"); printf (s, m, alt, m, v, pval); endif endfunction

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