Mercurial > octave-nkf
view scripts/statistics/tests/z_test.m @ 20654:b65888ec820e draft default tip gccjit
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author | Stefan Mahr <dac922@gmx.de> |
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date | Fri, 27 Feb 2015 16:59:36 +0100 |
parents | d9341b422488 |
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## Copyright (C) 1995-2015 Kurt Hornik ## ## This file is part of Octave. ## ## Octave 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 3 of the License, or (at ## your option) any later version. ## ## Octave 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 Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt}) ## Perform a Z-test of the null hypothesis @code{mean (@var{x}) == @var{m}} ## for a sample @var{x} from a normal distribution with unknown mean and known ## variance @var{v}. ## ## Under the null, the test statistic @var{z} follows a standard normal ## distribution. ## ## With the optional argument string @var{alt}, the alternative of interest ## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null ## is tested against the two-sided alternative ## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @qcode{">"}, the ## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"<"}, the one-sided alternative ## @code{mean (@var{x}) < @var{m}} is considered. The default is the two-sided ## case. ## ## The p-value of the test is returned in @var{pval}. ## ## If no output argument is given, the p-value of the test is displayed along ## with some information. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.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) print_usage (); endif if (! isvector (x)) error ("z_test: X must be a vector"); endif if (! isscalar (m)) error ("z_test: M must be a scalar"); endif if (! (isscalar (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 (! ischar (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 ("z_test: option %s not recognized", alt); endif if (nargout == 0) s = ["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 %!test %! ## Two-sided (also the default option) %! x = rand (10,1); n = length (x); %! u0 = 0.5; v = 1/12; # true mean, var %! pval = z_test (x, u0, v, "!="); %! if (mean (x) >= u0) %! zval = abs (norminv (0.5*pval)); %! else %! zval = -abs (norminv (0.5*pval)); %! endif %! unew = zval * sqrt (v/n) + u0; %! assert (mean (x), unew, 100*eps); %!test %! x = rand (10,1); n = length (x); %! u0 = 0.5; v = 1/12; %! pval = z_test (x, u0, v, ">"); %! zval = norminv (1-pval); %! unew = zval * sqrt (v/n) + u0; %! assert (mean (x), unew, 100*eps); %!test %! x = rand (10,1); n = length (x); %! u0 = 0.5; v = 1/12; %! pval = z_test (x, u0, v, "<"); %! zval = norminv (pval); %! unew = zval * sqrt (v/n) + u0; %! assert (mean (x), unew, 100*eps);