Mercurial > octave
view scripts/statistics/tests/t_test_2.m @ 21634:96518f623c91
Backed out changeset dcf8922b724b
author | Mike Miller <mtmiller@octave.org> |
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date | Wed, 20 Apr 2016 11:06:03 -0700 |
parents | dcf8922b724b |
children | bac0d6f07a3e |
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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 {} {[@var{pval}, @var{t}, @var{df}] =} t_test_2 (@var{x}, @var{y}, @var{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 @var{t} follows a Student distribution ## with @var{df} degrees of freedom. ## ## 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}) != mean ## (@var{y})}. If @var{alt} is @qcode{">"}, the one-sided alternative ## @code{mean (@var{x}) > mean (@var{y})} is used. Similarly for ## @qcode{"<"}, the one-sided alternative @code{mean (@var{x}) < mean ## (@var{y})} is used. 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. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Student's two-sample t test function [pval, t, df] = t_test_2 (x, y, alt) if (nargin < 2 || nargin > 3) print_usage (); endif if (! (isvector (x) && isvector (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 = tcdf (t, df); if (nargin == 2) alt = "!="; endif if (! ischar (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 ("t_test_2: option %s not recognized", alt); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction