Mercurial > octave
view scripts/statistics/tests/t_test.m @ 23219:3ac9f9ecfae5 stable
maint: Update copyright dates.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:39:29 -0500 |
parents | e9a0469dedd9 |
children | 092078913d54 |
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## Copyright (C) 1995-2017 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 (@var{x}, @var{m}, @var{alt}) ## For a sample @var{x} from a normal distribution with unknown mean and ## variance, perform a t-test of the null hypothesis ## @code{mean (@var{x}) == @var{m}}. ## ## Under the null, the test statistic @var{t} follows a Student distribution ## with @code{@var{df} = length (@var{x}) - 1} 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}) != ## @var{m}}. If @var{alt} is @qcode{">"}, the one-sided alternative ## @code{mean (@var{x}) > @var{m}} is considered. Similarly for @var{"<"}, ## 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. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Student's one-sample t test function [pval, t, df] = t_test (x, m, alt) if (nargin < 2 || nargin > 3) print_usage (); endif if (! isvector (x)) error ("t_test: X must be a vector"); endif if (! isscalar (m)) error ("t_test: M must be a scalar"); endif n = length (x); df = n - 1; t = sqrt (n) * (sum (x) / n - m) / std (x); cdf = tcdf (t, df); if (nargin == 2) alt = "!="; endif if (! ischar (alt)) error ("t_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 ("t_test: option %s not recognized", alt); endif if (nargout == 0) printf (" pval: %g\n", pval); endif endfunction %!test %! ## Two-sided (also the default option) %! x = rand (10,1); n = length (x); %! u0 = 0.5; # true mean %! xbar = mean (x); %! pval = t_test (x, u0, "!="); %! if (xbar >= u0) %! tval = abs (tinv (0.5*pval, n-1)); %! else %! tval = -abs (tinv (0.5*pval, n-1)); %! endif %! unew = tval * std(x)/sqrt(n) + u0; %! assert (xbar, unew, 100*eps); %!test %! x = rand (10,1); n = length (x); %! u0 = 0.5; %! pval = t_test (x, u0, ">"); %! tval = tinv (1-pval, n-1); %! unew = tval * std(x)/sqrt(n) + u0; %! assert (mean (x), unew, 100*eps); %!test %! x = rand (10,1); n = length (x); %! u0 = 0.5; %! pval = t_test (x, u0, "<"); %! tval = tinv (pval, n-1); %! unew = tval * std(x)/sqrt(n) + u0; %! assert (mean (x), unew, 100*eps);