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## Copyright (C) 1995-2013 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{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
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