update packages

[CreaPhase.git] / octave_packages / m / statistics / tests / welch_test.m

diff --git a/octave_packages/m/statistics/tests/welch_test.m b/octave_packages/m/statistics/tests/welch_test.m
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+## Copyright (C) 1995-2012 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}] =} welch_test (@var{x}, @var{y}, @var{alt})
+## For two samples @var{x} and @var{y} from normal distributions with
+## unknown means and unknown and not necessarily equal variances,
+## perform a Welch test of the null hypothesis of equal means.
+## Under the null, the test statistic @var{t} approximately 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 @code{"!="} or
+## @code{"<>"}, the null is tested against the two-sided alternative
+## @code{mean (@var{x}) != @var{m}}.  If @var{alt} is @code{">"}, the
+## one-sided alternative mean(x) > @var{m} is considered.  Similarly for
+## @code{"<"}, the one-sided alternative mean(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: Welch two-sample t test
+
+function [pval, t, df] = welch_test (x, y, alt)
+
+  if ((nargin < 2) || (nargin > 3))
+    print_usage ();
+  endif
+
+  if (! (isvector (x) && isvector (y)))
+    error ("welch_test: both X and Y must be vectors");
+  endif
+
+  n_x  = length (x);
+  n_y  = length (y);
+  mu_x = sum (x) / n_x;
+  mu_y = sum (y) / n_y;
+  v_x  = sumsq (x - mu_x) / (n_x * (n_x - 1));
+  v_y  = sumsq (y - mu_y) / (n_y * (n_y - 1));
+  c    = v_x / (v_x + v_y);
+  df   = 1 / (c^2 / (n_x - 1) + (1 - c)^2 / (n_y - 1));
+  t    = (mu_x - mu_y) / sqrt (v_x + v_y);
+  cdf  = tcdf (t, df);
+
+  if (nargin == 2)
+    alt  = "!=";
+  endif
+
+  if (! ischar (alt))
+    error ("welch_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 ("welch_test: option %s not recognized", alt);
+  endif
+
+  if (nargout == 0)
+    printf ("  pval: %g\n", pval);
+  endif
+
+endfunction