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scripts/statistics/tests/t_test_2.m

changeset 10289: 4b124317dc38
parent:93c65f2a5668
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (43 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007

     2##               Kurt Hornik

     3##

     4## This file is part of Octave.

     5##

     6## Octave is free software; you can redistribute it and/or modify it

     7## under the terms of the GNU General Public License as published by

     8## the Free Software Foundation; either version 3 of the License, or (at

     9## your option) any later version.

    10##

    11## Octave is distributed in the hope that it will be useful, but

    12## WITHOUT ANY WARRANTY; without even the implied warranty of

    13## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

    14## General Public License for more details.

    15##

    16## You should have received a copy of the GNU General Public License

    17## along with Octave; see the file COPYING.  If not, see

    18## <http://www.gnu.org/licenses/>.

    19

    20## -*- texinfo -*-

    21## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} t_test_2 (@var{x}, @var{y}, @var{alt})

    22## For two samples x and y from normal distributions with unknown means

    23## and unknown equal variances, perform a two-sample t-test of the null

    24## hypothesis of equal means.  Under the null, the test statistic

    25## @var{t} follows a Student distribution with @var{df} degrees of

    26## freedom.

    27##

    28## With the optional argument string @var{alt}, the alternative of

    29## interest can be selected.  If @var{alt} is @code{"!="} or

    30## @code{"<>"}, the null is tested against the two-sided alternative

    31## @code{mean (@var{x}) != mean (@var{y})}.  If @var{alt} is @code{">"},

    32## the one-sided alternative @code{mean (@var{x}) > mean (@var{y})} is

    33## used.  Similarly for @code{"<"}, the one-sided alternative @code{mean

    34## (@var{x}) < mean (@var{y})} is used.  The default is the two-sided

    35## case.

    36##

    37## The p-value of the test is returned in @var{pval}.

    38##

    39## If no output argument is given, the p-value of the test is displayed.

    40## @end deftypefn

    41

    42## Author: KH <Kurt.Hornik@wu-wien.ac.at>

    43## Description: Student's two-sample t test

    44

    45function [pval, t, df] = t_test_2 (x, y, alt)

    46

    47  if ((nargin < 2) || (nargin > 3))

    48        print_usage ();

    49  endif

    50

    51  if (! (isvector (x) && isvector (y)))

    52    error ("t_test_2: both x and y must be vectors");

    53  endif

    54

    55  n_x  = length (x);

    56  n_y  = length (y);

    57  df   = n_x + n_y - 2;

    58  mu_x = sum (x) / n_x;

    59  mu_y = sum (y) / n_y;

    60  v    = sumsq (x - mu_x) + sumsq (y - mu_y);

    61  t    = (mu_x - mu_y) * sqrt ((n_x * n_y * df) / (v * (n_x + n_y)));

    62  cdf  = t_cdf (t, df);

    63

    64  if (nargin == 2)

    65    alt = "!=";

    66  endif

    67

    68  if (! ischar (alt))

    69    error ("t_test_2: alt must be a string");

    70  endif

    71  if (strcmp (alt, "!=") || strcmp (alt, "<>"))

    72    pval = 2 * min (cdf, 1 - cdf);

    73  elseif strcmp (alt, ">")

    74    pval = 1 - cdf;

    75  elseif strcmp (alt, "<")

    76    pval = cdf;

    77  else

    78    error ("t_test_2: option %s not recognized", alt);

    79  endif

    80

    81  if (nargout == 0)

    82    printf ("  pval: %g\n", pval);

    83  endif

    84

    85endfunction