1 ## Copyright (C) 1995-2012 Kurt Hornik
3 ## This file is part of Octave.
5 ## Octave is free software; you can redistribute it and/or modify it
6 ## under the terms of the GNU General Public License as published by
7 ## the Free Software Foundation; either version 3 of the License, or (at
8 ## your option) any later version.
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
20 ## @deftypefn {Function File} {[@var{pval}, @var{f}, @var{df_num}, @var{df_den}] =} var_test (@var{x}, @var{y}, @var{alt})
21 ## For two samples @var{x} and @var{y} from normal distributions with
22 ## unknown means and unknown variances, perform an F-test of the null
23 ## hypothesis of equal variances. Under the null, the test statistic
24 ## @var{f} follows an F-distribution with @var{df_num} and @var{df_den}
25 ## degrees of freedom.
27 ## With the optional argument string @var{alt}, the alternative of
28 ## interest can be selected. If @var{alt} is @code{"!="} or
29 ## @code{"<>"}, the null is tested against the two-sided alternative
30 ## @code{var (@var{x}) != var (@var{y})}. If @var{alt} is @code{">"},
31 ## the one-sided alternative @code{var (@var{x}) > var (@var{y})} is
32 ## used. Similarly for "<", the one-sided alternative @code{var
33 ## (@var{x}) > var (@var{y})} is used. The default is the two-sided
36 ## The p-value of the test is returned in @var{pval}.
38 ## If no output argument is given, the p-value of the test is displayed.
41 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
42 ## Description: F test to compare two variances
44 function [pval, f, df_num, df_den] = var_test (x, y, alt)
46 if ((nargin < 2) || (nargin > 3))
50 if (! (isvector (x) && isvector (y)))
51 error ("var_test: both X and Y must be vectors");
54 df_num = length (x) - 1;
55 df_den = length (y) - 1;
56 f = var (x) / var (y);
57 cdf = fcdf (f, df_num, df_den);
64 error ("var_test: ALT must be a string");
66 if (strcmp (alt, "!=") || strcmp (alt, "<>"))
67 pval = 2 * min (cdf, 1 - cdf);
68 elseif (strcmp (alt, ">"))
70 elseif (strcmp (alt, "<"))
73 error ("var_test: option %s not recognized", alt);
77 printf ("pval: %g\n", pval);