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bartlett_test.m

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## This program 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 2, or (at your option)
## any later version.
## 
## This program 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 this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  [pval, chisq, df] = bartlett_test (x1, ...)
##
## Performs a Bartlett test for the homogeneity of variances in the data
## vectors x1, x2, ..., xk, where k > 1.
##
## Under the null of equal variances, the test statistic chisq
## approximately ollows a chi-square distribution with df degrees of
## freedom; pval is the p-value (1 minus the CDF of this distribution at
## chisq) of the test.
##
## If no output argument is given, the p-value is displayed.

## Author:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  Bartlett test for homogeneity of variances

function [pval, chisq, df] = bartlett_test (...)

  k = nargin;
  if (k < 2)
    usage ("[pval, chisq, df] = bartlett_test (x1, ...)");
  endif

  f = zeros (k, 1);
  v = zeros (k, 1);
  va_start ();
  for i = 1 : k;
    x = va_arg ();
    if (! is_vector (x))
      error ("bartlett_test:  all arguments must be vectors");
    endif
    f(i) = length (x) - 1;
    v(i) = var (x);
  endfor

  f_tot = sum (f);
  v_tot = sum (f .* v) / f_tot;
  c     = 1 + (sum (1 ./ f) - 1 / f_tot) / (3 * (k - 1));
  chisq = (f_tot * log (v_tot) - sum (f .* log (v))) / c;
  df    = k;
  pval  = 1 - chisquare_cdf (chisq, df);
  
  if (nargout == 0)
    printf("  pval:  %g\n", pval);
  endif

endfunction

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