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[CreaPhase.git] / octave_packages / m / statistics / tests / kruskal_wallis_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{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{})
+## Perform a Kruskal-Wallis one-factor "analysis of variance".
+##
+## Suppose a variable is observed for @var{k} > 1 different groups, and
+## let @var{x1}, @dots{}, @var{xk} be the corresponding data vectors.
+##
+## Under the null hypothesis that the ranks in the pooled sample are not
+## affected by the group memberships, the test statistic @var{k} is
+## approximately chi-square with @var{df} = @var{k} - 1 degrees of
+## freedom.
+##
+## If the data contains ties (some value appears more than once)
+## @var{k} is divided by
+##
+## 1 - @var{sum_ties} / (@var{n}^3 - @var{n})
+##
+## where @var{sum_ties} is the sum of @var{t}^2 - @var{t} over each group
+## of ties where @var{t} is the number of ties in the group and @var{n}
+## is the total number of values in the input data.  For more info on
+## this adjustment see "Use of Ranks in One-Criterion Variance Analysis"
+## in Journal of the American Statistical Association, Vol. 47,
+## No. 260 (Dec 1952) by William H. Kruskal and W. Allen Wallis.
+##
+## The p-value (1 minus the CDF of this distribution at @var{k}) is
+## returned in @var{pval}.
+##
+## If no output argument is given, the p-value is displayed.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Kruskal-Wallis test
+
+function [pval, k, df] = kruskal_wallis_test (varargin)
+
+  m = nargin;
+  if (m < 2)
+    print_usage ();
+  endif
+
+  n = [];
+  p = [];
+
+  for i = 1 : m;
+    x = varargin{i};
+    if (! isvector (x))
+      error ("kruskal_wallis_test: all arguments must be vectors");
+    endif
+    l = length (x);
+    n = [n, l];
+    p = [p, (reshape (x, 1, l))];
+  endfor
+
+  r = ranks (p);
+
+  k = 0;
+  j = 0;
+  for i = 1 : m;
+    k = k + (sum (r ((j + 1) : (j + n(i))))) ^ 2 / n(i);
+    j = j + n(i);
+  endfor
+
+  n = length (p);
+  k = 12 * k / (n * (n + 1)) - 3 * (n + 1);
+
+  ## Adjust the result to takes ties into account.
+  sum_ties = sum (polyval ([1, 0, -1, 0], runlength (sort (p))));
+  k = k / (1 - sum_ties / (n^3 - n));
+
+  df = m - 1;
+  pval = 1 - chi2cdf (k, df);
+
+  if (nargout == 0)
+    printf ("pval: %g\n", pval);
+  endif
+
+endfunction
+
+## Test with ties
+%!assert (abs(kruskal_wallis_test([86 86], [74]) - 0.157299207050285) < 0.0000000000001)