Mercurial > octave
view scripts/statistics/tests/kruskal_wallis_test.m @ 21546:f7f97d7e9294
doc: Wrap m-file docstrings to 79 characters + newline (80 total).
* isrecording.m, soundsc.m, delaunay3.m, cell2mat.m, cumtrapz.m, del2.m,
inputParser.m, interp1.m, interp3.m, narginchk.m, profile.m,
validateattributes.m, delaunayn.m, tsearchn.m, voronoin.m, brighten.m,
cmunique.m, colorcube.m, imfinfo.m, imshow.m, edit.m, orderfields.m, run.m,
warning_ids.m, ode23.m, ode45.m, odeget.m, integrate_adaptive.m, kahan.m,
ode_struct_value_check.m, runge_kutta_23.m, fminunc.m, fsolve.m, fzero.m,
pkg.m, build.m, specular.m, view.m, bar.m, barh.m, contour3.m, isosurface.m,
line.m, pie.m, pie3.m, quiver3.m, scatter.m, scatter3.m, stem3.m, stemleaf.m,
surfl.m, tetramesh.m, isfigure.m, mkpp.m, pchip.m, residue.m, splinefit.m,
rmpref.m, unique.m, eigs.m, ilu.m, factor.m, factorial.m, gallery.m, hankel.m,
histc.m, ols.m, finv.m, fpdf.m, kruskal_wallis_test.m, weekday.m:
Wrap m-file docstrings to 79 characters + newline (80 total).
author | Rik <rik@octave.org> |
---|---|
date | Sun, 27 Mar 2016 15:50:01 -0700 |
parents | 516bb87ea72e |
children | dcf8922b724b |
line wrap: on
line source
## Copyright (C) 1995-2015 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 {} {[@var{pval}, @var{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{}) ## Perform a @nospell{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 @nospell{William H. Kruskal and W. Allen Wallis}, ## @cite{Use of Ranks in One-Criterion Variance Analysis}, ## Journal of the American Statistical Association, Vol. 47, No. 260 (Dec ## 1952). ## ## 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 += (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 /= (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)