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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{pval}, @var{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{}) |
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21 ## Perform a Kruskal-Wallis one-factor "analysis of variance". |
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22 ## |
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23 ## Suppose a variable is observed for @var{k} > 1 different groups, and |
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24 ## let @var{x1}, @dots{}, @var{xk} be the corresponding data vectors. |
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25 ## |
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26 ## Under the null hypothesis that the ranks in the pooled sample are not |
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27 ## affected by the group memberships, the test statistic @var{k} is |
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28 ## approximately chi-square with @var{df} = @var{k} - 1 degrees of |
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29 ## freedom. |
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30 ## |
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31 ## The p-value (1 minus the CDF of this distribution at @var{k}) is |
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32 ## returned in @var{pval}. |
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33 ## |
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34 ## If no output argument is given, the p-value is displayed. |
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35 ## @end deftypefn |
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36 |
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37 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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38 ## Description: Kruskal-Wallis test |
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39 |
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40 function [pval, k, df] = kruskal_wallis_test (varargin) |
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41 |
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42 m = nargin; |
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43 if (m < 2) |
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44 print_usage (); |
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45 endif |
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46 |
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47 n = []; |
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48 p = []; |
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49 |
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50 for i = 1 : m; |
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51 x = varargin{i}; |
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52 if (! isvector (x)) |
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53 error ("kruskal_wallis_test: all arguments must be vectors"); |
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54 endif |
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55 l = length (x); |
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56 n = [n, l]; |
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57 p = [p, (reshape (x, 1, l))]; |
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58 endfor |
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59 |
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60 r = ranks (p); |
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61 |
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62 k = 0; |
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63 j = 0; |
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64 for i = 1 : m; |
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65 k = k + (sum (r ((j + 1) : (j + n(i))))) ^ 2 / n(i); |
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66 j = j + n(i); |
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67 endfor |
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68 |
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69 n = length (p); |
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70 k = 12 * k / (n * (n + 1)) - 3 * (n + 1); |
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71 df = m - 1; |
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72 pval = 1 - chisquare_cdf (k, df); |
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73 |
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74 if (nargout == 0) |
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75 printf ("pval: %g\n", pval); |
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76 endif |
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77 |
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78 endfunction |
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79 |
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80 |
