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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## usage: [pval, k, df] = kruskal_wallis_test (x1, ...) |
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18 ## |
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19 ## Perform a Kruskal-Wallis one-factor "analysis of variance". |
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20 ## |
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21 ## Suppose a variable is observed for k > 1 different groups, and let |
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22 ## x1, ..., xk be the corresponding data vectors. |
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23 ## |
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24 ## Under the null hypothesis that the ranks in the pooled sample are not |
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25 ## affected by the group memberships, the test statistic k is |
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26 ## approximately chi-square with df = k - 1 degrees of freedom. pval is |
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27 ## the p-value (1 minus the CDF of this distribution at k) of this test. |
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28 ## |
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29 ## If no output argument is given, the pval is displayed. |
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30 |
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31 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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32 ## Description: Kruskal-Wallis test |
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33 |
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34 function [pval, k, df] = kruskal_wallis_test (...) |
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35 |
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36 m = nargin; |
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37 if (m < 2) |
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38 usage ("[pval, k, df] = kruskal_wallis_test (x1, ...)"); |
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39 endif |
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40 |
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41 n = []; |
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42 p = []; |
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43 va_start; |
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44 for i = 1 : m; |
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45 x = va_arg (); |
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46 if (! is_vector (x)) |
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47 error ("kruskal_wallis_test: all arguments must be vectors"); |
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48 endif |
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49 l = length (x); |
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50 n = [n, l]; |
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51 p = [p, (reshape (x, 1, l))]; |
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52 endfor |
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53 |
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54 r = ranks (p); |
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55 |
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56 k = 0; |
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57 j = 0; |
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58 for i = 1 : m; |
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59 k = k + (sum (r ((j + 1) : (j + n(i))))) ^ 2 / n(i); |
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60 j = j + n(i); |
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61 endfor |
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62 |
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63 n = length (p); |
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64 k = 12 * k / (n * (n + 1)) - 3 * (n + 1); |
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65 df = m - 1; |
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66 pval = 1 - chisquare_cdf (k, df); |
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67 |
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68 if (nargout == 0) |
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69 printf ("pval: %g\n", pval); |
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70 endif |
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71 |
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72 endfunction |
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73 |
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74 |
