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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2006, |
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2 ## 2007 Kurt Hornik |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{pval}, @var{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{}) |
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22 ## Perform a Kruskal-Wallis one-factor "analysis of variance". |
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23 ## |
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24 ## Suppose a variable is observed for @var{k} > 1 different groups, and |
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25 ## let @var{x1}, @dots{}, @var{xk} be the corresponding data vectors. |
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26 ## |
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27 ## Under the null hypothesis that the ranks in the pooled sample are not |
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28 ## affected by the group memberships, the test statistic @var{k} is |
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29 ## approximately chi-square with @var{df} = @var{k} - 1 degrees of |
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30 ## freedom. |
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31 ## |
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32 ## If the data contains ties (some value appears more than once) |
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33 ## @var{k} is divided by |
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34 ## |
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35 ## 1 - @var{sum_ties} / (@var{n}^3 - @var{n}) |
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36 ## |
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37 ## where @var{sum_ties} is the sum of @var{t}^2 - @var{t} over each group |
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38 ## of ties where @var{t} is the number of ties in the group and @var{n} |
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39 ## is the total number of values in the input data. For more info on |
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40 ## this adjustment see "Use of Ranks in One-Criterion Variance Analysis" |
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41 ## in Journal of the American Statistical Association, Vol. 47, |
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42 ## No. 260 (Dec 1952) by William H. Kruskal and W. Allen Wallis. |
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43 ## |
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44 ## The p-value (1 minus the CDF of this distribution at @var{k}) is |
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45 ## returned in @var{pval}. |
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46 ## |
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47 ## If no output argument is given, the p-value is displayed. |
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48 ## @end deftypefn |
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49 |
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50 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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51 ## Description: Kruskal-Wallis test |
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52 |
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53 function [pval, k, df] = kruskal_wallis_test (varargin) |
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54 |
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55 m = nargin; |
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56 if (m < 2) |
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57 print_usage (); |
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58 endif |
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59 |
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60 n = []; |
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61 p = []; |
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62 |
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63 for i = 1 : m; |
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64 x = varargin{i}; |
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65 if (! isvector (x)) |
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66 error ("kruskal_wallis_test: all arguments must be vectors"); |
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67 endif |
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68 l = length (x); |
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69 n = [n, l]; |
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70 p = [p, (reshape (x, 1, l))]; |
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71 endfor |
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72 |
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73 r = ranks (p); |
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74 |
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75 k = 0; |
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76 j = 0; |
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77 for i = 1 : m; |
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78 k = k + (sum (r ((j + 1) : (j + n(i))))) ^ 2 / n(i); |
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79 j = j + n(i); |
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80 endfor |
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81 |
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82 n = length (p); |
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83 k = 12 * k / (n * (n + 1)) - 3 * (n + 1); |
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84 |
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85 ## Adjust the result to takes ties into account. |
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86 sum_ties = sum (polyval ([1, 0, -1, 0], runlength (sort (p)))); |
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87 k = k / (1 - sum_ties / (n^3 - n)); |
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88 |
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89 df = m - 1; |
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90 pval = 1 - chisquare_cdf (k, df); |
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91 |
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92 if (nargout == 0) |
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93 printf ("pval: %g\n", pval); |
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94 endif |
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95 |
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96 endfunction |
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97 |
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98 ## Test with ties |
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99 %!assert (abs(kruskal_wallis_test([86 86], [74]) - 0.157299207050285) < 0.0000000000001) |
