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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 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{pval}, @var{chisq}, @var{df}] =} chisquare_test_homogeneity (@var{x}, @var{y}, @var{c}) |
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19 ## Given two samples @var{x} and @var{y}, perform a chisquare test for |
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20 ## homogeneity of the null hypothesis that @var{x} and @var{y} come from |
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21 ## the same distribution, based on the partition induced by the |
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22 ## (strictly increasing) entries of @var{c}. |
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23 ## |
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24 ## For large samples, the test statistic @var{chisq} approximately follows a |
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25 ## chisquare distribution with @var{df} = @code{length (@var{c})} |
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26 ## degrees of freedom. |
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27 ## |
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28 ## The p-value (1 minus the CDF of this distribution at @var{chisq}) is |
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29 ## returned in @var{pval}. |
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30 ## |
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31 ## If no output argument is given, the p-value is displayed. |
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32 ## @end deftypefn |
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33 |
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34 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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35 ## Description: Chi-square test for homogeneity |
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36 |
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37 function [pval, chisq, df] = chisquare_test_homogeneity (x, y, c) |
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38 |
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39 if (nargin != 3) |
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40 usage ("[pval, chisq, df] = chisquare_test_homogeneity (x, y, c)"); |
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41 endif |
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42 |
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43 if (! (is_vector(x) && is_vector(y) && is_vector(c))) |
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44 error ("chisquare_test_homogeneity: x, y and c must be vectors"); |
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45 endif |
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46 ## Now test c for strictly increasing entries |
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47 df = length (c); |
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48 if (any ( (c(2 : df) - c(1 : (df - 1))) <= 0)) |
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49 error ("chisquare_test_homogeneity: c must be increasing"); |
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50 endif |
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51 |
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52 c = [(reshape (c, 1, df)), Inf]; |
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53 l_x = length (x); |
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54 x = reshape (x, l_x, 1); |
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55 n_x = sum (x * ones (1, df+1) < ones (l_x, 1) * c); |
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56 l_y = length (y); |
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57 y = reshape (y, l_y, 1); |
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58 n_y = sum(y * ones (1, df+1) < ones (l_y, 1) * c); |
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59 chisq = l_x * l_y * sum ((n_x/l_x - n_y/l_y).^2 ./ (n_x + n_y)); |
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60 pval = 1 - chisquare_cdf (chisq, df); |
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61 |
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62 if (nargout == 0) |
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63 printf(" pval: %g\n", pval); |
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64 endif |
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65 |
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66 endfunction |
