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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, z] = wilcoxon_test (x, y [, alt]) |
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18 ## |
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19 ## For two matched-pair sample vectors x and y, perform a Wilcoxon |
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20 ## signed-rank test of the null hypothesis PROB(x > y) == 1/2. |
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21 ## Under the null, the test statistic z approximately follows a |
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22 ## standard normal distribution. |
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23 ## |
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24 ## With the optional argument string alt, the alternative of interest |
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25 ## can be selected. |
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26 ## If alt is "!=" or "<>", the null is tested against the two-sided |
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27 ## alternative PROB(x > y) != 1/2. |
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28 ## If alt is ">", the one-sided alternative PROB(x > y) > 1/2 is |
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29 ## considered, similarly for "<". |
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30 ## The default is the two-sided case. |
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31 ## |
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32 ## pval is the p-value of the test. |
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33 ## |
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34 ## If no output argument is given, the p-value of the test is displayed. |
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35 |
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36 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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37 ## Description: Wilcoxon signed-rank test |
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38 |
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39 function [pval, z] = wilcoxon_test (x, y, alt) |
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40 |
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41 if ((nargin < 2) || (nargin > 3)) |
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42 usage ("[pval, z] = wilcoxon_test (x, y [, alt])"); |
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43 endif |
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44 |
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45 if (! (is_vector (x) && is_vector (y) && (length (x) == length (y)))) |
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46 error ("wilcoxon_test: x and y must be vectors of the same length"); |
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47 endif |
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48 |
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49 n = length (x); |
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50 x = reshape (x, 1, n); |
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51 y = reshape (y, 1, n); |
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52 d = x - y; |
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53 d = d (find (d != 0)); |
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54 n = length (d); |
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55 if (n > 0) |
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56 r = ranks (abs (d)); |
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57 z = sum (r (find (d > 0))); |
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58 z = ((z - n * (n + 1) / 4) / sqrt (n * (n + 1) * (2 * n + 1) / 24)); |
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59 else |
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60 z = 0; |
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61 endif |
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62 |
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63 cdf = stdnormal_cdf (z); |
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64 |
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65 if (nargin == 2) |
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66 alt = "!="; |
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67 endif |
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68 |
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69 if (! isstr (alt)) |
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70 error("wilcoxon_test: alt must be a string"); |
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71 elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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72 pval = 2 * min (cdf, 1 - cdf); |
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73 elseif (strcmp (alt, ">")) |
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74 pval = 1 - cdf; |
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75 elseif (strcmp (alt, "<")) |
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76 pval = cdf; |
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77 else |
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78 error (sprintf ("wilcoxon_test: option %s not recognized", alt)); |
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79 endif |
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80 |
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81 if (nargout == 0) |
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82 printf (" pval: %g\n", pval); |
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83 endif |
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84 |
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85 endfunction |
