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1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2006, 2007 |
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2 ## 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{z}] =} wilcoxon_test (@var{x}, @var{y}, @var{alt}) |
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22 ## For two matched-pair sample vectors @var{x} and @var{y}, perform a |
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23 ## Wilcoxon signed-rank test of the null hypothesis PROB (@var{x} > |
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24 ## @var{y}) == 1/2. Under the null, the test statistic @var{z} |
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25 ## approximately follows a standard normal distribution when @var{n} > 25. |
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26 ## |
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27 ## @strong{Warning}: This function assumes a normal distribution for @var{z} |
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28 ## and thus is invalid for @var{n} <= 25. |
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29 ## |
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30 ## With the optional argument string @var{alt}, the alternative of |
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31 ## interest can be selected. If @var{alt} is @code{"!="} or |
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32 ## @code{"<>"}, the null is tested against the two-sided alternative |
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33 ## PROB (@var{x} > @var{y}) != 1/2. If alt is @code{">"}, the one-sided |
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34 ## alternative PROB (@var{x} > @var{y}) > 1/2 is considered. Similarly |
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35 ## for @code{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < |
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36 ## 1/2 is considered. The default is the two-sided case. |
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37 ## |
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38 ## The p-value of the test is returned in @var{pval}. |
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39 ## |
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40 ## If no output argument is given, the p-value of the test is displayed. |
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41 ## @end deftypefn |
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42 |
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43 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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44 ## Description: Wilcoxon signed-rank test |
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45 |
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46 function [pval, z] = wilcoxon_test (x, y, alt) |
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47 |
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48 if (nargin < 2 || nargin > 3) |
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49 print_usage (); |
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50 endif |
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51 |
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52 if (! (isvector (x) && isvector (y) && (length (x) == length (y)))) |
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53 error ("wilcoxon_test: x and y must be vectors of the same length"); |
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54 endif |
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55 |
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56 n = length (x); |
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57 x = reshape (x, 1, n); |
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58 y = reshape (y, 1, n); |
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59 d = x - y; |
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60 d = d (find (d != 0)); |
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61 n = length (d); |
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62 if (n > 25) |
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63 r = ranks (abs (d)); |
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64 z = sum (r (find (d > 0))); |
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65 z = ((z - n * (n + 1) / 4) / sqrt (n * (n + 1) * (2 * n + 1) / 24)); |
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66 else |
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67 error ("wilcoxon_test: implementation requires more than 25 different pairs"); |
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68 endif |
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69 |
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70 cdf = stdnormal_cdf (z); |
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71 |
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72 if (nargin == 2) |
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73 alt = "!="; |
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74 endif |
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75 |
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76 if (! ischar (alt)) |
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77 error("wilcoxon_test: alt must be a string"); |
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78 elseif (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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79 pval = 2 * min (cdf, 1 - cdf); |
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80 elseif (strcmp (alt, ">")) |
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81 pval = 1 - cdf; |
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82 elseif (strcmp (alt, "<")) |
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83 pval = cdf; |
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84 else |
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85 error ("wilcoxon_test: option %s not recognized", alt); |
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86 endif |
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87 |
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88 if (nargout == 0) |
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89 printf (" pval: %g\n", pval); |
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90 endif |
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91 |
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92 endfunction |
