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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 2, or (at your option) |
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8 ## any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{pval}, @var{z}] =} u_test (@var{x}, @var{y}, @var{alt}) |
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22 ## For two samples @var{x} and @var{y}, perform a Mann-Whitney U-test of |
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23 ## the null hypothesis PROB (@var{x} > @var{y}) == 1/2 == PROB (@var{x} |
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24 ## < @var{y}). Under the null, the test statistic @var{z} approximately |
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25 ## follows a standard normal distribution. Note that this test is |
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26 ## equivalent to the Wilcoxon rank-sum test. |
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27 ## |
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28 ## With the optional argument string @var{alt}, the alternative of |
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29 ## interest can be selected. If @var{alt} is @code{"!="} or |
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30 ## @code{"<>"}, the null is tested against the two-sided alternative |
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31 ## PROB (@var{x} > @var{y}) != 1/2. If @var{alt} is @code{">"}, the |
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32 ## one-sided alternative PROB (@var{x} > @var{y}) > 1/2 is considered. |
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33 ## Similarly for @code{"<"}, the one-sided alternative PROB (@var{x} > |
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34 ## @var{y}) < 1/2 is considered. The default is the two-sided case. |
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35 ## |
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36 ## The p-value of the test is returned in @var{pval}. |
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37 ## |
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38 ## If no output argument is given, the p-value of the test is displayed. |
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39 ## @end deftypefn |
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40 |
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41 ## This implementation is still incomplete---for small sample sizes, |
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42 ## the normal approximation is rather bad ... |
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43 |
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44 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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45 ## Description: Mann-Whitney U-test |
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46 |
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47 function [pval, z] = u_test (x, y, alt) |
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48 |
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49 if ((nargin < 2) || (nargin > 3)) |
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50 print_usage (); |
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51 endif |
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52 |
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53 if (! (isvector (x) && isvector (y))) |
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54 error ("u_test: both x and y must be vectors"); |
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55 endif |
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56 |
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57 n_x = length (x); |
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58 n_y = length (y); |
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59 r = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]); |
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60 z = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ... |
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61 / sqrt (n_x * n_y * (n_x + n_y + 1) / 12); |
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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 (! ischar (alt)) |
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70 error("u_test: alt must be a string"); |
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71 endif |
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72 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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73 pval = 2 * min (cdf, 1 - cdf); |
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74 elseif (strcmp (alt, ">")) |
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75 pval = cdf; |
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76 elseif (strcmp (alt, "<")) |
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77 pval = 1 - cdf; |
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78 else |
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79 error ("u_test: option %s not recognized", alt); |
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80 endif |
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81 |
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82 if (nargout == 0) |
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83 printf (" pval: %g\n", pval); |
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84 endif |
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85 |
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86 endfunction |
