Mercurial > octave
annotate scripts/statistics/tests/u_test.m @ 21634:96518f623c91
Backed out changeset dcf8922b724b
| author | Mike Miller <mtmiller@octave.org> |
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| date | Wed, 20 Apr 2016 11:06:03 -0700 |
| parents | dcf8922b724b |
| children | bac0d6f07a3e |
| rev | line source |
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1 ## Copyright (C) 1995-2015 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3200 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 18 |
| 3454 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {} {[@var{pval}, @var{z}] =} u_test (@var{x}, @var{y}, @var{alt}) |
| 3454 | 21 ## For two samples @var{x} and @var{y}, perform a Mann-Whitney U-test of |
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22 ## the null hypothesis |
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23 ## PROB (@var{x} > @var{y}) == 1/2 == PROB (@var{x} < @var{y}). |
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24 ## |
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25 ## Under the null, the test statistic @var{z} approximately follows a |
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26 ## standard normal distribution. Note that this test is equivalent to the |
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27 ## Wilcoxon rank-sum test. |
| 3200 | 28 ## |
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29 ## With the optional argument string @var{alt}, the alternative of interest |
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30 ## can be selected. If @var{alt} is @qcode{"!="} or @qcode{"<>"}, the null |
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31 ## is tested against the two-sided alternative |
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32 ## PROB (@var{x} > @var{y}) != 1/2. If @var{alt} is @qcode{">"}, the one-sided |
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33 ## alternative PROB (@var{x} > @var{y}) > 1/2 is considered. Similarly for |
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34 ## @qcode{"<"}, the one-sided alternative PROB (@var{x} > @var{y}) < 1/2 is |
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35 ## considered. The default is the two-sided case. |
| 3200 | 36 ## |
| 3454 | 37 ## The p-value of the test is returned in @var{pval}. |
| 3426 | 38 ## |
| 3200 | 39 ## If no output argument is given, the p-value of the test is displayed. |
| 3454 | 40 ## @end deftypefn |
| 3426 | 41 |
| 3200 | 42 ## This implementation is still incomplete---for small sample sizes, |
| 43 ## the normal approximation is rather bad ... | |
| 44 | |
| 5428 | 45 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 46 ## Description: Mann-Whitney U-test |
| 3200 | 47 |
| 48 function [pval, z] = u_test (x, y, alt) | |
| 3426 | 49 |
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50 if (nargin < 2 || nargin > 3) |
| 6046 | 51 print_usage (); |
| 3200 | 52 endif |
| 3426 | 53 |
| 4030 | 54 if (! (isvector (x) && isvector (y))) |
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55 error ("u_test: both X and Y must be vectors"); |
| 3200 | 56 endif |
| 57 | |
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58 n_x = length (x); |
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59 n_y = length (y); |
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60 r = ranks ([(reshape (x, 1, n_x)), (reshape (y, 1, n_y))]); |
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61 z = (sum (r(1 : n_x)) - n_x * (n_x + n_y + 1) / 2) ... |
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62 / sqrt (n_x * n_y * (n_x + n_y + 1) / 12); |
| 3200 | 63 |
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64 cdf = stdnormal_cdf (z); |
| 3426 | 65 |
| 3200 | 66 if (nargin == 2) |
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67 alt = "!="; |
| 3200 | 68 endif |
| 69 | |
| 5443 | 70 if (! ischar (alt)) |
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71 error ("u_test: ALT must be a string"); |
| 3200 | 72 endif |
| 73 if (strcmp (alt, "!=") || strcmp (alt, "<>")) | |
| 74 pval = 2 * min (cdf, 1 - cdf); | |
| 75 elseif (strcmp (alt, ">")) | |
| 76 pval = cdf; | |
| 77 elseif (strcmp (alt, "<")) | |
| 78 pval = 1 - cdf; | |
| 79 else | |
| 3456 | 80 error ("u_test: option %s not recognized", alt); |
| 3200 | 81 endif |
| 82 | |
| 83 if (nargout == 0) | |
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Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
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84 printf (" pval: %g\n", pval); |
| 3200 | 85 endif |
| 3426 | 86 |
| 3200 | 87 endfunction |
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88 |