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1 ## Copyright (C) 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 3 of the License, or (at |
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8 ## your option) 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, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {[@var{pval}, @var{tsq}] =} hotelling_test (@var{x}, @var{m}) |
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21 ## For a sample @var{x} from a multivariate normal distribution with unknown |
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22 ## mean and covariance matrix, test the null hypothesis that @code{mean |
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23 ## (@var{x}) == @var{m}}. |
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24 ## |
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25 ## Hotelling's @math{T^2} is returned in @var{tsq}. Under the null, |
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26 ## @math{(n-p) T^2 / (p(n-1))} has an F distribution with @math{p} and |
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27 ## @math{n-p} degrees of freedom, where @math{n} and @math{p} are the |
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28 ## numbers of samples and variables, respectively. |
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29 ## |
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30 ## The p-value of the test is returned in @var{pval}. |
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31 ## |
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32 ## If no output argument is given, the p-value of the test is displayed. |
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33 ## @end deftypefn |
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34 |
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35 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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36 ## Description: Test for mean of a multivariate normal |
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37 |
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38 function [pval, Tsq] = hotelling_test (x, m) |
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39 |
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40 if (nargin != 2) |
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41 print_usage (); |
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42 endif |
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43 |
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44 if (isvector (x)) |
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45 if (! isscalar (m)) |
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46 error ("hotelling_test: if x is a vector, m must be a scalar"); |
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47 endif |
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48 n = length (x); |
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49 p = 1; |
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50 elseif (ismatrix (x)) |
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51 [n, p] = size (x); |
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52 if (n <= p) |
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53 error ("hotelling_test: x must have more rows than columns"); |
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54 endif |
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55 if (isvector (m) && length (m) == p) |
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56 m = reshape (m, 1, p); |
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57 else |
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58 error ("hotelling_test: if x is a matrix, m must be a vector of length columns (x)"); |
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59 endif |
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60 else |
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61 error ("hotelling_test: x must be a matrix or vector"); |
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62 endif |
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63 |
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64 d = mean (x) - m; |
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65 Tsq = n * d * (cov (x) \ d'); |
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66 pval = 1 - f_cdf ((n-p) * Tsq / (p * (n-1)), p, n-p); |
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67 |
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68 if (nargout == 0) |
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69 printf (" pval: %g\n", pval); |
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70 endif |
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71 |
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72 endfunction |
