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Backed out changeset dcf8922b724b
author Mike Miller <mtmiller@octave.org>
date Wed, 20 Apr 2016 11:06:03 -0700
parents dcf8922b724b
children bac0d6f07a3e
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1 ## Copyright (C) 1996-2015 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 {} {[@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
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23 ## @code{mean (@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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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 - fcdf ((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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72 endfunction
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