Mercurial > octave
annotate scripts/statistics/tests/hotelling_test_2.m @ 23084:ef4d915df748
maint: Merge stable to default.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 23 Jan 2017 14:27:48 -0500 |
| parents | 3a2b891d0b33 e9a0469dedd9 |
| children | 092078913d54 |
| rev | line source |
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1 ## Copyright (C) 1996-2016 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 | |
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7 ## the Free Software Foundation; either version 3 of the License, or |
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8 ## (at 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 |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 ## GNU General Public License for more details. |
| 3426 | 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{tsq}] =} hotelling_test_2 (@var{x}, @var{y}) |
| 3454 | 21 ## For two samples @var{x} from multivariate normal distributions with |
| 22 ## the same number of variables (columns), unknown means and unknown | |
| 23 ## equal covariance matrices, test the null hypothesis @code{mean | |
| 24 ## (@var{x}) == mean (@var{y})}. | |
| 3200 | 25 ## |
| 6754 | 26 ## Hotelling's two-sample @math{T^2} is returned in @var{tsq}. Under the null, |
| 27 ## @tex | |
| 28 ## $$ | |
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29 ## {(n_x+n_y-p-1) T^2 \over p(n_x+n_y-2)} |
| 6754 | 30 ## $$ |
| 31 ## @end tex | |
| 32 ## @ifnottex | |
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33 ## |
| 3454 | 34 ## @example |
| 35 ## (n_x+n_y-p-1) T^2 / (p(n_x+n_y-2)) | |
| 36 ## @end example | |
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37 ## |
| 6754 | 38 ## @end ifnottex |
| 3454 | 39 ## @noindent |
| 40 ## has an F distribution with @math{p} and @math{n_x+n_y-p-1} degrees of | |
| 41 ## freedom, where @math{n_x} and @math{n_y} are the sample sizes and | |
| 42 ## @math{p} is the number of variables. | |
| 43 ## | |
| 44 ## The p-value of the test is returned in @var{pval}. | |
| 3200 | 45 ## |
| 46 ## If no output argument is given, the p-value of the test is displayed. | |
| 3454 | 47 ## @end deftypefn |
| 3200 | 48 |
| 5428 | 49 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 50 ## Description: Compare means of two multivariate normals |
| 3426 | 51 |
| 3200 | 52 function [pval, Tsq] = hotelling_test_2 (x, y) |
| 3426 | 53 |
| 3200 | 54 if (nargin != 2) |
| 6046 | 55 print_usage (); |
| 3200 | 56 endif |
| 3426 | 57 |
| 4030 | 58 if (isvector (x)) |
| 3200 | 59 n_x = length (x); |
| 4030 | 60 if (! isvector (y)) |
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61 error ("hotelling_test_2: if X is a vector, Y must also be a vector"); |
| 3200 | 62 else |
| 63 n_y = length (y); | |
| 64 p = 1; | |
| 65 endif | |
| 4030 | 66 elseif (ismatrix (x)) |
| 3200 | 67 [n_x, p] = size (x); |
| 68 [n_y, q] = size (y); | |
| 69 if (p != q) | |
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70 error ("hotelling_test_2: X and Y must have the same number of columns"); |
| 3200 | 71 endif |
| 72 else | |
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73 error ("hotelling_test_2: X and Y must be matrices (or vectors)"); |
| 3200 | 74 endif |
| 3426 | 75 |
| 3200 | 76 d = mean (x) - mean (y); |
| 77 S = ((n_x - 1) * cov (x) + (n_y - 1) * cov (y)) / (n_x + n_y - 2); | |
| 78 Tsq = (n_x * n_y / (n_x + n_y)) * d * (S \ d'); | |
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79 pval = 1 - fcdf ((n_x + n_y - p - 1) * Tsq / (p * (n_x + n_y - 2)), |
| 3426 | 80 p, n_x + n_y - p - 1); |
| 81 | |
| 3200 | 82 if (nargout == 0) |
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83 printf (" pval: %g\n", pval); |
| 3200 | 84 endif |
| 3426 | 85 |
| 6754 | 86 endfunction |