X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Fstatistics%2Ftests%2Fhotelling_test.m;fp=octave_packages%2Fm%2Fstatistics%2Ftests%2Fhotelling_test.m;h=6759a35178b01d16d0592899f0bd1d9986bc7505;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278 diff --git a/octave_packages/m/statistics/tests/hotelling_test.m b/octave_packages/m/statistics/tests/hotelling_test.m new file mode 100644 index 0000000..6759a35 --- /dev/null +++ b/octave_packages/m/statistics/tests/hotelling_test.m @@ -0,0 +1,72 @@ +## Copyright (C) 1996-2012 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{pval}, @var{tsq}] =} hotelling_test (@var{x}, @var{m}) +## For a sample @var{x} from a multivariate normal distribution with unknown +## mean and covariance matrix, test the null hypothesis that @code{mean +## (@var{x}) == @var{m}}. +## +## Hotelling's @math{T^2} is returned in @var{tsq}. Under the null, +## @math{(n-p) T^2 / (p(n-1))} has an F distribution with @math{p} and +## @math{n-p} degrees of freedom, where @math{n} and @math{p} are the +## numbers of samples and variables, respectively. +## +## The p-value of the test is returned in @var{pval}. +## +## If no output argument is given, the p-value of the test is displayed. +## @end deftypefn + +## Author: KH +## Description: Test for mean of a multivariate normal + +function [pval, Tsq] = hotelling_test (x, m) + + if (nargin != 2) + print_usage (); + endif + + if (isvector (x)) + if (! isscalar (m)) + error ("hotelling_test: if X is a vector, M must be a scalar"); + endif + n = length (x); + p = 1; + elseif (ismatrix (x)) + [n, p] = size (x); + if (n <= p) + error ("hotelling_test: X must have more rows than columns"); + endif + if (isvector (m) && length (m) == p) + m = reshape (m, 1, p); + else + error ("hotelling_test: if X is a matrix, M must be a vector of length columns (X)"); + endif + else + error ("hotelling_test: X must be a matrix or vector"); + endif + + d = mean (x) - m; + Tsq = n * d * (cov (x) \ d'); + pval = 1 - fcdf ((n-p) * Tsq / (p * (n-1)), p, n-p); + + if (nargout == 0) + printf (" pval: %g\n", pval); + endif + +endfunction