## Copyright (C) 2014 Tony Richardson ## ## 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{h}, @var{pval}, @var{ci}, @var{stats} ] =} ## vartest (@var{x}, @var{y}) ## ## {[@var{h}, @var{pval}, @var{ci}, @var{stats} ] =} ## vartest (@var{x}, @var{y}, @var{Name}, @var{Value}) ## ## Perform a F-test for equal variances. ## ## If the second argument @var{y} is a vector, a paired-t test of the ## hypothesis mean(x) = mean(y) is performed. ## ## The argument @var{alpha} can be used to specify the significance level ## of the test (the default value is 0.05). The string ## argument @var{tail}, can be used to select the desired alternative ## hypotheses. If @var{alt} is @qcode{"both"} (default) the null is ## tested against the two-sided alternative @code{mean (@var{x}) != @var{m}}. ## If @var{alt} is @qcode{"right"} the one-sided ## alternative @code{mean (@var{x}) > @var{m}} is considered. ## Similarly for @qcode{"left"}, the one-sided alternative @code{mean ## (@var{x}) < @var{m}} is considered. When @var{vartype} is 'equal' ## the variances are assumed to be equal (this is the default). When ## @var{vartype} is 'unequal' the variances are not assumed equal. ## When argument @var{x} is a matrix the @var{dim} argument can be ## used to selection the dimension over which to perform the test. ## (The default is the first non-singleton dimension.) ## ## If @var{h} is 0 the null hypothesis is accepted, if it is 1 the null ## hypothesis is rejected. The p-value of the test is returned in @var{pval}. ## A 100(1-alpha)% confidence interval is returned in @var{ci}. @var{stats} ## is a structure containing the value of the test statistic (@var{tstat}), ## the degrees of freedom (@var{df}) and the sample standard deviation ## (@var{sd}). ## ## @end deftypefn ## Author: Tony Richardson ## Description: Test for mean of a normal sample with known variance function [h, p, ci, stats] = vartest(x, v, varargin) % Set default arguments alpha = 0.05; tail = 'both'; % Find the first non-singleton dimension of x dim = min(find(size(x)~=1)); if isempty(dim), dim = 1; end i = 1; while ( i <= length(varargin) ) switch lower(varargin{i}) case 'alpha' i = i + 1; alpha = varargin{i}; case 'tail' i = i + 1; tail = varargin{i}; case 'dim' i = i + 1; dim = varargin{i}; otherwise error('Invalid Name argument.',[]); end i = i + 1; end if ~isa(tail, 'char') error('tail argument to vartest must be a string\n',[]); end s_var = var(x, 0, dim); df = size(x, dim) - 1; stats.chisqstat = df*s_var/v; % Based on the "tail" argument determine the P-value, the critical values, % and the confidence interval. switch lower(tail) case 'both' p = 2*chi2cdf(stats.chisqstat,df); i = (p > 1); p(i) = 2*(1-chi2cdf(stats.chisqstat(i),df)); ci = [df*s_var ./ (chi2inv(1-alpha/2,df)); df*s_var ./ (chi2inv(alpha/2,df))]; case 'left' p = chi2cdf(stats.chisqstat,df); chi2crit = chi2inv(alpha,df); ci = [zeros(size(stats.chisqstat)); df*s_var ./ (chi2inv(alpha,df))]; case 'right' p = 1 - chi2cdf(stats.chisqstat,df); chi2crit = chi2inv(1-alpha,df); ci = [df*s_var ./ (chi2inv(1-alpha,df)); inf*ones(size(stats.chisqstat))]; otherwise error('Invalid fourth (tail) argument to vartest\n',[]); end % Reshape the ci array to match MATLAB shaping if and(isscalar(stats.chisqstat), dim==2) ci = ci(:)'; elseif size(stats.chisqstat,2)