% -*- texinfo -*-
% @deftypefn {Function File} {[@var{pval}, @var{tsq}] =} hotelling_test_2 (@var{x}, @var{y})
% For two samples @var{x} from multivariate normal distributions with
% the same number of variables (columns), unknown means and unknown
% equal covariance matrices, test the null hypothesis @code{mean
% (@var{x}) == mean (@var{y})}.
%
% Hotelling's two-sample @math{T^2} is returned in @var{tsq}. Under the null,
%
% @tex
% $$
% {n_x+n_y-p-1) T^2 \over p(n_x+n_y-2)}
% $$
% @end tex
% @ifnottex
% @example
% (n_x+n_y-p-1) T^2 / (p(n_x+n_y-2))
% @end example
% @end ifnottex
%
% @noindent
% has an F distribution with @math{p} and @math{n_x+n_y-p-1} degrees of
% freedom, where @math{n_x} and @math{n_y} are the sample sizes and
% @math{p} is the number of variables.
%
% 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