% -*- texinfo -*-
% @deftypefn {Function File} {[@var{pval}, @var{k}, @var{df}] =} kruskal_wallis_test (@var{x1}, @dots{})
% Perform a Kruskal-Wallis one-factor 'analysis of variance'.
%
% Suppose a variable is observed for @var{k} > 1 different groups, and
% let @var{x1}, @dots{}, @var{xk} be the corresponding data vectors.
%
% Under the null hypothesis that the ranks in the pooled sample are not
% affected by the group memberships, the test statistic @var{k} is
% approximately chi-square with @var{df} = @var{k} - 1 degrees of
% freedom.
%
% If the data contains ties (some value appears more than once)
% @var{k} is divided by
%
% 1 - @var{sum_ties} / (@var{n}^3 - @var{n})
%
% where @var{sum_ties} is the sum of @var{t}^2 - @var{t} over each group
% of ties where @var{t} is the number of ties in the group and @var{n}
% is the total number of values in the input data. For more info on
% this adjustment see 'Use of Ranks in One-Criterion Variance Analysis'
% in Journal of the American Statistical Association, Vol. 47,
% No. 260 (Dec 1952) by William H. Kruskal and W. Allen Wallis.
%
% The p-value (1 minus the CDF of this distribution at @var{k}) is
% returned in @var{pval}.
%
% If no output argument is given, the p-value is displayed.
% @end deftypefn