% -*- 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

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