Kruskal-Wallis rank sum test

KruskalWallisTest{T<:Real}(groups::AbstractVector{T}...)

Perform Kruskal Wallis rank sum test of the null hypothesis that the location parameters of the distribution of the \(n\) observations are the same in each of the groups \(\mathcal{G}\) against the alternative hypothesis that they differ in at least one.

The Kruskal-Wallis test is an extension of the Mann-Whitney U test to more than two groups.

The p-value is computed using a chi-square approximation to the distribution of the test statistic \(H_c=\frac H C\):

\[\begin{split}H &= \frac{12}{n(n+1)} \sum_{g \in \mathcal{G}} \frac{R_g^2}{n_g} - 3(n+1)\\ C &= 1-\frac{1}{n^3-n}\sum_{t \in \mathcal{T}} (t^3-t),\end{split}\]

where \(\mathcal{T}\) is the set of the counts of tied values at each tied position, \(n_g\) is the number of observations and \(R_g\) is the rank sum in group g. See references for further details.

Implements: pvalue

References:

  • Meyer, J.P, Seaman, M.A., Expanded tables of critical values for the Kruskal-Wallis H statistic. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, April 2006.