# 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.