### Kruskal-Wallis and multiple comparisons

#### Chapter 3 continued

__The Kruskal-Wallis test__

The KW statistic has the form of SST based on ranks, so a permutation KW
test can be based on SST(ranks). Alternatively, we can obtain a large sample approximation
to the permutation distribution by using a scaling factor of 1/S_{R}^{2
}, where S_{R}^{2} = N(N+1)/12 for
ranks without ties.

For data sets with ties, S_{R}^{2}
is calculated as the sample variance of the adjusted ranks.

__Conditions favoring the K-W test; use of general scores.__