Kruskal-Wallis Test

From Q
Jump to: navigation, search

This is a non-parametric version of the F-Test (ANOVA). The test statistic is:

H = (\sum_{j=1}^g\sum_{i=1}^{n_j}w_{ij}-1)\frac{\sum_{j=1}^g\sum_{i=1}^{n_j} w_{ij} (\bar{r}_{\cdot j} - \bar{r})^2}{\sum_{j=1}^g\sum_{i=1}^{n_j} w_{ij} (r_{ij} - \bar{r})^2}


n_j is the number of observations in group j of ggroups,
r_{ij} is the rank of the ith observation from group j where the ranking is computed across all the groups with a 1 assigned to the lowest value and the average rank is used for ties,
n = \sum^g_{j=1} n_j,
w_{ij} is the Calibrated Weight,
\bar{r}_{\cdot j} = \frac{\sum_{i=1}^{n_j}{w_{ij} r_{ij}}}{{\sum_{i=1}^{n_j}w_{ij}}},
\bar{r} = \frac{\sum_{j=1}^g\sum_{i=1}^{n_j}w_{ij} r_{ij}}{\sum_{j=1}^g\sum_{i=1}^{n_j}w_{ij}},
p\approx \Pr(\chi^2_{g-1} \ge H)

See also