Kruskal-wallis One-way Analysis Of Variance

Since it is a non-parametric method, the Kruskal-Wallis test does not assume a Normal population, unlike the analogous one-way Analysis Of Variance .

METHOD

# Rank all data from all groups together.
# The test statistic is given by:

K = (N-1)rac{\sum_{i=1}^g n_i(\bar{r}_{i\cdot} - \bar{r})^2}{\sum_{i=1}^g\sum_{j=1}^{n_i}(r_{ij} - \bar{r})^2}

, where:

$n_g$ is the number of observations in group $g$

$r_{ij}$ is observation $j$ from group $i$

$N$ is the total number of observations across all groups

$\bar{r}_{i\cdot} = rac{\sum_{j=1}^{n_i}{r_{ij}}}{n_i}$ ,

$\bar{r}$ is the average of all the $r_{ij}$ , equal to $(N+1)/2$ .

:Notice that the denominator of the expression for $K$ is exactly $(N-1)N(N+1)/12$ .

P-value

\mathbf{P}(\chi^2_{N-g} \ge K)

	CATEGORIES ABOUT KRUSKAL-WALLIS ONE-WAY ANALYSIS OF VARIANCE

	statistical tests

	analysis of variance

	non-parametric statistics

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Kruskal-wallis One-way Analysis Of Variance

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