# Kruskal-Wallis one-way analysis of variance

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In statistics, the **Kruskal-Wallis one-way analysis of variance** by ranks (named after William Kruskal and Allen Wallis) is a non-parametric method. Intuitively, it is identical to a one-way analysis of variance, with the data replaced by their ranks.

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: , where:
- is the number of observations in group
- is observation from group
- is the total number of observations across all groups
- ,
- is the average of all the , equal to .
- Notice that the denominator of the expression for is exactly .

- Finally, the p-value is approximated by . If some n
_{i}'s are small the distribution of K can be quite different from this.

## See also

## References

- William H. Kruskal and W. Allen Wallis. Use of ranks in one-criterion variance analysis.
*Journal of the American Statistical Association***47**(260): 583–621, December 1952.es:Prueba de Kruskal-Wallis

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