# Kruskal-Wallis one-way analysis of variance

*34,189*pages on

this wiki

## Redirected from Kruskal-Wallis test

Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language |
Individual differences |
Personality |
Philosophy |
Social |

Methods |
Statistics |
Clinical |
Educational |
Industrial |
Professional items |
World psychology |

**Statistics:**
Scientific method ·
Research methods ·
Experimental design ·
Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

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.

## MethodEdit

- 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 alsoEdit

## ReferencesEdit

- 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

This page uses Creative Commons Licensed content from Wikipedia (view authors). |