# Eta-squared from Kruskal-Wallis in R

Is it possible to calculate Eta-squared from Kruskal-Wallis test results? I know how to do it by hand for the ANOVA or Mann-Whitney using the Z-statistics, but i must use the KW test for my current data. The KW test using the "kruskal.test" function gives a "Chi-squared" value instead of Z-statistics, so i am not sure how to do it by hand.

I need to make conclusions that "factor (X) explains ___ of the variance in Y". So producing Eta-squared (or similar) is necessary.

Thank you

• You can't say much about the variance since it is a rank-based test. – Michael M Oct 25 '19 at 6:22
• What makes you say you must do a Kruskal-Wallis test? – Glen_b Oct 26 '19 at 6:45

## 1 Answer

There is an effect size statistic for the Kruskal-Wallis test called "eta-squared". For the calculation, see Tomczak and Tomczak ( http://tss.awf.poznan.pl/files/3_Trends_Vol21_2014__no1_20.pdf ). This statistic is in fact based on the H statistic, not the z value. However, as @michaelm points out, the interpretation of this "eta-squared" will not be about the variance. I have some reluctance about this statistic, and the related epsilon-squared, as it seems that most readers don't have a good sense of how to interpret the value. There are other options for effect size statistics. My recommendation would be pairwise or maximum Vargha and Delaney's A. There's some discussion of effect size statisitcs for KW here: https://www.researchgate.net/post/Anyone_know_how_to_calculate_eta_squared_for_a_Kruskal-Wallis_analysis .