Kruskal-Wallis Test
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Example: the yield of 15 plots under three different fertilizers, five plots each. Does any fertilizer tend to yield more — without assuming the data are normal? Change the values to work out your own case.
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What each term means
- Statistic H
- Measures how far the groups' mean ranks are from the overall mean rank. With no difference between groups, it roughly follows a chi-square with k − 1 degrees of freedom.
- Scale Factor
- N is the total number of observations. The factor puts H on the chi-square's scale.
- Sum of Squared Ranks (Rⱼ²/nⱼ)
- Rⱼ is the sum of group j's ranks, after sorting all the values together. Groups with high values gather high ranks.
- Expected Value (3(N + 1))
- What the sum would give if every group had the same mean rank, (N + 1)/2. Subtracted, it leaves just the deviation.
When to use it, assumptions and alternatives: the Kruskal-Wallis test in the statistical tests catalog.