Statistics Toolbox

Kruskal-Wallis Test

In One-Way Analysis of Variance (ANOVA) we used one-way analysis of variance to determine if the bacteria counts of milk varied from shipment to shipment. Our one-way analysis rested on the assumption that the measurements were independent, and that each had a normal distribution with a common variance and with a mean that was constant in each column. We concluded that the column means were not all the same. Let's repeat that analysis using a nonparametric procedure.

The Kruskal-Wallis test is a nonparametric version of one-way analysis of variance. The assumption behind this test is that the measurements come from a continuous distribution, but not necessarily a normal distribution. The test is based on an analysis of variance using the ranks of the data values, not the data values themselves. Output includes a table similar to an anova table, and a box plot.

We can run this test as follows.

• p = kruskalwallis(hogg)
  p =
      0.0020
  

The low p-value means the Kruskal-Wallis test results agree with the one-way analysis of variance results.

Robust Regression

Friedman's Test