When to use it The most common use of the Kruskal—Wallis test is when you have one nominal variable and one measurement variable , an experiment that you would usually analyze using one-way anova , but the measurement variable does not meet the normality assumption of a one-way anova. Figure 5: Graphing the results It is tricky to know how to visually display the results of a Kruskal—Wallis test. For this reason, I don't recommend the Kruskal-Wallis test as an alternative to one-way anova.
There would be a large difference in the central tendencies. Wilcoxon signed-rank test. Similar tests One-way anova is more powerful and a lot easier to understand than the Kruskal—Wallis test, so unless you have a true ranked variable, you should use it. In the case of three groups with only four units in each, the pattern would, for example, look as follows:. In this example, SPSS produces a p-value of.
Dominance in relation to age, sex, and competitive contexts in a group of free-ranging domestic dogs. What's new? You calculate the sum of the ranks for each group, then the test statistic, H. Cafazzo et al. H is given by a rather formidable formula that basically represents the variance of the ranks among groups, with an adjustment for the number of ties. Paired t —test.
Gravetter, F. It gives a P value of 0. Handbook of Biological Statistics John H. If there are relatively small number of observations, you could put the individual observations on a bar graph, with the value of the measurement variable on the Y axis and its rank on the X axis, and use a different pattern for each value of the nominal variable.
If there are values with the same characteristics in the different samples, i. Figure 1: Mean ranks Note: Some people have the attitude that unless you have a large sample size and can clearly demonstrate that your data are normal, you should routinely use Kruskal—Wallis; they think it is dangerous to use one-way anova, which assumes normality, when you don't know for sure that your data are normal.
N less than 5 in each group seems to be the accepted definition of "too small. For the example data, the mean rank for DNA is 10.
I have put together a spreadsheet to do the Kruskal—Wallis test on up to 20 groups, with up to 1000 observations per group. It tests whether the mean ranks are the same in all the groups. Kinds of biological variables.