Data set: SameMean
Rank-based nonparametric tests do not answer the same question as the corresponding parametric procedure. Many people assume that these nonparametric tests are testing for group medians. This is not always true. Rank- based tests can be interpreted as testing for the median only if the shapes and scales of the populations are the same. The following exercise illustrates this point by providing an example where the medians and the means are identical but nonparametric tests will reject the null hypothesis.
Use the SameMean data to conduct the Kruskal-Wallis test. Calculate the mean and median for each group. What conclusions can you draw from the data?