Testing the homogeneity of diversity measures: a general framework

We discuss the problem of testing the homogeneity of entropy (or diversity) measures, as an extension of asymptotic results concerning the distribution of a reasonable homogeneity statistic. The proposed improvements are based upon corrections similar to those of Satterwhaitte and other authors. As an alternative approach, we also consider a bootstrap procedure. The problem of making multiple comparisons of diversity measures is considered, using either an asymptotic or a bootstrap approach. The use of these methods is illustrated using data, concerning the problem of the extinction of dinosaurs. Finally, we present the results of a simulation study, to determine the relative merits of these methods. The main conclusion is that the corrections to the asymptotic theory and the bootstrap procedure show a good balance between precision and moderate computational cost.