Multiple comparison of entropies with application to dinosaur biodiversity

Did the biodiversity of dinosaurs decline, or did it remain more or less co nstant before their mass extinction 65 million years ago? Sheehan et al. (1 991, Science, 835-839) reported that the biodiversity of families of dinosa ur species remained more or less constant preceding their extinction, sugge sting extinction due to a cataclysmic event such as an asteroid strike. But that claim was based on the incorrect interpretation that a large p value associated with a test of null hypothesis of equality supports that null hy pothesis. To assess whether there is a basis for such a claim, we formulate the problem as one of practical equivalence, in analogy to bioequivalence. We then develop reliable practical equivalence confidence intervals for di fferences of entropies by applying the bootstrap-t technique to a nearly pi votal quantity. Confidence intervals for changes in the biodiversity of din osaurs are then computed, allowing the reader to assess whether there is ev idence of near constancy of dinosaur biodiversity before extinction.