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Multiple comparison of entropies with application to dinosaur biodiversity. (English) Zbl 1059.62647

Summary: Did the biodiversity of dinosaurs decline, or did it remain more or less constant before their mass extinction 65 million years ago? Sheehan et al. [Science, 835–839 (1991)] reported that the biodiversity of families of dinosaur species remained more or less constant preceding their extinction, suggesting 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 hypothesis. 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 differences of entropies by applying the bootstrap-t technique to a nearly pivotal quantity. Confidence intervals for changes in the biodiversity of dinosaurs are then computed, allowing the reader to assess whether there is evidence of near constancy of dinosaur biodiversity before extinction.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J15 Paired and multiple comparisons; multiple testing
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References:

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