Hypothesis testing with Raoʹs quadratic entropy and its application to Dinosaur biodiversity

Entropy indices, such as Shannon entropy and Gini-Simpson index, have been used for analysing biological diversities. However, these entropy indices are based on abundance of the species only and they do not take differences between the species into consideration. Rao’s quadratic entropy has found many applications in different fields including ecology. Further, the quadratic entropy (QE) index is the only ecological diversity index that reflects both the differences and abundances of the species. The problem of testing of hypothesis of the equality of QEs is formulated as a problem of comparing practical equivalence intervals. Simulation experiments are used to compare various equivalence intervals. Previously analyzed dinosaur data are used to illustrate the methods for determining biodiversity.