A Common problem in ecology is to determine whether the diversity of a biol
ogical community has changed over time or in response to a disturbance. Thi
s involves testing the null hypothesis that diversity is constant against t
he alternative hypothesis that it has changed. As the power of this test ma
y be low, Fritsch and Hsu (1999, Biometrics 55, 1300-1305) proposed reversi
ng the null and alternative hypothesis. Here, I return to the original form
ulation and point out that power can be improved by adopting a parametric m
odel for relative abundances and by testing against an ordered alternative.