Abstract
The usual statistical tests of trend are inappropriate for demonstrating the absence of trend. This is because failure to reject the {} hypothesis of no trend does not prove that {} hypothesis. The appropriate statistical method is based on an equivalence test. The {} hypothesis is that the trend is not zero, i.e., outside an a priori specified equivalence region defining trends that are considered to be negligible. This {} hypothesis can be tested with two one-sided tests. A proposed equivalence region for trends in population size is a log-linear regression slope of (20.0346, 0.0346). This corresponds to a half-life or doubling time of 20 years for population size. A less conservative region is (20.0693, 0.0693), which corresponds to a halving or doubling time of 10 years. The approach is illustrated with data on four amphibian populations; one provides significant evidence of no trend.
Keywords
Ambystoma,
amphibian decline,
Desmognathus,
equivalence tests,
population trends,
statistical power,
testing for no effect
Citation
Dixon, Philip M.; Pechmann, Joseph H.K. 2005. A statistical test to show negligible trend. Ecology, 86(7), 2005, pp. 1751?1756