Testing for Bounded Trend: Amphibian Declines and Amphibian Fluctuations
 
by
 
Philip Dixon, Savannah River Ecology Lab, University of Georgia
 
Abstract
 

In many studies, the absence of trend is as interesting as the presence of a trend. For example, part of an ongoing debate about amphibian decline focuses on the interpretation of studies that show no significant decline. Are these populations first-order stationary (lacking a meaningful trend), or are important trends masked by large random fluctuations? This can be answered by considering tests of the interval null hypothesis that the observed trend lies outside of a region considered equivalent to no trend. I develop tests of bounded trend for two commonly used trend statistics: log-linear slope and Kendall's tau. Asymptotic properties of Kendall's tau for non-null trends are briefly described. Bootstrapping and permutation approaches are shown to give slightly different answers. These tests are used to evaluate trend and the absence of trend in three amphibian populations.