A statistical test to show negligible trend

The usual statistical tests of trend are inappropriate for demonstrating the absence of trend. This is because failure to reject the null hypothesis of no trend does not prove that null hypothesis. The appropriate statistical method is based on an equivalence test. The null 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 null 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 (-0.0346, 0.0346). This corresponds to a half-life or doubling time of 20 years for population size. A less conservative region is (-0.0693, 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.