Detecting trends in raptor counts: power and type I error rates of various statistical tests
We conducted simulations that estimated power and type I error rates of statistical tests for detecting trends in raptor population count data collected from a single monitoring site. Results of the simulations were used to help analyze count data of bald eagles (Haliaeetus leucocephalus) from 7 national forests in Michigan, Minnesota, and Wisconsin during 1980-1989. Seven statistical tests were evaluated, including simple linear regression on the log scale and linear regression with a permutation test. Using 1,000 replications each, we simulated n = 10 and n = 50 years of count data and trends ranging from -5 to 5% change/year. We evaluated the tests at 3 critical levels (alpha = 0.01, 0.05, and 0.10) for both upper- and lower-tailed tests. Exponential count data were simulated by adding sampling error with a coefficient of variation of 40% from either a log-normal or autocorrelated log-normal distribution. Not surprisingly, tests performed with 50 years of data were much more powerful than tests with 10 years of data. Positive autocorrelation inflated alpha-levels upward from their nominal levels, making the tests less conservative and more likely to reject the null hypothesis of no trend. Of the tests studied, Cox and Stuart's test and Pollard's test clearly had lower power than the others. Surprisingly, the linear regression t-test, Collins' linear regression permutation test, and the nonparametric Lehmann's and Mann's tests all had similar power in our simulations. Analyses of the count data suggested that bald eagles had increasing trends on at least 2 of the 7 national forests during 1980-1989.