Statistical power in analyses of population trend data

We developed a Monte Carlo simulation approach to examine statistical power in analysis of population trend data. Our stepwise approach was to perform a regression analysis to test the null hypothesis that the slope of the time series regression line was equal to 0 (i.e., H-o:b = 0 for population count data collected over i years), to use Monte Carlo simulations to calculate the statistical power of the test of H-o:b = 0 when H-o was not rejected, and to estimate sample size requirements within and across years to detect a population trend at a specified power, Type I error, and coefficient of variation. To demonstrate this approach and illustrate important considerations when conducting power analysis, we analyzed 5 sets of shorebird count data collected by a single observer in the International Shorebird Survey, Marco River, Florida, in 1975 and 1980 to 1987. Our approach to determining statistical power in analysis of trends in population count data offers improvements over previously described methods because it is a straightforward approach to simultaneously evaluating the relationship between variance, sample size, effect size, alpha, and power, and it allows assessment over a range of sample sizes, providing a means for planning and evaluating sampling designs for trend tests at multiple levels of statistical precision.