Statistical power to detect main and interactive effects on the attributes of small-mammal populations

Abstract

Statistical power is an important consideration in the design of experiments, because resources invested in an experiment may be wasted if it is unlikely to produce statistically significant results when real effects or differences exist. Using data from toxicological experiments on seminatural populations of small mammals, we examined the power of statistical tests for main and interactive effects. Our objectives were to evaluate the efficacy of actively reducing within-treatment variation in order to increase power and compare the power provided by several response variables commonly measured in population studies. Controlling population size (N) before treatment increased power to detect effects on N but decreased power to detect effects on population growth (r). For a specified reduction in N, r provided higher power than N. Fractional measures of recruitment generally provided low power, especially when N was low (<20 animals). Power to detect an interaction of two adverse treatments depended on the magnitudes of their main effects, as well as the magnitude of interactive effects. Estimating or predicting effect size is more complex and difficult for interactive effects than for main effects. We conclude that researchers can increase the probability of detecting real effects by choosing response variables with relatively low inherent variability. However, efforts to actively reduce within-treatment variation may have unanticipated repercussions in natural systems.