ABSTRACT
The genesis and reasons for testing hypotheses of proportional means rather than of equal means in aquatic mesocosm studies are presented in this paper. Symbolically, the hypotheses of proportional and equal means may be expressed, respectively, as μT = bμC and μT = μC, with μT and μC standing for the treatment and control means. Special consideration is given to the minimum sample sizes permitted for such studies in the U.S. EPA’s technical guidance document Aquatic Mesocosm Tests to Support Pesticide Registrations. A measure of effect size is defined as a function of b, the coefficient of proportionality, and the within treatments standard deviation. Characteristics of theoretical sampling distributions are summarized for two designs with multiple treatments and for a two-treatment design, all with a minimal total sample size and each with tests for equality of means. Characteristics of empirical sampling distributions are summarized for the two treatment design with tests for proportional means.
