Statistical power in comparative aquaculture studies

A formula is derived for the statistical power in a nested or hierarchical analysis of variance (ANOVA). Data from several salmonid growth trials are analysed to obtain values for the variance between tanks and within tanks in a hierarchical experimental design. These figures are used to calculate the minimum values of fish sample rates and numbers of tanks required to achieve a statistical power of 80% in a comparative experiment; the most cost-effective design is estimated. For a comparative trial using Atlantic salmon from first feeding for a period of 3 months, a design to detect a difference of at least 1.2 g between treatments requires no fewer than five tanks and a sample rate of 5000 individuals from each tank. Using cost estimates from the Marine Institute, an optimal design requires eight tanks and a sample of 77 fish per tank. Smaller values for the variances or a less sensitive experiment will reduce the minimum number of tanks and fish. The calculations are applicable to any hierarchical experiment with appropriate values for the parameters. (C) 2003 Elsevier Science B.V. All rights reserved.