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.