Title: Statistical power analysis in fish growth studies

Final project
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Supervisors: Helgi Thorarensen


The objective of this project was to estimate the variance in growth studies of different species of fish and use this information to model the expected effects of number of replications and individuals within replication on the statistical power of fish growth studies. Coefficient of variation amongst fish in the same tank (CV-error) and among tanks receiving the same treatment (CV-within) were calculated from 24 independent growth studies on Arctic charr, Atlantic cod, turbot, halibut and tilapia. This information was then used to estimate the effect of number of replications and fish within each tank (n) on the statistical power when effect size was 15% of the grand mean. Furthermore, the effect of replication, and n the minimum effect size that would give 80% statistical power was estimated. Both CV-error and CV-within increased during the experiments and in most studies they stabilised. The mean final CV-error was 30.6±1% and ranged from 15% to 56%. The CV-within treatment ranged from 0% to 12% with a mean value of 4.5±0.04%. Both CV-error and CV-within decrease with fish body mass (P < 0.05); and their values at termination are positively correlated (P < 0.05) with those at stocking. As expected, statistical power increased when n and level of replication increased. The statistical power nearly doubled when the level of replication increased from duplicate to triplicate. However, further increase in replication had smaller effect on statistical power. When CV-error and CV-within were at mean levels, the statistical power increased with sample size up to an n of 50-100. Beyond that, comparatively less effect is realised. Effect size less than 20% of the grand mean with statistical power over 80% is only attainable when the CV-within is less than 5%. Effect size less than 10% is attainable when CV-within is low and treatments are tested at least in triplicates. The results suggest that when CV-error and CV-within are medium or low the optimum design of growth experiments is to test treatments in triplicates or quadruplicates with n of 50-100 individuals. Special effort should be made to keep variance between tanks receiving the same treatment at minimum in order to minimize effect size.

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