Experimental design and statistical analyses of fish growth studies

Abstract

Every year, numerous studies are published that compare the effects of different factors on the growth of aquaculture fish. However, comparatively little attention has been given to the experimental designs of these studies - in how many rearing units should each treatment be replicated, how many fish should be in each tank (n) and how should the data be analysed. The reliability of the results increases with increased replication and n. In reality, however, the experimental design must strike a balance between limited resources and the reliability of the statistical analysis. A survey of recent publications in Aquaculture suggests, that most (83%) aquaculture growth studies apply each treatment in triplicates with an average of 26 fish in each tank (range: 4 to 100). The minimum difference that can reliably be detected with statistical analyses is determined by the number of replications of each treatment, n, the variance of the data and the number of treatments applied. In the present study, we accumulated information on the variance of data in aquaculture growth studies on different species to estimate the minimum detectable difference and to assist researchers in designing experiments effectively. These results suggest that the variance is similar for different aquaculture species and, therefore, the same designs (level of replication and n) are suitable for studies on different species of fish.

The minimum difference (MDD) in mean body-mass of different treatment groups that can be detected in a typical aquaculture study (triplicates, 25 fish in each tank and average variance) with 80% statistical power (less than 20% chance of Type II error) is around 26% of the grand mean. Increasing the n from 25 to 100 will reduce the MDD to 19% of the grand mean, while a further increase in n will have comparatively lesser effect. Increasing replication to quadruplicates or sextuplicates (with n as 100), will further reduce the MDD to 16% and 12% of the grand mean respectively. MDD under 10% of the grand mean is only possible when fish for the experiment are selected within a narrow size range to reduce variance.

Simulations were performed, where samples (experiments) were repeatedly drawn from artificial populations with identical distribution and with the same experimental design as is commonly used in growth studies. Two of the populations had dose-dependent responses to treatment while one population showed no response to treatment. The resulting data was analysed with a mixed model ANOVA and by fitting either polynomials or asymptotic models to the data. Contrary to earlier suggestions, the critical treatment (minimum treatment to generate maximum response) estimated with the ANOVA approached more closely the population responses than did the critical treatments estimated with the non-linear models