Statistical aspects of aquaculture research: optimum block size in pond experiments

The sensitivity of any treatment comparisons in pond experiments is often limited by large variability among ponds. Standard techniques of increasing the number of replicate ponds to account for the large variability may be inappropriate as only a limited number of ponds may be available for any one experiment. This paper considers various 'balanced incomplete block' designs and compares their use with 'completely randomized designs' and 'randomized complete block' designs. With simulated data, it is shown that 'balanced incomplete block' designs can reduce the standard error of a treatment estimate by as much as 50%, and reduce confidence intervals by 25%, although increases of similar sizes may be experienced. The pattern of allocation of blocks to ponds by neighbour or by pond number shows no clear distinction in estimation improvement. Where missing ponds occur a large increase in imprecision may be experienced. These results are supported by data from nonuniformity experiments, Further work is needed to explore block structures for specific types of treatment that may influence the patterns of variability to different extents.