A common control group - optimising the experiment design to maximise sensitivity.

Methods for choosing an appropriate sample size in animal experiments have received much attention in the statistical and biological literature. Due to ethical constraints the number of animals used is always reduced where possible. However, as the number of animals decreases so the risk of obtaining inconclusive results increases. By using a more efficient experimental design we can, for a given number of animals, reduce this risk. In this paper two popular cases are considered, where planned comparisons are made to compare treatments back to control and when researchers plan to make all pairwise comparisons. By using theoretical and empirical techniques we show that for studies where all pairwise comparisons are made the traditional balanced design, as suggested in the literature, maximises sensitivity. For studies that involve planned comparisons of the treatment groups back to the control group, which are inherently more sensitive due to the reduced multiple testing burden, the sensitivity is maximised by increasing the number of animals in the control group while decreasing the number in the treated groups.