3.1.3. Effect size

A third factor affecting decisions about sample size in experimental design is referred to as effect size (Cohen, 1988). As an illustration, if experimental treatments with a pesticide decrease honey bee food intake to 90% that of controls, more replication is needed to achieve statistical significance than if food intake is reduced to 10% that of controls (note that one’s objective should be to find biologically meaningful results rather than statistical significance). This is because treatment has a greater effect size in the latter situation. Effect size and statistical significance are substantially intertwined, and there are equations, called power analyses (see section 3.2.1.), for calculating sample sizes needed for statistical significance once effect size is known.

Without preliminary trials, effect size, and also statistical power, may be impossible to know in advance. If one’s objective is statistical significance, and one knows effect size, one can continue to sample until significance is achieved. However, this approach is biased in favour of a preferred result. Moreover, it introduces the environmental influence of time; results one achieves in spring may not be replicated in summer e.g. Scheiner et al., (2003) reported seasonal variation in proboscis extension responses (previously called proboscis extension reflexes; also see Frost et al., 2012). Removing the influence of time requires that one decides in advance of replication, and accepts results one obtains. Without preliminary trials, it will always be preferable to maintain as many properly randomised cages as possible. A related factor that will influence sample size is mortality rate of honey bees in cages; if control group mortality rates are 20% for individual bees, one will want to increase the number of bees by at least 20%, and even more if variability in mortality rates is high. Alternatively, without knowledge of effect size, one should design an experiment with sufficient replicates such that an effect size of biological relevance can be measured.