ABSTRACT
A medical study was to be designed to compare the potency of three cardiac substances. In the study, a suitable dilution of one of the three substances was slowly infused into an anesthetized guinea pig and the dosage at which the pig died was recorded. The main research goal was to determine whether significant differences existed among the three substances in terms of potency measured as the dosage at death. The guinea pigs were quite homogeneous in weight and age, and the laboratory enviroment and measurement procedures could reasonably be assumed to be identical. So it was decided that a completely randomized design could be used to collect data. It was also decided that a potency difference of 8 = 5 or larger between any two subtances should be detected with a probability of at least (3 = 0.80, since a potency difference of 8 = 5 was regarded as substantial. From this information,
it was clear that the problem consisted of pairwise comparisons among three treatments in a standard one-way analysis of variance layout. So, Tukey's procedure for pairwise comparisons seemed to be appropriate. It was agreed that the Type-I familywise error (FWE) rate should be controlled at about a == 0.05. The difficulty was to determine how many observations should be required from each of the three treatments, since there was little information on the variances of the observations. The variance, however, was assumed to be the same for all three treatments.
