On the Probability That the Best Chicken Stock Will Come Out Best in a Single Random Sample Test

Abstract

WHEN samples taken from several stocks (or strains, varieties, etc.) are compared with a view to selecting the best stock, it is of interest to know the probability of correct selection. The problem of computing this probability is complicated by the fact that the true stock means are usually either fixed but unknown, or else are themselves a more or less random sample from a larger population. Some mathematical expressions for the probabilities of correct selection in the latter case, assuming a normal distribution of the true stock means, were given by Dunnett (1960), but they involve multiple integrals which have not been numerically evaluated so far.On the other hand, the conditional probability of correct selection given any particular fixed configuration of the true stock means is much simpler to compute. Assuming (as usual) that the data for individual layers are normally distributed around the true stock means, X1,…