Selecting the Best One of Several Binomial Populations

Tables have been -prepared for use in any experiment designed to selec that particular one of k binomial processes or populations with the highest (long time) yield or the highest probability of success. Before experimentation the experimenter chooses two constants d* and P* (0 d* ^ 1; 0 ^ P* 1) and specifies that he would like to guarantee a probability of at least P* of a correct selection whenever the true difference between the longtime yields associated with the best and the second best processes is at least d*. The tables show the smallest number of units required per process to be put on test to satisfy this specification. Separate tables are given for k = 2, 3, 4 and 10. Each table gives the result for d* = 0.05 (0.05) 0.50 and for P* = 0.50, 0.60, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, and 0.99. For values of d* and P* not considered in the tables, graphs are given on which interpolation can be carried out. Graphs have also been constructed to make possible an interpolation or extrapolation for other values of k. An alternative specification is given for use when the experimenter has some a priori knowledge of the processes and their probabilities of success. This specification is then compared with the original specification. Applications of these tables to different types of problems are considered. INTRODUCTION AND SUMMARY A frequently encountered problem is that of selecting the "best" one of k (k ^ 2) processes or populations on the basis of the same number n of observations from each process.