A fixed sample size procedure for selecting the ‘best’ of k negative binomial populations is developed. Selection is made in such a way that the probability of correct selection is at least P* whenever the distance between the probabilities of success is at least δ*. The exponent r is assumed to be known and the same for all populations. Extensive computer calculations * were employed to obtain the exact least favorable configuration. The smallest sample sizes needed to meet specifications (P*,δ*) are tabulated for r=1(1)5; δ*=0.05(0.05)0.55 and P*=0.75, 0.80, 0.90, 0.95, 0.98, 0.99 involving k=3(1)6, 8, 10 populations.
