Approximating the Probability of Identifying the Most Effective Treatment for the Case of Normal Distributions Having Unknown and Unequal Variances

Abstract

When comparing k normal populations, an investigator might want to know the probability that the population with the largest population mean will have the largest sample mean. Put another way, what is the probability of correctly identifying the most effective treatment? The paper describes and illustrates methods of approximating this probability when the variances are unknown and possibly unequal. The results described here can also be used to measure the extent to which the populations differ for one another.