Determining whether an experimental group is stochastically larger than a control

Let μ x and μ y be the means of a control and an experimental group, respectively. The usual method of comparing the two groups is in terms of μ x ‐μ y by testing H 0 :μ x = μ y . This approach might suffice when the corresponding distributions differ only in location. When the distributions differ in other respects, a shift function can be more informative. For example, it might be the case that the typical subjects who perform poorly under a standard method will, on the average, benefit from a new treatment, while the new treatment is actually detrimental for the typical subject who does well under the established procedure. Another possibility, which is illustrated in the paper, is that μ y >μ x might be true even though for most subjects the experimental group is detrimental. This paper describes a simple method for determining whether these situations have occurred.