Classifying k normal populations with respect to a control: making at most Incorrect Decisions
This paper is concerned with classifying k normal populations as better or worse than a control with a goal of making at most incorrect decisions. These populations are first compared by their means assuming their variances to be equal and known. Next, the comparisons are based on their variances assuming their means to be known or unknown. Rules are proposed when the control is known or unknown and exact solutions are tabulated. A modified goal of making at most m1 incorrect decisions in classifying better populations, and making at most incorrect decisions in classifying worse populations is also investigated. Generalizations to location and scale parameter families of distributions are discussed.