Multiple Comparisons

Abstract

In Exercise 3.13 we discover that the probability of simultaneously making three correct inferences, when each of the three individually has P(correct inference) = 1— α= 0.95, is only (1 — α)³ = .95³ = 0.857. Alternatively, the probability of making at least one incorrect inference is 1— 0.857 = 0.143 ≈ 3α. In general, the more simultaneous inferences we make at one time, the smaller the probability that all are correct. In this chapter we learn how to control the probability that all inferences are simultaneously correct. We usually phrase the goal as controlling the probability of making at least one incorrect inference.