Confidence Intervals for a Binomial Parameter Based on Multistage Tests

Abstract

Several methods are developed for the construction of confidence intervals for the binomial success probability p following multistage experimentation. We consider analogues of one-stage methods proposed by Sterne (1954, Biometrika 41, 275-278), Crow (1956, Biometrika 43, 423-435), and Blyth and Still (1983, Journal of the American Statistical Association 78, 108-116). The proposed confidence intervals are implemented and compared with the Clopper-Pearson tail intervals given by Jennison and Turnbull (1983, Technometrics 25, 49-58) for the four three-stage testing procedures of Fleming (1982, Biometrics 38, 143-151). The new intervals have (i) uniformly shorter total length summed over all outcomes, (ii) nearly uniformly shorter expected length, and (iii) closer to nominal probability of coverage. An easily computed Crow-Blyth-Still-type construction is particularly attractive for practical application.