Two-Stage Plans Compared with Fixed-Sample-Size and Wald SPRT Plans

Abstract Abstract Within the Neyman-Pearson framework of hypothesis testing with fixed-error-level specifications, two-stage designs are obtained such that sample size is minimized when the alternative hypothesis is true. Normally distributed variates with known variance and binomially distributed variates are considered. It is shown that when the alternative hypothesis is true, these optimal two-stage designs generally achieve between one-half and two-thirds of the ASN differential between the two extremes of analogous fixed-sample designs (maximum ASN) and item-by-item Wald SPRT design (minimum ASN when alternative hypothesis is true).