A new class of sequential testing procedures, sequential conditional p
robability ratio tests (SCPRT's), is proposed. These procedures have t
he property of having a maximum sample size no larger than a fixed-sam
ple test with an almost identical power function. The efficiency of th
e SCPRT, in terms of expected sample size, is close to that of Wald's
SPRT. Group sequential testing procedures derived from the SCPRT are n
ot restricted to the choices of group sizes and number of groups. At t
he same time, the SCPRT, the group-SCPRT, and the reference fixed samp
le size test (RFSST) are agreeable in the sense of having very small p
robability of leading to different rejection/acceptance results. For t
he SCPRT or the group-SCPRT, stopping boundaries are decided by approp
riate deflection factors determined by controlling absorption probabil
ities of a random bridge on the SCPRT boundaries. In this article the
basic idea for the SCPRT is introduced in a general setup. But example
s and technical discussions are restricted mainly to dichotomous distr
ibutions, in which the power functions and expected sample sizes for t
he sequential procedures can be easily computed by a method developed
by Xiong.