CHAPTER5Two-SidedTestswithEarlyStoppingUndertheNullHypothesis5.1IntroductionWereturntothetwo-sidedtestingproblemofChapters2and3butnowconsidertestswhichallowearlystoppingtoaccept,aswellastoreject,thenullhypothesis.FollowingthegeneraltreatmentofnormaldatadescribedinChapter3,wesupposestandardizedstatisticsZ1,...,ZKavailableatanalysesk=1,...,K,followthecanonicaljointdistribution(3.1),inparticular,Zk∼N(θ√Ik,1)whereIkistheinformationforθavailableatanalysisk.Ourobjectiveistotest,groupsequentially,thenullhypothesisH0:θ=0withTypeIerrorprobabilityαandpower1−βatsomespecifiedalternativeθ=±δ.AgeneralgroupsequentialtestwithpossibleearlystoppingtoacceptH0isdefinedbypairsofconstants(ak,bk)with0≤ak
