Two-Stage Procedures for Comparing Treatments with a Control: Elimination at the First Stage and Estimation at the Second Stage
✍ Scribed by Professor Robert E. Bechhofer; Professor Charles W. Dunnett; Professor Ajit C. Tamhane
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 991 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0323-3847
No coin nor oath required. For personal study only.
✦ Synopsis
We consider the problem of comparing 8 set of p , test treatments with a control treatment. This is to be accomplished in twostages 88 follows: I n the first stage, N, observations are allocated among the pi treatments and the control, and the subset selection procedure of GUPTA and SOBBL (1968) k employed to eliminate "inferior'' treatments. In the second stage, N2 observations are allocated among the (randomly) selected subset of pz( S p i ) trestmenta and the control, and joint confidence interval estimates of the treatment versus control differences are calculated using DUNNETT'S (1966) procedure. Here both N, nndNz are assumed to be fixed in advance, and the so-called square root rule is used to allocate obeervatione nmong the treatments and the control in each stage.
Dunnett's procedure is applied using two different types of estimates of the treatment versus control mean differences: The unpooled estimates sre based on only the data obtained in the second stage, while the pooled estimates are based on the data obtained in both stages. The procedure based on unpooled estimates uses the critical point from a pz-variate Student t-distribution, while that based on pooled estimates uses the critical point from a p,-variate Student t-distribution. The two procedures and a composite of the two are compared via Monte Cnrlo simulation. It is shown that the expected value of p z determines which procedure yields shorter confidence intervals on the average. Extensions of the procedures to the case of unequal sample sizes nre given. Applicability of the proposed two-stage procedures to a drug screening problem is discussed.