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On bounds for the efficiency of block designs for comparing test treatments with a control. (English) Zbl 0642.62044
We study the class of augmented balanced incomplete block desings, which are used for comparing a control treatment with a set of test treatments. Under the A-criterion we establish a condition that enables us to determine the most efficient augmented design and we suggest some methods to compute a lower bound for the efficiency of these designs. For $$3\leq k\leq 10$$, $$v\geq k$$, we list the parameters of the most efficient designs with a lower bound for their efficiency or, if known, mention their optimality.

##### MSC:
 62K05 Optimal statistical designs 62K10 Statistical block designs
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##### References:
 [1] Bechhofer, R.E.; Tamhane, A.C., Incomplete block designs for comparing treatments with a control: general theory, Technometrics, 23, 45-57, (1981) · Zbl 0472.62080 [2] Cox, D.R., Planning of experiments, (1958), Wiley New York · Zbl 0084.15802 [3] Hedayat, A.S.; Majumdar, D., A-optimal incomplete block designs for control-test treatment comparisons, Technometrics, 26, 363-370, (1984) · Zbl 0549.62049 [4] Hedayat, A.S.; Majumdar, D., Families of A-optimal block designs for comparing test treatments with a control, Ann. statist., 13, 757-767, (1985) · Zbl 0586.62113 [5] Jacroux, M., On the determination and construction of MV-optimal block designs for comparing test treatment, J. statist. plann. inference, 15, 205-225, (1987) · Zbl 0598.62088 [6] Majumdar, D.; Notz, W.I., Optimal incomplete block designs for comparing treatments with a control, Ann. statist., 11, 258-266, (1983) · Zbl 0507.62070 [7] Stufken, J., On optimal and highly efficient block designs for comparing test treatments with a control, () [8] Stufken, J., A-optimal block designs for comparing test treatments with a control, Ann. statist., 15, 1629-1638, (1987) · Zbl 0629.62077
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