EFFICIENCY OF CONNECTED BINARY BLOCK DESIGNS WHEN A SINGLE OBSERVATION IS UNAVAILABLE

SUBIR GHOSH^{1}, SANPEI KAGEYAMA^{2} AND RAHUL MUKERJEE^{3}

1Department of Statistics, University of California, Riverside, CA 92521-0138, U.S.A.

2Mathematics Education, Faculty of School Education, Hiroshima University, Minami-ku, Hiroshima 734, Japan 3Indian Institute of Management, Joka, Diamond Harbour Road, Post Box No. 16757 Alipore Post Office, Calcutta 700027, India

(Received June 11, 1990; revised June 7, 1991)

Abstract. In this paper the problem of finding the design efficiency is considered when a single observation is unavailable in a connected binary block design. The explicit expression of efficiency is found for the resulting design when the original design is a balanced incomplete block design or a group divisible, singular or semiregular or regular with λ_{1} = 0, design. The efficiency does not depend on the position of the unavailable observation. For a regular group divisible design with λ_{1} > 0, the efficiency depends on the position of the unavailable observation. The bounds, both lower and upper, on the efficiency are given in this situation. The efficiencies of designs resulting from a balanced incomplete block design and a group divisible design are in fact high when a single observation is unavailable.

Key words and phrases: Balanced incomplete block design, connectedness, efficiency, group divisible design, robustness.