Balance, efficiency and orthogonality concepts in block designs

• Published in: Journal of statistical planning and inference Vol. 36; no. 2; pp. 283 - 300
• Main Author: CALINSKI, T
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 01.08.1993; New York,NY Elsevier Science; Amsterdam
• Subjects: BIB design; Block design; concurrences; connectedness; efficiency balance; Exact sciences and technology; Experimental design; general balance; Mathematics; orthogonality; pairwise balance; Probability and statistics; Sciences and techniques of general use; Statistics; total balance; variance balance; weighted concurrences; efficiency balance; BIB design; Block design; total balance; variance balance; general balance; concurrences; weighted concurrences; connectedness; pairwise balance; orthogonality; 62K10; Incomplete block design; General balance; Connected design; Balanced design; Concurrency
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/0378-3758(93)90131-O

Some of the most basic terms and concepts used in connection with the balancing of treatments in block experiments are reexamined. In particular, two rival concepts of balance are considered. The first is based on the equality of weighted concurrences, and is commonly called variance balance. The other is based on the proportionality of weighted concurrences to the products of the relevant treatment replications, and is usually called efficiency balance. Their implications for estimating contrasts of treatment parameters are derived and discussed. As a consequence, the terminology used for these two concepts is questioned and some advantage of the second concept in relation to the randomization model is indicated. A reference to the notion of general balance is also made.