On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

Constructions of efficiency-balanced designs

We present a number of methods of constructing efficiency-balanced binary block designs which are design patterns for simplification of statistical analysis. Furthermore, a method of construction of an efficiency-balanced block design with v+1 treatments from one with v treatments is generally characterized.     

Incomplete block designs for symmetrical parallel line assays

New series of incomplete block designs for symmetrical parallel lines are proposed. From these designs important contrasts like L_p, L₁ and L′₁ are estimated free from block effects. In addition to these, other odd order contrasts are also estimated orthogonal to block effects. The designs are shown to have simple analysis.     

The efficiency and optimality characterization of certain six-Treatment incomplete-Block designs emanating from some quasi-Semi-Latin squares

Incomplete-block designs were constructed from three types of three-factor block-structured combinatorial designs which are not necessarily semi-Latin squares but whose treatments are ab initio arranged as in the semi-Latin square. The basic consideration for the construction involves the exploitation of the different block structures of the experimental units of the Quasi-semi-Latin Squares (QSLS) for the same treatments. All the emanating designs are found to be connected, only the designs in nine blocks are both variance- and efficiency-balanced and offer gain in efficiency but lead to about 46 percent loss of information.