Optimality Criteria for Incomplete Block Designs

Optimal Incomplete Block Designs

Optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs compiled. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion tha...

Incomplete Block Designs

1. Introduction These designs were introduced by Yates in order to eliminate heterogeneity to a greater extent than is possible with randomized blocks and Latin squares when the number of treatments is large. The precision of the estimate of a treatment effect depends on the number of replications of the treatment-the larger the number of replications, the more is the precision. Similar is the ...

Splitting balanced incomplete block designs

Laplacian eigenvalues and optimality: I. Block designs

On the Type-1 Optimality of Nearly Balanced Incomplete Block Designs with Small Concurrence Range

The class of nearly balanced incomplete block designs with concurrence range l, or NBBD(l), is defined. This extends previous notions of “most balanced” designs to cover settings where off-diagonal entries of the concurrence matrix must differ by a positive integer l ≥ 2. Sufficient conditions are found for optimality of NBBD(2)’s under type-1 criteria, then used to establish Aand D-optimality ...