Some universally optimal row-column designs with empty nodes. (English) Zbl 0735.62072

Stewart, Frances P.; Bradley, Ralph A.

Biometrika 78, No. 2, 337-348 (1991).

Summary: General forms of the reduced coefficient matrix for estimation of treatment effects and the intrablock analysis of variance of row-column designs with \(n\) experimental units and \(v\) treatments are obtained. These results are used to identify desirable properties for row-column designs with empty nodes. A need for such designs is apparent when the blocking criteria are implemented in sequence and empty nodes do not represent wasted experimental units. The construction and properties of three special classes of row-column designs with some empty nodes are discussed and examples given. In particular, it is shown that, if a row- column design belongs to one of these classes, then it is universally optimal for specified design parameters, where universally optimal designs are designs that maximize a generalized optimality criterion.

MSC:

62K05	Optimal statistical designs
62K10	Statistical block designs
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

reduced coefficient matrix; estimation of treatment effects; intrablock analysis of variance of row-column designs; empty nodes; universally optimal; generalized optimality criterion; multidimensional block design; structurally incomplete row-column design; variance balance