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Variance balanced generalized nested row-column designs with empty diagonal cells. (English) Zbl 0854.62071

In recent literature, nested row-column designs have drawn considerable attention. They are useful in multi-site trials for eliminating heterogeneity in two directions. The designs that have appeared so far in the literature have non-empty cells in the row-column design at each site. Due to resource constraints, one may have to consider designs allowing empty cells in some row-column cells at each site. We call such designs Generalized Nested Row-Column Designs. We construct designs from the class of generalized nested row-column designs with empty diagonal cells and provide their analysis.
The designs considered in this paper have \(v = m(m - 1)\) treatments (labeled \(0,1,2, \dots, v - 2, \infty)\) arranged in \(s\) squares of \(m\) rows and \(m\) columns such that the main diagonal cells in each square do not receive a treatment and every square provides a complete replication of the treatments. In fact, the cells not receiving treatments may be in any transversal of the square. Without loss of generality we assume it to be the main diagonal.

MSC:

62K10 Statistical block designs
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