Some comments on gerechte designs. I. Analysis for uncorrelated errors

Gerechte designs are row and column designs which have an additional blocking structure formed by spatially compact regions. In this paper, and a companion paper (BAILEY et al. 1990) we consider the correct analysis of these designs. In this paper we discuss the purpose of gerechte designs, and we note that the regions are not orthogonal to rows and columns. This means that the usual sums of squares for row, columns and regions are not additive. We show how the correct analysis can be performed, either through the use of appropriate formulae, or by the use of a statistical package. In the companion paper we show that the correct analysis cannot be justified by a randomization argument, and we outline other developments in analysis and design that may be more satisfactory.