Abstract
THE RECTANGULAR LATTICES considered in this note are the designs for agricultural variety trials, and similar experiments, discussed by Harshbarger briefly in [1] and more fully in [2]. The analysis of variance involves determination of two components (a) and (b) of the sum of squares for blocks eliminating varieties (and replications), and of the within-block error sum of squares. In [2] the withinand between-block error variances are estimated by somewhat elaborate linear combinations of these three sums of squares. It would of course be simpler (after computing the analysis of variance as before) to use, besides the within-block error sum of squares, merely the sum of Components (a) and (b). The object of this note is to show that the simpler method is generally better. The design is for p(p + 1) varieties (p ? 2) in incomplete blocks of p plots. The varieties are allotted to the p(p + 1) ordered pairs of unequal integers (i, j) of Fig. 1:
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