Lattice squares

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Abstract
A new method of analysing the results of experiments arranged in lattice (quasi-Latin) square designs is described. By this method the information contained in the inter-row and inter-column comparisons is recovered. The procedure followed is to estimate the actual accuracy of the inter-row and inter-column comparisons relative to intra-row and column comparisons, and assign weights proportional to these relative accuracies. The methods of computation by which this procedure can be carried out expeditiously are described in detail, and are illustrated by two experiments carried out at Rothamsted and Woburn. The gains in accuracy obtained in these two experiments (as compared with ordinary randomized blocks) were approximately 30% and 60% respectively, allowing for losses of information due to inaccuracies of weighting.