Analysis for an Experiment Designed As Augmented Lattice Square Design

Augmented experiment designs are used internationally for screening large numbers of new genotypes used in early generations of plant-breeding programs. Any experiment design (complete block, incomplete block, row-column, or other) may be selected for the standard treatments replicated r times each. The blocks, incomplete blocks, or rows and columns are enlarged to accommodate the new treatments usually included only once in the experiment. The lattice square experiment design controls variation within each complete block in two directions (rows and columns). Augmented lattice square designs (ALSDs) are easily constructed as described by Federer, W. T. (2002) in “Construction and Analysis of an Augmented Lattice Square Design,” Biometrical Journal 44(2):251-257. ALSDs can accommodate c = 2k or 3k check or standard cultivars in r = k complete blocks and n = k 2(k - 2) or k 2(k - 3) new genotypes. An ALSD with k = 4 = r, c = 8, and n = 32 illustrates a statistical analysis. A trend analysis using polynomial regression is used. The following data are presented for all sixty-four responses.