Relative efficiency of incomplete block designs using corn uniformity trial data
1942
Zuber, M.S.
Four incomplete block designs, the lattice square, balanced lattice, lattice, and triple lattice, were applied to corn uniformity trial data assuming 25, 49, 81, and 121 varieties in plots 2 by 5, 4 by 5, and 2 by 10 hills in size. The average of all designs computed without the recovery of inter-block information showed a gain of 25% in favor of the incomplete block designs over the randomized complete block. When these same designs were computed recovering inter-block information an average gain of 36% in favor of the incomplete blocks was shown. Of the various designs studied, computed by the old method, the lattice square with k+1 and k+1 replications showed gains of 32 and 31%, respectively. The precision for the other designs was as follows: Balanced lattice, 26%; lattice, 18%; and triple lattice, 17%. The coefficient of variation and standard error of the mean were used to study the adaptation of plot size and shape to the various designs. The results obtained indicated that the 2 by 5 hill plot with twice as many replications yet occupying the same area of land as the 4 by 5 and 2 by 10 hill plots was the most advantageous. The 2 by 10 hill plots and the 4 by 5 hill plots followed in order. The 2 by 10 hill plot was superior to the 4 by 5 hill plot even in the lattice square designs. This was probably due to the fact that the soil heterogeneity ran mainly in one direction. The study of the shape of an incomplete block indicated that the more compact these blocks can be made the more efficient the design will become. The compactness of an incomplete block may be adjusted by the movement of plots within a block or by changing the shape of the plots within an incomplete block.
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