Using extensions to Robertson's (1957) method for finding the optimum test design, factors affecting the improvement from testing were studied. Other than the heritability, the ratio of the number tested (N) to the number required for breeding stock (T) has the largest effect on the improvement expected, the improvement being roughly proportional to the logarithm of this ratio. The type of family and the number in the test group which compose the optimum design, also depend largely on the ratio N/T. Accuracy in evaluation is required when only few animals are selected (N/T high), but small test groups from large families are necessary when large numbers of breeding stock are required (N/T low).

Testing schemes differ basically in their selection procedure and only secondarily in their designs. The advantage resulting from the tested animals being themselves selected is in proportion to what part they constitute of the total selected.

Another consideration is how the testing is integrated with the population breeding structure. Maximum improvement will be obtained if the testing facilities are restricted to a nucleus group of breeders, and full opportunity for selection is made in their stocks. The increased improvement this providesis accumulated in this nucleus group of herds and gradually passed down to the rest of the herds. Otherwise the improvement will be greatest when each breeder can use sires from families which have performed well in thetesting.