ABSTRACT
This chapter discusses a large number of designs that do not possess the property of variance balance. A. W. Davis and W. B. Hall proposed a class of cyclic cross-over designs which exist for any number of treatments and periods, by extending cyclic incomplete block designs. The advantage of the Davis-Hall designs in comparison with other existing designs such as the H. D. Patterson and H. L. Lucas designs is that their efficiencies are comparable to those designs but tend to require fewer subjects. The result of the high covariance is poor separability between treatment and carryover effects. Therefore, two period designs should be avoided as much as possible. The aim of the tied-double designs is to approximate as close as possible a situation where the variances of differences among treatments are nearly equal to the variances of differences among carryover effects.
