ABSTRACT
Many of the designs that possess variance balance were catalogued by H. D. Patterson and H. L. Lucas. That monumental study also included many designs not possessing variance balance. The treatments are to be assigned randomly to the letters of the alphabet. In addition, some other forms of randomization may be required. The treatment and carryover parameters are orthogonal, and the variances of the treatment parameters are the same as that of the carryover parameters. The chapter discusses the effect of adding an extra period to a two-period balanced design and found that there were dramatic improvements in the efficiencies of the treatment and carryover parameters. Balaam designs have the property of variance balance, as can be seen from the incidence matrices for treatment versus carryover. Each treatment is preceded equally often by each other treatment.
