Extra-Period Change-Over Designs

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Abstract
This paper deals with extra-period designs obtained by repeating the treatment pattern of the last period of any design in a general class of basic change-over designs. The basic designs are derived from Latin squares or incomplete Latin squares and satisfy certain conditions of balance which facilitate the estimation of direct and first residual effects. The extra-period designs have the useful property that the estimates of direct effects are orthogonal with the estimates of first residual effects. The construction and analysis of the extra-period designs are described. As with the basic designs, the estimates of error given by the method of fitting constants for direct and residual effects are biased. Nearly unbiased estimates of the errors of residual effects can be obtained with certain types of design. The efficiencies and uses of extra-period designs are discussed in general terms. The designs are likely to be most useful when increased accuracy is required in the estimates of residual and permanent effects. They can, however, also be used to advantage to extend for one further period an experiment which would otherwise have to be terminated, and to provide balanced designs in blocks of two units.

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