Extra-Period Change-Over Designs

Designs involving cyclical arrangements of treatments are frequently used in experiments extending over several periods in order to reduce errors due to variation between experimental units. These designs are known as change-over designs. In the simplest type of change-over design the sequences of treatments are determined by the columns of one or more Latin squares. Any Latin square can be used when the effects of treatments do not persist beyond the period of application. Frequently, however, it is desirable to take residual effects into account. Change-over designs which provide for the estimation of first residual effects, i.e., residual effects in the period immediately after application, have been devised by Cochran, Autrey, and Cannon [1941] and Williams [1949] using special Latin squares. The residual effects are estimated by introducing additional constants into the ordinary analysis of Latin squares. For details of these designs and their analysis reference can be made to the review of the subject by Cochran and Cox [1957, p. 133]. Designs which permit the number of periods to be less than the number of treatments have been investigated by Patterson [1951, 1952]. These designs consist of series of incomplete Latin squares and are analysed accordingly with provision for first residual effects. Yates [1951], Lucas [1957], and Cochran and Cox [1957] have pointed out that in the analysis of change-over designs (a) residual effects are less accurately determined than direct effects