The present paper was designed to propose the statistical procedure for two-treatment switch-back, or double reversal, design with blocks where the number of individuals were unequal not only in blocks but also in the treatment sequence groups within blocks. The statistical model assumed for Yijklm, the performance of the kth individual of the mth experimental period of the lth treatment of the jth treatment sequence group in the ith block, was as follows:
Yijklm=μ+Bi+Sj+(BS)ij+cijk+Tl+Pm+(BT)il+(BP)im+(ST)jl+(SP)jm+(TP)lm+eijklm where μ, Bi, Sj, cijk, Tl, Pm and eijklm were mean and the ith block, the jth treatment sequence group, the ijkth individual, the lth treatment and the mth experimental period effects and random error, respectively, and (BS)ij, (BT)il, (BP)im, (ST)jl, (SP)jm (TP)lm were the corresponding interaction effects to the respective elements, and all elements, except cijk and eijklm being random variables, were fixed constants. Application of the procedure proposed in this paper to a study on the effect of milking at unequal intervals on milk yield in dairy cows illustrated the validity and usefulness of the procedure. The hypotheses for adopting the switch-back design were also discussed.
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