Doubly Balanced Incomplete Block Designs for Experiments in which the Treatment Effects are Correlated

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Abstract
In some balanced incomplete block expts. observations within a block are correlated to a degree beyond that attributable to block differences. A non-parametric approach using ranks obviates this difficulty but usually results in a loss of information. The author proposes a continuous, parametric model for this situation in which the solution to the normal equations is rendered simple if the design is restricted by double balancing. That is, all possible pairs of treatments must appear together in a block an equal number of times and similarly for all possible triplets of treatments. Formulas for computing the analysis of variance, treatment means, standard errors and efficiencies are derived, and their use is illustrated with an example. Six plans for this design are given in detail and the design in general is compared with other balanced incomplete block designs previously described.