Abstract: A cross-validatory choice of weights for combining intrablock and interblock estimates of treatments in a Balanced Incomplete Block (B.I.B.) design only was proposed by Jensen and Stone. In this paper, this method is extended to any incomplete block design. The weights for a B.I.B. design are expressed in terms of the sums of squares in the analysis of variance of the B.I.B. design. This has enabled us to compare this method to other methods in the literature and establish properties such as unbiasedness and uniform betterness of the combined estimates. The weights for a regular Group Divisible design are also provided.
Key words and phrases: Cross-validation, combining inter- and intrablock information, incomplete block designs.