Some Aspects of Recovery of Interblock Information.

Abstract

In the analysis of an incomplete block design under the usual additive model for block and treatment effects, if the block effects are considered to be r and om, one can obtain information about the treatment effects by considering contrasts of observations both within and between blocks. The information obtained from contrasts within blocks is called intrablock information and that obtained from contrasts between blocks is called interblock information. In this dissertation, various aspects of recovery of interblock information are studied for several designs. First, the cross-validatory choice of weights proposed by Jensen and Stone (1976) for combining intrablock and interblock information in balanced incomplete block designs is investigated. By expressing these weights in a much simpler form, their similarity to other weights suggested in the literature is demonstrated and their properties are examined. In addition, it is shown how Jensen and Stone's cross-validatory procedure for obtaining the weights in balanced incomplete block designs can be extended to other binary incomplete block designs. Second, weights suggested in the literature for binary incomplete block designs are reformulated for use in n-ary incomplete block designs. The properties of the resulting combined estimates are also examined. Third, since methods have been given for constructing second order rotatable response surface designs with nonorthogonal blocking, and these designs require fewer design points than the corresponding orthogonal designs, it is shown how interblock information can be recovered in such designs to increase the precision of the response surface coefficients. Finally, for symmetric factorial designs, the estimation of treatment contrasts formed from orthogonal polynomials is considered, with and without interblock information. It is shown that the use of trigonometric factor levels introduced by Bailey (1982) may lead to more precise estimates for those treatment contrasts of interest than the use of the more common equally spaced factor levels.