On the construction of designs with three-way blocking

Abstract

Experimental designs under two-way blocking structure are used to separate out two cross-classified non-interacting sources of variation in the experimental material. However, there may exist situations wherein the experimental area contain some stony patches or other features that tend to clump in compact areas where these designs cannot capture the variability due to these compact areas. For such situations, experimental designs that are capable of removing three sources of variability can be more advantageously used. In this paper, some methods of constructing designs under three-way blocking structure have been developed. Joint information matrix has been derived and the efficiency factor of these designs has been computed as compared to an orthogonal design. List of parameters of the designs obtained has been prepared for number of treatments < 25 along with the efficiency factor for each design.