The basic contrasts of an experimental design with special reference to the analysis of data

Abstract

The least squares solution for a block design is considered in some detail for both the intrablock and the interblock cases. It leads to the identification of certain contrasts, here called basic, that are estimated independently and with efficiency factors that are readily determined. Basic contrasts indicate possible partitions of the treatment sum of squares and aid in the computation of the appropriate analysis of variance. Also they help to clarify the relationship between three methods of computing the analysis for the general case of block designs, namely those of (i) Tocher, (ii) Kuiper and Corsten and (iii) Wilkinson.