MULTI-FACTOR BALANCED BLOCK DESIGNS WITH COMPLETE ADJUSTED ORTHOGONALITY FOR ALL PAIRS OF TREATMENT FACTORS

A new series of multi-factor balanced block designs is introduced. Each of these designs has the following properties: (i) each of its k– 1 treatment factors is disposed in a cyclic or multi-cyclic balanced incomplete block design with parameters (v,b,r,k,Λ) = (a(k-l) + 1,a²(k-1) +a, ak, k, k) (a > 1); (ii) the incidence of any one of the treatment factors on any other is balanced; and (iii) after adjustment for blocks only, the relationship between any two of the treatment factors is that of adjusted orthogonality. The treatment factors are thus orthogonal to one another in the within-blocks stratum of the analysis of variance. The designs provide a benchmark with which other designs may be compared.