Characteristics for distinguishing among balanced incomplete block designs with repeated blocks (Q1069629)

The class \({\mathcal B}\) of balanced incomplete block designs with parameters v,b,r,k,\(\lambda\) considered here includes designs with repeated blocks. Attention to date has centered on constructing the members of \({\mathcal B}\) and on finding the minimum number of distinct blocks \(d\leq b\). Under the classical model, the usual statistical characteristics do not distinguish among members of \({\mathcal B}\); however, effects related to block totals can be used as distinguishing characteristics. A competing effects model is introduced and is shown to distinguish among members of \({\mathcal B}\). This model is appropriate for intercropping, marketing, and survey investigations. The model is applied to the ten nonisomorphic BIB designs with parameters 7,21,9,3,3. A computer algorithm for obtaining the pairwise treatment by block incidence matrix of this model is given.