Balanced incomplete Latin square designs

Mingyao Ai, Kang Li, Senmao Liu, Dennis K.J. Lin

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Latin squares have been widely used to design an experiment where the blocking factors and treatment factors have the same number of levels. For some experiments, the size of blocks may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Latin squares (BILS) is proposed. A general method for constructing BILS is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Latin squares. The optimality of the proposed BILS designs is investigated. It is shown that the proposed transversal BILS designs are asymptotically optimal for all the row, column and treatment effects. The relative efficiencies of a delete-one-transversal BILS design with respect to the optimal designs for both cases are also derived; it is shown to be close to 100%, as the order becomes large.

Original languageEnglish (US)
Pages (from-to)1575-1582
Number of pages8
JournalJournal of Statistical Planning and Inference
Issue number9
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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