Strongly linear trend-free block designs and 1-factors of representative graphs

Win Chin Lin, John Stufken

Research output: Contribution to journalArticlepeer-review


We consider the existence of strongly linear trend-free block designs. Using a graph to represent a block design, we show that the problem of finding strongly linear trend-free block designs corresponds to a well-known problem in graph theory. This connection enables a characterization of all block designs that, through a judicious assignment of the treatments to the units within each block, can be made strongly linear trend-free, and makes available efficient algorithms for finding such assignments.

Original languageEnglish (US)
Pages (from-to)375-386
Number of pages12
JournalJournal of Statistical Planning and Inference
Issue number1-2
StatePublished - Aug 1 2002
Externally publishedYes


  • Block design
  • Edmonds' blossom algorithm
  • Linear trend
  • Perfect matching
  • Systematic design
  • Tutte's 1-factor theorem

ASJC Scopus subject areas

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


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