Design of order-of-addition experiments

Jiayu Peng, Rahul Mukerjee, Dennis K.J. Lin

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


We present a procedure that divides a set of experimental units into two groups that are similar on a prespecified set of covariates and are almost as random as with a complete randomization. Under complete randomization, the difference in the standardized average between treatment and control is Op(n−1/2), which may be material in small samples. We present an algorithm that reduces imbalance to Op(n−3) for one covariate and Op{n−(1+2/p)} for p covariates, but whose assignments are, strictly speaking, nonrandom. In addition to the metric of maximum eigenvalue of allocation variance, we introduce two metrics that capture departures from randomization and show that our assignments are nearly as random as complete randomization in terms of all measures. Simulations illustrate the results, and inference is discussed. An R package to generate designs according to our algorithm and other popular designs is available.

Original languageEnglish (US)
Pages (from-to)683-694
Number of pages12
Issue number3
StatePublished - Sep 1 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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