Conditional Optimal Design in Three- and Four-Level Experiments

Larry V. Hedges, Michael Borenstein

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The precision of estimates of treatment effects in multilevel experiments depends on the sample sizes chosen at each level. It is often desirable to choose sample sizes at each level to obtain the smallest variance for a fixed total cost, that is, to obtain optimal sample allocation. This article extends previous results on optimal allocation to four-level cluster randomized designs and randomized block designs. It also introduces the idea of constrained optimal allocation, where the sample size at one or more levels is fixed by considerations other than cost or sampling variation. Explicit formulas are given for constrained optimal allocation in three- and four-level designs.

Original languageEnglish (US)
Pages (from-to)257-281
Number of pages25
JournalJournal of Educational and Behavioral Statistics
Issue number4
StatePublished - Aug 2014


  • cluster randomized trial
  • multisite design
  • optimal design
  • randomized block design

ASJC Scopus subject areas

  • Education
  • Social Sciences (miscellaneous)


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