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Conditional Optimal Design in Three- and Four-Level Experiments

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  • Larry V. Hedges
  • Michael Borenstein

Abstract

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.

Suggested Citation

  • Larry V. Hedges & Michael Borenstein, 2014. "Conditional Optimal Design in Three- and Four-Level Experiments," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 257-281, August.
    • Handle: RePEc:sae:jedbes:v:39:y:2014:i:4:p:257-281
    DOI: 10.3102/1076998614534897
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    References listed on IDEAS

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    1. repec:mpr:mprres:5863 is not listed on IDEAS
    2. Larry V. Hedges & E. C. Hedberg, 2013. "Intraclass Correlations and Covariate Outcome Correlations for Planning Two- and Three-Level Cluster-Randomized Experiments in Education," Evaluation Review, , vol. 37(6), pages 445-489, December.
    3. repec:mpr:mprres:7080 is not listed on IDEAS
    4. repec:mpr:mprres:6811 is not listed on IDEAS
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