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On Optimizing Multi-Level Designs: Power Under Budget Constraints
Australian and New Zealand Journal of Statistics (2005)
  • Todd C. Headrick, Southern Illinois University Carbondale
  • Bruno D. Zumbo, University of British Columbia
This paper derives a procedure for efficiently allocating the number of units in multi-level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A method is also described for optimizing designs when variance component estimates are not available. Case studies are provided to demonstrate the method.
  • Budget Constraint,
  • Effect Size; Lagrange Multiplier,
  • Level of Randomization,
  • Multi-Level Design,
  • Optimization,
  • Power,
  • Variance Components
Publication Date
Citation Information
Todd C. Headrick and Bruno D. Zumbo. "On Optimizing Multi-Level Designs: Power Under Budget Constraints" Australian and New Zealand Journal of Statistics Vol. 47 Iss. 2 (2005)
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