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Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization

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  • Xiaofeng Liu

Abstract

This article considers optimal sample allocation between the treatment and control condition in multilevel designs when the costs per sampling unit vary due to treatment assignment. Optimal unequal allocation may reduce the cost from that of a balanced design without sacrificing any power. The optimum sample allocation ratio depends only on the cost ratio between the treatment and control regardless of whether the randomization of sampling units occurs at levels 1, 2, or 3. Power functions for the exact tests for the main effect of treatment are derived for prototypical multilevel designs with unequal sample sizes in the treatment and control condition.

Suggested Citation

  • Xiaofeng Liu, 2003. "Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization," Journal of Educational and Behavioral Statistics, , vol. 28(3), pages 231-248, September.
    • Handle: RePEc:sae:jedbes:v:28:y:2003:i:3:p:231-248
    DOI: 10.3102/10769986028003231
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    Cited by:

    1. Md Abu Manju & Math J. J. M. Candel & Gerard J. P. van Breukelen, 2019. "SamP2CeT: an interactive computer program for sample size and power calculation for two-level cost-effectiveness trials," Computational Statistics, Springer, vol. 34(1), pages 47-70, March.
    2. Kari Tokola & Andreas Lundell & Jaakko Nevalainen & Hannu Oja, 2014. "Design and cost optimization for hierarchical data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(2), pages 130-148, May.
    3. Jiin-Huarng Guo, 2012. "Optimal sample size planning for the Wilcoxon--Mann--Whitney and van Elteren tests under cost constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(10), pages 2153-2164, June.

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