Optimal sample sizes for Welch's test under various allocation and cost considerations

Show Li Jan, Gwowen Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The issue of the sample size necessary to ensure adequate statistical power has been the focus of considerableattention in scientific research. Conventional presentations of sample size determination do not consider budgetary and participant allocation scheme constraints, although there is some discussion in the literature. The introduction of additional allocation and cost concerns complicates study design, although the resulting procedure permits a practical treatment of sample size planning. This article presents exact techniques for optimizing sample size determinations in the context of Welch (Biometrika, 29, 350-362, 1938) test of the difference between two means under various design and cost considerations. The allocation schemes include cases in which (1) the ratio of group sizes is given and (2) one sample size is specified. The cost implications suggest optimally assigning subjects (1) to attain maximum power performance for a fixed cost and (2) to meet adesignated power level for the least cost. The proposed methods provide useful alternatives to the conventional procedures and can be readily implemented with the developed R and SAS programs that are available as supplemental materials from brm. psychonomic-journals. org/content/supplemental.

Original languageEnglish
Pages (from-to)1014-1022
Number of pages9
JournalBehavior Research Methods
Issue number4
StatePublished - 1 Dec 2011


  • Behrens-Fisher problem
  • Power
  • Study design

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