Optimal sample sizes for precise interval estimation of Welch's procedure under various allocation and cost considerations

Gwowen Shieh*, Show Li Jan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Welch's (Biometrika 29: 350-362, 1938) procedure has emerged as a robust alternative to the Student's t test for comparing the means of two normal populations with unknown and possibly unequal variances. To facilitate the advocated statistical practice of confidence intervals and further improve the potential applicability of Welch's procedure, in the present article, we consider exact approaches to optimize sample size determinations for precise interval estimation of the difference between two means under various allocation and cost considerations. The desired precision of a confidence interval is assessed with respect to the control of expected half-width, and to the assurance probability of interval half-width within a designated value. Furthermore, the design schemes in terms of participant allocation and cost constraints include (a) giving the ratio of group sizes, (b) specifying one sample size, (c) attaining maximum precision performance for a fixed cost, and (d) meeting a specified precision level for the least cost. The proposed methods provide useful alternatives to the conventional sample size procedures. Also, the developed programs expand the degree of generality for the existing statistical software packages and can be accessed at brm. psychonomic-journals. org/content/ supplemental.

Original languageEnglish
Pages (from-to)202-212
Number of pages11
JournalBehavior Research Methods
Volume44
Issue number1
DOIs
StatePublished - 1 Mar 2012

Keywords

  • Behrens-Fisher problem
  • Precision
  • Study design

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