Approximate sample size formulas for testing group mean differences when variances are unequal in one-way ANOVA

Jiin Huarng Guo, Wei Ming Luh

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

This study proposes an approach for determining appropriate sample size for Welch's F test when unequal variances are expected. Given a certain maximum deviation in population means and using the quantile of F and t distributions, there is no need to specify a noncentrality parameter and it is easy to estimate the approximate sample size needed for heterogeneous one-way ANOVA. The theoretical results are validated by a comparison to the results from a Monte Carlo simulation. Simulation results for the empirical power indicate that the sample size needed by the proposed formulas can almost always achieve the desired power level when Welch's F test is applied to data that are conditionally nonnormal and heterogeneous. Two illustrative examples of the use of the proposed procedure are given to calculate balanced and optimal sample sizes, respectively. Moreover, three sample size tables for two-, four-, and six-group problems are provided, respectively, for practitioners.

Original languageEnglish
Pages (from-to)959-971
Number of pages13
JournalEducational and Psychological Measurement
Volume68
Issue number6
DOIs
Publication statusPublished - 2008 Dec

All Science Journal Classification (ASJC) codes

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Applied Mathematics

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