On sample size calculation for 2×2 fixed-effect ANOVA when variances are unknown and possibly unequal

Jiin Huarng Guo, Wei Ming Luh

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The factorial 2 × 2 fixed-effect ANOVA is a procedure used frequently in scientific research to test mean differences between-subjects in all of the groups. But if the assumption of homogeneity is violated, the test for the row, column, and the interaction effect might be invalid or less powerful. Therefore, for planning research in the case of unknown and possibly unequal variances, it is worth developing a sample size formula to obtain the desired power. This article suggests a simple formula to determine the sample size for 2 × 2 fixed-effect ANOVA for heterogeneous variances across groups.We use the approximate Welch t test and consider the variance ratio to derive the formula. The sample size determination requires two-step iterations but the approximate sample sizes needed for the main effect and the interaction effect can be determined separately with the specified power. The present study also provides an example and a SAS program to facilitate the calculation process.

Original languageEnglish
Pages (from-to)417-425
Number of pages9
JournalBritish Journal of Mathematical and Statistical Psychology
Volume62
Issue number2
DOIs
Publication statusPublished - 2009 May 1

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Arts and Humanities (miscellaneous)
  • Psychology(all)

Fingerprint Dive into the research topics of 'On sample size calculation for 2×2 fixed-effect ANOVA when variances are unknown and possibly unequal'. Together they form a unique fingerprint.

Cite this