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On sample size calculation for 2×2 fixed‐effect ANOVA when variances are unknown and possibly unequal
Author(s) -
Guo JiinHuarng,
Luh WeiMing
Publication year - 2009
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711008x322853
Subject(s) - homogeneity (statistics) , sample size determination , mathematics , statistics , analysis of variance , factorial experiment , variance (accounting) , factorial , interaction , one way analysis of variance , main effect , sample (material) , levene's test , nominal level , confidence interval , mathematical analysis , chemistry , accounting , chromatography , business
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.