Repeated Measures ANOVA and adjusted F-tests when sphericity is violated: Which procedure is best?

Abstract

Introduction: One-way repeated measures ANOVA requires sphericity. Research indicates that violation of this assumption has an important impact on Type I error. Although more advanced alternative procedures exist, most classical texts recommend the use of adjusted F-tests, which are frequently employed because they are intuitive, easy to apply, and available in most statistical software. Adjusted F-tests differ in the procedure used to estimate the corrective factor ε, the most common being the Greenhouse-Geisser (F-GG) and Huynh-Feldt (F-HF) adjustments. Although numerous studies have analyzed the robustness of these procedures, the results are inconsistent, thus highlighting the need for further research. Methods: The aim of this simulation study was to analyze the performance of the Fstatistic, F-GG, and F-HF in terms of Type I error and power in one-way designs with normal data under a variety of conditions that may be encountered in real research practice. Values of ε were fixed according to the Greenhouse–Geisser procedure (ε). We manipulated the number of repeated measures (3, 4, and 6) and sample size (from 10 to 300), with ε values ranging from the lower to its upper limit. Results: Overall, the results showed that the F-statistic becomes more liberal as sphericity violation increases, whereas both F-HF and F-GG control Type I error; of the two, F-GG is more conservative, especially with large values of ε and small samples. Discussion: If different statistical conclusions follow from application of the two tests, we recommend using F-GG for ε values below 0.60, and F-HF for ε values equal to or above 0.60.