Repeated Measures ANOVA and adjusted F-tests when sphericity is violated: Which procedure is best?
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 emplo...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/205662 |
| Acceso en línea: | https://hdl.handle.net/2445/205662 |
| Access Level: | acceso abierto |
| Palabra clave: | Models lineals (Estadística) Anàlisi de variància Ciències socials Linear models (Statistics) Analysis of variance Social sciences |
| Sumario: | 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. |
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