Speakers
Abstract
Background. Recent studies have shown that repeated measures analysis of variance (RM-ANOVA) is generally robust to violation of normality provided the sphericity assumption is fulfilled. However, violation of sphericity has an important impact in terms of Type I error. In this scenario, the Greenhouse-Geisser (F-GG) and Huynh-Feldt (F-HF) adjustments have been widely used as alternatives to the F-statistic. However, the performance of both F-GG and F-HF remains unclear when sphericity is violated under very extreme violation of normality. Objective. The aim of this study was to analyse the performance of the F-statistic, F-GG and F-HF in terms of Type I error, with designs including three repeated measures, very extreme violation of normality (i.e. γ1 = 3, γ2 = 21), epsilon values ranging from the lower to its upper limit (from .50 to 1), and a wide range of sample sizes (from 10 to 300). Method. Monte Carlo simulation was performed, with results being interpreted according to Bradley’s liberal criterion. Results. F-GG and F-HF are generally robust when normality is violated, provided that there is no extreme violation of sphericity (i.e. epsilon values ≤ .60). In this case, their robustness depends on the sample size, and they are liberal with small sample sizes. Conclusions. The more severe the violation of both normality and sphericity, the larger the sample size needed to achieve robustness of F-GG and F-HF. Further studies with a larger number of repeated measures are needed to analyse robustness of these statistics with extreme violation of both normality and sphericity. This research was supported by grant PID2020-113191GB-I00 from the MCIN/AEI/10.13039/501100011033.
| Poster | Type I error of repeated measures ANOVA with non-sphericity and very extreme deviation from normality |
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| Keywords | Greenhouse-Geisser, Huynh-Feldt, ANOVA, repeated measures |
