Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit?

Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit? Inconsistencies in the research findings on F-test robustness to variance heterogeneity could be related to the lack of a standard criterion to assess robustness or to the different measures used to quantify heterogeneity. In the present paper we use Monte Carlo simulation to systematically examine the Type I error rate of F-test under heterogeneity. One-way, balanced, and unbalanced designs with monotonic patterns of variance were considered. Variance ratio (VR) was used as a measure of heterogeneity (1.5, 1.6, 1.7, 1.8, 2, 3, 5, and 9), the coefficient of sample size variation as a measure of inequality between group sizes (0.16, 0.33, and 0.50), and the correlation between variance and group size as an indicator of the pairing between them (1, .50, 0, −.50, and −1). Overall, the results suggest that in terms of Type I error a VR above 1.5 may be established as a rule of thumb for considering a potential threat to F-test robustness under heterogeneity with unequal sample sizes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Behavior Research Methods Springer Journals

Effect of variance ratio on ANOVA robustness: Might 1.5 be the limit?

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Publisher
Springer US
Copyright
Copyright © 2017 by Psychonomic Society, Inc.
Subject
Psychology; Cognitive Psychology
eISSN
1554-3528
D.O.I.
10.3758/s13428-017-0918-2
Publisher site
See Article on Publisher Site

Abstract

Inconsistencies in the research findings on F-test robustness to variance heterogeneity could be related to the lack of a standard criterion to assess robustness or to the different measures used to quantify heterogeneity. In the present paper we use Monte Carlo simulation to systematically examine the Type I error rate of F-test under heterogeneity. One-way, balanced, and unbalanced designs with monotonic patterns of variance were considered. Variance ratio (VR) was used as a measure of heterogeneity (1.5, 1.6, 1.7, 1.8, 2, 3, 5, and 9), the coefficient of sample size variation as a measure of inequality between group sizes (0.16, 0.33, and 0.50), and the correlation between variance and group size as an indicator of the pairing between them (1, .50, 0, −.50, and −1). Overall, the results suggest that in terms of Type I error a VR above 1.5 may be established as a rule of thumb for considering a potential threat to F-test robustness under heterogeneity with unequal sample sizes.

Journal

Behavior Research MethodsSpringer Journals

Published: Jun 22, 2017

References

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