A NEW TEST FOR EQUALITY OF VARIANCES FOR k NORMAL POPULATIONS

Bhat, B. R.; Badade, Meena; Rao, K. Aruna

doi:10.1081/sac-120004313

Communications in Statistics: Simulation and Computation

2002

DOI: 10.1081/sac-120004313

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A NEW TEST FOR EQUALITY OF VARIANCES FOR k NORMAL POPULATIONS

B. R. Bhat¹,

Meena Badade²,

K. Aruna Rao³

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Cited by 2 publications

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“…One of the biggest advantages of following these steps is that applied researchers do not need to use any traditional homogeneity tests (e.g., Bartlett, 1937;Cochran, 1941;Hartley, 1950;Levene, 1960), which are known to rely on other assumptions that might not be met (Bhat, Badade, & Aruna Rao, 2002;Conover, Johnson, & Johnson, 1981;Harwell et al, 1992;Moder, 2007;Sharma & Kibria, 2013;Zimmerman, 2004). Moreover, researchers can locate the specific variance conditions and characteristics of their data in the tables provided and see directly if F-test is robust or not.…”

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confidence: 99%

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

et al. 2017

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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.

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mentioning

confidence: 99%

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

et al. 2017

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Post-hoc tests in one-way ANOVA: The case for normal distribution

Juarros-Basterretxea,

Aonso-Diego,

Postigo

et al. 2024

Methodology

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When one-way ANOVA is statistically significant, a multiple comparison problem arises, hence post-hoc tests are needed to elucidate between which groups significant differences are found. Different post-hoc tests have been proposed for each situation regarding heteroscedasticity and sample size groups. This study aims to compare the Type I error (α) rate of 10 post-hoc tests in four different conditions based on heteroscedasticity and balance between-group sample size. A Montecarlo simulation study was carried out on a total of 28 data sets, with 10,000 resamples in each, distributed through four conditions. One-way ANOVA tests and post-hoc tests were conducted to estimate the α rate at a 95% confidence level. The percentage of times the null hypothesis was falsely refused is used to compare the tests. Three out of four conditions demonstrated considerable variability among sample sizes. However, the best post-hoc test in the second condition (heteroscedastic and balance group) did not depend on simple size. In some cases, inappropriate post-hoc tests were more accurate. Homoscedasticity and balance between-group sample size should be considered for appropriate post-hoc test selection.

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A NEW TEST FOR EQUALITY OF VARIANCES FOR k NORMAL POPULATIONS

Cited by 2 publications

References 8 publications

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?

Post-hoc tests in one-way ANOVA: The case for normal distribution

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