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A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances

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  • Xu, Li-Wen
  • Yang, Fang-Qin
  • Abula, Aji’erguli
  • Qin, Shuang

Abstract

In this article we consider the Two-Way ANOVA model with unequal cell frequencies without the assumption of equal error variances. For the problem of testing no interaction effects and equal main effects, we propose a parametric bootstrap (PB) approach and compare it with existing the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the generalized F-test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up.

Suggested Citation

  • Xu, Li-Wen & Yang, Fang-Qin & Abula, Aji’erguli & Qin, Shuang, 2013. "A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 172-180.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:172-180
    DOI: 10.1016/j.jmva.2012.10.008
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    References listed on IDEAS

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    1. Krishnamoorthy, K. & Lu, Fei & Mathew, Thomas, 2007. "A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5731-5742, August.
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    Cited by:

    1. Mondal, Anjana & Sattler, Paavo & Kumar, Somesh, 2023. "Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. Milica Maricic & Jose A. Egea & Veljko Jeremic, 2019. "A Hybrid Enhanced Scatter Search—Composite I-Distance Indicator (eSS-CIDI) Optimization Approach for Determining Weights Within Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 497-537, July.
    3. Friedrich, Sarah & Pauly, Markus, 2018. "MATS: Inference for potentially singular and heteroscedastic MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 166-179.
    4. Burim Ramosaj & Markus Pauly, 2019. "Predicting missing values: a comparative study on non-parametric approaches for imputation," Computational Statistics, Springer, vol. 34(4), pages 1741-1764, December.
    5. Feng, Fei & Yang, Rui & Meng, Jinhao & Xie, Yi & Zhang, Zhiguo & Chai, Yi & Mou, Lisha, 2022. "Electrochemical impedance characteristics at various conditions for commercial solid–liquid electrolyte lithium-ion batteries: Part. 2. Modeling and prediction," Energy, Elsevier, vol. 243(C).
    6. Konietschke, Frank & Bathke, Arne C. & Harrar, Solomon W. & Pauly, Markus, 2015. "Parametric and nonparametric bootstrap methods for general MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 291-301.
    7. Sadooghi-Alvandi, S.M. & Malekzadeh, A., 2014. "Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 133-140.
    8. Xu, Li-Wen, 2015. "Parametric bootstrap approaches for two-way MANOVA with unequal cell sizes and unequal cell covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 291-303.

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