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A bootstrap test for equality of variances

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  • Cahoy, Dexter O.

Abstract

We introduce a bootstrap procedure to test the hypothesis Ho that K+1 variances are homogeneous. The procedure uses a variance-based statistic, and is derived from a normal-theory test for equality of variances. The test equivalently expressed the hypothesis as , where [eta]i's are log contrasts of the population variances. A box-type acceptance region is constructed to test the hypothesis Ho. Simulation results indicated that our method is generally superior to the Shoemaker and Levene tests, and the bootstrapped version of the Levene test in controlling the Type I and Type II errors.

Suggested Citation

  • Cahoy, Dexter O., 2010. "A bootstrap test for equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2306-2316, October.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:10:p:2306-2316
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    References listed on IDEAS

    as
    1. Shoemaker L.H., 2003. "Fixing the F Test for Equal Variances," The American Statistician, American Statistical Association, vol. 57, pages 105-114, May.
    2. Ralph O'Brien, 1978. "Robust techniques for testing heterogeneity of variance effects in factorial designs," Psychometrika, Springer;The Psychometric Society, vol. 43(3), pages 327-342, September.
    3. Lim, Tjen-Sien & Loh, Wei-Yin, 1996. "A comparison of tests of equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 287-301, July.
    4. W. G. S. Hines & R. J. O'Hara Hines, 2000. "Increased Power with Modified Forms of the Levene (Med) Test for Heterogeneity of Variance," Biometrics, The International Biometric Society, vol. 56(2), pages 451-454, June.
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    Cited by:

    1. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.
    2. I. Parra-Frutos, 2013. "Testing homogeneity of variances with unequal sample sizes," Computational Statistics, Springer, vol. 28(3), pages 1269-1297, June.
    3. I. Parra-Frutos, 2016. "Preliminary tests when comparing means," Computational Statistics, Springer, vol. 31(4), pages 1607-1631, December.
    4. Boudt, Kris & Cornelissen, Jonathan & Croux, Christophe, 2012. "Jump robust daily covariance estimation by disentangling variance and correlation components," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 2993-3005.
    5. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
    6. Ali Akbar Jafari & Javad Shaabani, 2020. "Comparing scale parameters in several gamma distributions with known shapes," Computational Statistics, Springer, vol. 35(4), pages 1927-1950, December.
    7. Ramos-Guajardo, Ana Belén & Lubiano, María Asunción, 2012. "K-sample tests for equality of variances of random fuzzy sets," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 956-966.

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