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Preliminary tests when comparing means

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  • I. Parra-Frutos

    (University of Murcia)

Abstract

The aim of this paper is to find a procedure to test equal means that is robust at the significance level. A simulation study is conducted to compare the performance of different strategies, including unconditionally applying the bootstrap ANOVA and twelve adaptive tests that take in pre-testing normality, homoscedasticity and skewness. Various final tests of equal means have been considered, like the ANOVA, bootstrap ANOVA, Welch, Brown–Forsythe and bootstrap James test. Our simulation results reveal that the usual adaptive test used by applied researchers (based on testing normality and homoscedasticity to choose from the ANOVA, Welch and Kruskal–Wallis tests) performs poorly. The simulation results show that preliminary tests may improve the performance of a test, and that this depends on the pre-tests chosen. In particular, we find that using decisions on normality to select the right homoscedasticity test and then choosing between the Brown–Forsythe test and the bootstrap ANOVA leads to controlling the Type I error rate in all of the settings studied.

Suggested Citation

  • I. Parra-Frutos, 2016. "Preliminary tests when comparing means," Computational Statistics, Springer, vol. 31(4), pages 1607-1631, December.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-016-0656-4
    DOI: 10.1007/s00180-016-0656-4
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    References listed on IDEAS

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    1. 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.
    2. Dieter Rasch & Klaus Kubinger & Karl Moder, 2011. "The two-sample t test: pre-testing its assumptions does not pay off," Statistical Papers, Springer, vol. 52(1), pages 219-231, February.
    3. 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.
    4. Cahoy, Dexter O., 2010. "A bootstrap test for equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2306-2316, October.
    5. I. Parra-Frutos, 2013. "Testing homogeneity of variances with unequal sample sizes," Computational Statistics, Springer, vol. 28(3), pages 1269-1297, June.
    6. Isabel Parra-Frutos, 2009. "The behaviour of the modified Levene’s test when data are not normally distributed," Computational Statistics, Springer, vol. 24(4), pages 671-693, December.
    7. Kimihiro Noguchi & Yulia Gel, 2010. "Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 897-913.
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