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Comparison of quantiles for several normal populations

Author

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  • Li, Xinmin
  • Tian, Lili
  • Wang, Juan
  • Muindi, Josephia R.

Abstract

For the purpose of comparison between several independent populations, many procedures exist for testing equality of means or medians among the groups. However, the mean or the median do not determine the entire distribution. This paper addresses the problem of testing the equality of quantiles of several normal distributions. We propose an approximate test based on large sample method and an exact procedure based on a generalized p-value. An extensive simulation study was conducted to evaluate the size and powers of these two tests. Simulation results show that the generalized p-value approach performs very satisfactorily even for small samples while the approximate method exhibits poor Type I error control. A robustness study was done for power-exponential distribution and t-distribution. Finally, the proposed methods are applied to two real examples.

Suggested Citation

  • Li, Xinmin & Tian, Lili & Wang, Juan & Muindi, Josephia R., 2012. "Comparison of quantiles for several normal populations," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2129-2138.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2129-2138
    DOI: 10.1016/j.csda.2012.01.002
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    References listed on IDEAS

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    1. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    2. 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.
    3. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    4. Tian, Lili, 2006. "Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1156-1162, November.
    5. Li, Xinmin, 2009. "A generalized p-value approach for comparing the means of several log-normal populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1404-1408, June.
    6. Huang, Li-Fei & Johnson, Richard A., 2006. "Confidence regions for the ratio of percentiles," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 384-392, February.
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    Cited by:

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    2. Maichanou, Ahamadou & Dan Baky, Agada, 2022. "Private Intra-household Transfers as a Palliative for the Incompleteness of Social Protection: Evidence from Niger," African Journal of Economic Review, African Journal of Economic Review, vol. 10(2), March.

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