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Testing the equality of a large number of normal population means

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  • Park, Junyong
  • Park, DoHwan

Abstract

It is challenging to consider the problem of testing the equality of normal population means when the number of populations is large compared to the sample sizes. In ANOVA with the assumption of homogeneous variance, the F-test is known as an exact test. When variances are heterogeneous, due to the complication, there are various tests with only approximate forms–either approximate chi-square or approximate F-test. Two types of tests are proposed with their asymptotic normality as the number of population increases. p-values from those tests are adjusted based on higher order asymptotics such as Edgeworth expansion so that the proposed tests can be considered even for moderate values of k. Numerical studies including simulations and real data examples are presented with comparison to existing tests.

Suggested Citation

  • Park, Junyong & Park, DoHwan, 2012. "Testing the equality of a large number of normal population means," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1131-1149.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:5:p:1131-1149
    DOI: 10.1016/j.csda.2011.08.017
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    References listed on IDEAS

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    1. Joachim Hartung & Dogan Argaç & Kepher Makambi, 2002. "Small sample properties of tests on homogeneity in one—way Anova and Meta—analysis," Statistical Papers, Springer, vol. 43(2), pages 197-235, April.
    2. Saha, Krishna K. & Bilisoly, Roger, 2009. "Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3305-3313, July.
    3. 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.
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    1. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Alba-Fernández, M.V. & Jiménez-Gamero, M.D. & Jiménez-Jiménez, F., 2024. "Testing for proportions when data are classified into a large number of groups," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 588-600.

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