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An Application of the Theory of Spherical Distributions in Multiple Mean Comparison

In: Contemporary Experimental Design, Multivariate Analysis and Data Mining

Author

Listed:
  • Jiajuan Liang

    (University of New Haven)

  • Man-Lai Tang

    (Hang Seng Management College)

  • Jing Yang

    (Tianjin Medical University)

  • Xuejing Zhao

    (Lanzhou University)

Abstract

Multiple normal mean comparison without the equal-variance assumption is frequently encountered in medical and biological problems. Classical analysis of variance (ANOVA) requires the assumption of equal variances across groups. When variations across groups are found to be different, classical ANOVA method is essentially inapplicable for multiple mean comparison. Although various approximation methods have been proposed to solve the classical Behrens-Fisher problem, there exists computational complexity in approximating the null distributions of the proposed tests. In this paper we employ the theory of spherical distributions to construct a class of exact F-tests and a simple generalized F-test for multiple mean comparison. The methods in this paper actually provide a simple exact solution and a simple approximate solution to the classical Behrens-Fisher problem in the case of balanced sample designs. A simple Monte Carlo study shows that the recommended tests have fairly good power performance. An analysis on a real medical dataset illustrates the application of the new methods in medicine.

Suggested Citation

  • Jiajuan Liang & Man-Lai Tang & Jing Yang & Xuejing Zhao, 2020. "An Application of the Theory of Spherical Distributions in Multiple Mean Comparison," Springer Books, in: Jianqing Fan & Jianxin Pan (ed.), Contemporary Experimental Design, Multivariate Analysis and Data Mining, chapter 0, pages 189-199, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46161-4_12
    DOI: 10.1007/978-3-030-46161-4_12
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