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Comparing the variances of several treatments with that of a control treatment: Theory and applications

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  • Jingsen Kong
  • Hezhi Lu

Abstract

A common and important problem in medicine, economics and environmental studies is the comparison of the variances of several treatments with that of a control treatment. Among the existing methods, Spurrier’s optimal test based on multivariate F distribution has exact type I error rates. However, it requires equal sample sizes among the treatment groups. To extend the application scope, in this paper, we propose a new efficient test for comparing several variances with a control using the marginal inferential model (MIM). Simulation studies show that the MIM test guarantees the exact type I error rate whether the sample size is equal or unequal. Moreover, the power of the MIM test is competitive with that of Spurrier’s optimal test. Finally, two real examples are used to demonstrate the application of the proposed method.

Suggested Citation

  • Jingsen Kong & Hezhi Lu, 2024. "Comparing the variances of several treatments with that of a control treatment: Theory and applications," PLOS ONE, Public Library of Science, vol. 19(1), pages 1-16, January.
    • Handle: RePEc:plo:pone00:0296376
    DOI: 10.1371/journal.pone.0296376
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    References listed on IDEAS

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    1. Ryan Martin & Chuanhai Liu, 2013. "Inferential Models: A Framework for Prior-Free Posterior Probabilistic Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 301-313, March.
    2. Koon-Shing Kwong, 2001. "An algorithm for construction of multiple hypothesis testing," Computational Statistics, Springer, vol. 16(1), pages 165-171, March.
    3. Singh, Parminder & Gill, Amar Nath & Kumar, Narendra, 2009. "A test of homogeneity of several variances against tree ordered alternative," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2315-2320, November.
    4. Singh, Parminder & Goyal, Anju & Gill, A.N., 2010. "A note on comparing several variances with a control variance," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1995-2002, December.
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