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A note on comparing several variances with a control variance

Author

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  • Singh, Parminder
  • Goyal, Anju
  • Gill, A.N.

Abstract

Consider the problem of comparing variances of k populations with the variance of a control population. When the experimenter has a prior expectation that the variances of k populations are not less than the variance of a control population, one-sided simultaneous confidence intervals provide more inferential sensitivity than two-sided simultaneous confidence intervals. But the two-sided simultaneous confidence intervals have advantages over the one-sided simultaneous confidence intervals as they provide both lower and upper bounds for the parameters of interest. In this article, a new multiple comparison procedure is developed for comparing several variances with a control variance, which provides two-sided simultaneous confidence intervals for the ratios of variances with the control variance and maintains the inferential sensitivity of one-sided simultaneous confidence intervals. Computation of the critical constants for the implementation of the proposed procedure is discussed and the selected critical constants are tabulated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1995-2002
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.

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    1. Philip Pallmann & Ludwig Hothorn & Gemechis Djira, 2014. "A Levene-type test of homogeneity of variances against ordered alternatives," Computational Statistics, Springer, vol. 29(6), pages 1593-1608, December.

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