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Confidence Intervals for Ratios of Means and Medians

Author

Listed:
  • Douglas G. Bonett

    (8787University of California, Santa Cruz)

  • Robert M. Price Jr.

    (4154East Tennessee State University)

Abstract

In studies where the response variable is measured on a ratio scale, a ratio of means or medians provides a standardized measure of effect size that is an alternative to the popular standardized mean difference. Confidence intervals for ratios of population means and medians in independent-samples designs and paired-samples designs are proposed as supplements to the independent-samples t test and paired-samples t test. The performance of the proposed confidence intervals are evaluated in a simulation study. The proposed confidence interval methods are extended to the case of a 2 × m factorial design that includes propensity score stratification and meta-analysis as special cases. R functions that implement the recommended confidence intervals are provided in the Supplemental Material file, available in the online version of this article, and are illustrated with several examples.

Suggested Citation

  • Douglas G. Bonett & Robert M. Price Jr., 2020. "Confidence Intervals for Ratios of Means and Medians," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 750-770, December.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:6:p:750-770
    DOI: 10.3102/1076998620934125
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    References listed on IDEAS

    as
    1. Maritz, J. S., 1991. "Estimating the covariance matrix of bivariate medians," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 305-309, October.
    2. Hirschberg, Joe & Lye, Jenny, 2010. "A Geometric Comparison of the Delta and Fieller Confidence Intervals," The American Statistician, American Statistical Association, vol. 64(3), pages 234-241.
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