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Graphical Procedures for Multiple Comparisons Under General Dependence


  • Christopher J. Bennett
  • Brennan S. Thompson


It has been more than half a century since Tukey first introduced graphical displays that relate nonoverlap of confidence intervals to statistically significant differences between parameter estimates. In this article, we show how Tukey’s graphical overlap procedure can be modified to accommodate general forms of dependence within and across samples. We also develop a procedure that can be used to more effectively resolve rankings within the tails of the distributions of parameter values, thereby generalizing existing methods for “multiple comparisons with the best.” We show that these new procedures retain the simplicity of Tukey’s original procedure, while maintaining asymptotic control of the familywise error rate under very general conditions. Simple examples are used throughout to illustrate the procedures. Supplementary materials for this article are available online.

Suggested Citation

  • Christopher J. Bennett & Brennan S. Thompson, 2016. "Graphical Procedures for Multiple Comparisons Under General Dependence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1278-1288, July.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:515:p:1278-1288
    DOI: 10.1080/01621459.2015.1093941

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    References listed on IDEAS

    1. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    3. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
    4. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
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    Cited by:

    1. Brennan S Thompson & Matthew D Webb, 2019. "A simple, graphical approach to comparing multiple treatments," Econometrics Journal, Royal Economic Society, vol. 22(2), pages 188-205.
    2. Jean-Marie DUFOUR & Lynda KHALAF & Marcel VOIA, 2013. "Finite-Sample Resampling-Based Combined Hypothesis Tests, with Applications to Serial Correlation and Predictability," Cahiers de recherche 13-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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