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The power of visualizing distributional differences: formal graphical n-sample tests

Author

Listed:
  • Konstantinos Konstantinou

    (Chalmers University of Technology and University of Gothenburg)

  • Tomáš Mrkvička

    (University of South Bohemia)

  • Mari Myllymäki

    (Natural Resources Institute Finland (Luke))

Abstract

Classical tests are available for the two-sample test of correspondence of distribution functions. From these, the Kolmogorov–Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose modifications of the Kolmogorov–Smirnov test with higher power. The proposed tests are based on the so-called global envelope test which allows for graphical interpretation, similarly as the Kolmogorov–Smirnov test. The tests are based on rank statistics and are suitable also for the comparison of n samples, with $$n \ge 2$$ n ≥ 2 . We compare the alternatives for the two-sample case through an extensive simulation study and discuss their interpretation. Finally, we apply the tests to real data. Specifically, we compare the height distributions between boys and girls at different ages, the sepal length distributions of different flower species, and distributions of standardized residuals from a time series model for different exchange courses using the proposed methodologies.

Suggested Citation

  • Konstantinos Konstantinou & Tomáš Mrkvička & Mari Myllymäki, 2025. "The power of visualizing distributional differences: formal graphical n-sample tests," Computational Statistics, Springer, vol. 40(5), pages 2553-2582, June.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:5:d:10.1007_s00180-024-01569-z
    DOI: 10.1007/s00180-024-01569-z
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    References listed on IDEAS

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    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Naveen N. Narisetty & Vijayan N. Nair, 2016. "Extremal Depth for Functional Data and Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1705-1714, October.
    5. Sivan Aldor-Noiman & Lawrence D. Brown & Andreas Buja & Wolfgang Rolke & Robert A. Stine, 2013. "The Power to See: A New Graphical Test of Normality," The American Statistician, Taylor & Francis Journals, vol. 67(4), pages 249-260, November.
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