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

Konstantinos Konstantinou (), Tomáš Mrkvička and Mari Myllymäki
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Konstantinos Konstantinou: Chalmers University of Technology and University of Gothenburg
Tomáš Mrkvička: University of South Bohemia
Mari Myllymäki: Natural Resources Institute Finland (Luke)

Computational Statistics, 2025, vol. 40, issue 5, No 10, 2553-2582

Abstract: 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.

Keywords: Distribution comparison; Global envelope test; Multiple comparison problem; Permutation test; Significance testing; Simultaneous testing (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01569-z

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