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On testing the equality between interquartile ranges

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Abstract

The interquartile range is a statistical measure well suited to describe the variability of the data at hand, both at the population level and for sample data. The interquartile range is particularly useful when the distribution of the data is asymmetric or irregularly shaped. Here, the use of the interquartile range is investigated when the main aim is to compare the variability of two distributions using two independent random samples, without the need to make any distributional assumptions. Several techniques are compared through numerical studies and real data examples, with a particular attention given to the use of sample quantiles based on the Harrel-Davis estimator or the quantile regression.

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Acknowledgements

The authors wish to thank two anonymous reviewers for their helpful comments.

Author information

Authors and Affiliations

  1. University Giustino Fortunato, Benevento, Italy

    Luca Greco

  2. Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, USA

    George Luta

  3. Department of Psychology, University of Southern California, Los Angeles, USA

    Rand Wilcox

Authors
  1. Luca Greco
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  2. George Luta
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  3. Rand Wilcox
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Correspondence to Luca Greco.

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Appendix

Appendix

See Tables 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23.

Table 5 Data generation scheme (a)
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Table 6 Data generation scheme (a)
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Table 7 Data generation scheme (b)
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Table 8 Data generation scheme (b)
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Table 9 Data generation scheme (c)
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Table 10 Data generation scheme (c)
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Table 11 Data generation scheme (d)
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Table 12 Data generation scheme (d)
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Table 13 Data generation scheme (e)
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Table 14 Data generation scheme (e)
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Table 15 Data generation scheme (f)
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Table 16 Data generation scheme (f)
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Table 17 Data generation scheme (g)
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Table 18 Data generation scheme (g)
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Table 19 Data generation scheme (ap)
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Table 20 Data generation scheme (cp)
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Table 21 Data generation scheme (dp)
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Table 22 Data generation scheme (ep)
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Table 23 Data generation scheme (fp)
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Greco, L., Luta, G. & Wilcox, R. On testing the equality between interquartile ranges. Comput Stat (2023). https://doi.org/10.1007/s00180-023-01415-8

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  • DOI: https://doi.org/10.1007/s00180-023-01415-8

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