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Tests on asymmetry for ordered categorical variables

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  • Ingo Klein
  • Monika Doll

Abstract

Skewness is a well-established statistical concept for continuous and, to a lesser extent, for discrete quantitative statistical variables. However, for ordered categorical variables, limited literature concerning skewness exists, although this type of variables is common for behavioral, educational, and social sciences. Suitable measures of skewness for ordered categorical variables have to be invariant with respect to the group of strictly increasing, continuous transformations. Therefore, they have to depend on the corresponding maximal-invariants. Based on these maximal-invariants, we propose a new class of skewness functionals, show that members of this class preserve a suitable ordering of skewness and derive the asymptotic distribution of the corresponding skewness statistic. Finally, we show the good power behavior of the corresponding skewness tests and illustrate these tests by applying real data examples.

Suggested Citation

  • Ingo Klein & Monika Doll, 2021. "Tests on asymmetry for ordered categorical variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(7), pages 1180-1198, May.
    • Handle: RePEc:taf:japsta:v:48:y:2021:i:7:p:1180-1198
    DOI: 10.1080/02664763.2020.1757045
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    Cited by:

    1. Weiß, Christian H. & Ruiz Marín, Manuel & Keller, Karsten & Matilla-García, Mariano, 2022. "Non-parametric analysis of serial dependence in time series using ordinal patterns," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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