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Tests on asymmetry for ordered categorical variables

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  • Klein, Ingo
  • Doll, Monika

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 almost no 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 illustrated these tests by applying real data examples.

Suggested Citation

  • Klein, Ingo & Doll, Monika, 2018. "Tests on asymmetry for ordered categorical variables," FAU Discussion Papers in Economics 03/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    • Handle: RePEc:zbw:iwqwdp:032018
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    References listed on IDEAS

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    Keywords

    Ordered Categorical Variables; Skewness Analysis; Skewness Ordering; Maximalinvariants;
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