Tests on asymmetry for ordered categorical variables

Ingo Klein and Monika Doll

No 03/2018, FAU Discussion Papers in Economics from Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics

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.

Keywords: Ordered Categorical Variables; Skewness Analysis; Skewness Ordering; Maximalinvariants (search for similar items in EconPapers)
Date: 2018
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:iwqwdp:032018

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