Tests on asymmetry for ordered categorical variables

Klein I, Doll M (2020)

Publication Language: English

Publication Type: Journal article

Publication year: 2020

Journal

Journal of Applied Statistics Taylor & Francis (Routledge): STM, Behavioural Science and Public Health Titles / Taylor & Francis (Routledge)

DOI: 10.1080/02664763.2020.1757045

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.

Authors with CRIS profile

Ingo Klein Lehrstuhl für Statistik und Ökonometrie Monika Lieb Lehrstuhl für Statistik und Ökonometrie

How to cite

APA:

Klein, I., & Doll, M. (2020). Tests on asymmetry for ordered categorical variables. Journal of Applied Statistics. https://dx.doi.org/10.1080/02664763.2020.1757045

MLA:

Klein, Ingo, and Monika Doll. "Tests on asymmetry for ordered categorical variables." Journal of Applied Statistics (2020).

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