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Quality & Quantity

, Volume 51, Issue 1, pp 435–458 | Cite as

Fundamental characteristics and statistical analysis of ordinal variables: a review

  • Michele Lalla
Article

Abstract

The measurement of several concepts used in social sciences generates an ordinal variable, which is characterized by rawness of the output values and presents some much debated problems in data analysis. In fact, the need for effective analysis is easily satisfied with parametric models that deal with quantitative variables. However, the peculiarities of the ordinal scales, and the crude values produced by them, limit the use of parametric models, which has generated conflicting favourable and unfavourable views of the parametric approach. The main distinctive features of ordinal scales, some of which are critical points and nodal issues, are illustrated here along with the construction processes. Among the traditional procedures, the most common ordinal scales are described, including the Likert, semantic differential, feeling thermometers, and the Stapel scale. A relative new method, based on fuzzy sets, can be used to handle and generate ordinal variables. Therefore, the structure of a fuzzy inference system is exemplified in synthetic terms to show the treatment of ordinal variables to obtain one or more response variables. The nature of ordinal variables influences the interpretation and selection of many strategies used for their analysis. Four approaches are illustrated (nonparametric, parametric, latent variables, and fuzzy inference system), highlighting their potential and drawbacks. The modelling of an ordinal dependent variable (loglinear models, ordinary parametric models or logit and probit ordinal models, latent class models and hybrid models) is affected by the various approaches.

Keywords

Measurement Fuzzy sets Feeling thermometer Semantic differential Likert scale Stapel scale 

Notes

Acknowledgments

Part of this paper, specifically Sect. 2, has been previously published (Lalla 2015) in the volume edited by Sefano Campostrini, Giulio Ghellini, and Arjuna Tuzzi (2015), a collection of papers written by pupils and colleagues in honour of Professor Lorenzo Bernardi, who was a fine, versatile, and brilliant academic and social statistician. Overall, he was a master, a mentor and a friend for many of us. This paper is dedicated to his memory.

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Economics “Marco Biagi”, CAPP (Centre for the Analysis of Public Policies)University of Modena and Reggio EmiliaModenaItaly

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