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Statistics of Ordinal Variation

Author

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  • JULIAN BLAIR

    (Santa Rosa, California)

  • MICHAEL G. LACY

    (Colorado State University)

Abstract

Whereas measures of variation in nominal data have long been recognized and used by sociologists, measures of variation for ordered categorical data have received little attention. The authors discuss the potential usefulness of ordinal dispersion statistics in sociology and define a broad class of such measures, some of which have previously been proposed in other forms. This article focuses on two statistics, termed l 2 and l, which are [0 - 1] normed measures of concentration or dispersion, and illustrates their use for two purposes: measuring inequality and cultural consensus. The bias, variance, and use of these statistics in inference are discussed. The article concludes with a substantive application of these statistics and a comparison to the performance of conventional variation statistics.

Suggested Citation

  • Julian Blair & Michael G. Lacy, 2000. "Statistics of Ordinal Variation," Sociological Methods & Research, , vol. 28(3), pages 251-280, February.
    • Handle: RePEc:sae:somere:v:28:y:2000:i:3:p:251-280
    DOI: 10.1177/0049124100028003001
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    Cited by:

    1. Stephen P. Jenkins, 2020. "Better off? Distributional comparisons for ordinal data about personal well-being," New Zealand Economic Papers, Taylor & Francis Journals, vol. 54(3), pages 211-238, September.
    2. Martyna Kobus, 2014. "On the measurement of polarization for ordinal data," Working Papers 325, ECINEQ, Society for the Study of Economic Inequality.
    3. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.

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