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Statistics and the Theory of Measurement

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  • D. J. Hand

Abstract

Just as there are different interpretations of probability, leading to different kinds of inferential statements and different conclusions about statistical models and questions, so there are different theories of measurement, which in turn may lead to different kinds of statistical model and possibly different conclusions. This has led to much confusion and a long running debate about when different classes of statistical methods may legitimately be applied. This paper outlines the major theories of measurement and their relationships and describes the different kinds of models and hypotheses which may be formulated within each theory. One general conclusion is that the domains of applicability of the two major theories are typically different, and it is this which helps apparent contradictions to be avoided in most practical applications.

Suggested Citation

  • D. J. Hand, 1996. "Statistics and the Theory of Measurement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 445-473, May.
    • Handle: RePEc:bla:jorssa:v:159:y:1996:i:3:p:445-473
    DOI: 10.2307/2983326
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    Cited by:

    1. Shizuhiko Nishisato, 2016. "Book Review," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 242-245, March.
    2. Rohana Yusoff & Roziah Mohd Janor, 2014. "Generation of an Interval Metric Scale to Measure Attitude," SAGE Open, , vol. 4(1), pages 21582440135, January.
    3. Thomas King, 2013. "A framework for analysing social sequences," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(1), pages 167-191, January.
    4. Dennis Cook, R. & Forzani, Liliana, 2023. "On the role of partial least squares in path analysis for the social sciences," Journal of Business Research, Elsevier, vol. 167(C).
    5. C Mar-Molinero & J Mingers, 2007. "An evaluation of the limitations of, and alternatives to, the Co-Plot methodology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 874-886, July.
    6. Shizuhiko Nishisato, 2016. "Book Review," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 242-245, March.
    7. Irena Ograjenšek & Iddo Gal, 2016. "Enhancing Statistics Education by Including Qualitative Research," International Statistical Review, International Statistical Institute, vol. 84(2), pages 165-178, August.

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