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Introduction

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Book cover The Measurement of Association

Abstract

This chapter provides an introduction to the next nine chapters, a brief introduction to the two models of statistical inference—the population model and the permutation model. An overview of the remaining nine chapters concludes the chapter.

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Notes

  1. 1.

    There are two prominent statisticians with the surname Pearson: Karl Pearson, the father, and Egon S. Pearson, the son. Unless specified otherwise, in this book “Pearson” refers to Karl Pearson (1857–1936).

  2. 2.

    The Neyman–Pearson population model is named for Jerzy Neyman (1894–1981) and Egon Pearson (1895–1980) and the Fisher–Pitman permutation model is named for Ronald Aylmer Fisher (1890–1962) and Edward James George Pitman (1897–1993).

  3. 3.

    Other typologies of scales of measurement exist. See, for example, those by Anderson , Balilevsky , and Hum [2], Mosteller and Tukey [22], and Pfanzagl [23].

  4. 4.

    Kelvins are named for Scottish physicist William Thomson, Lord Kelvin of Largs (1866–1892).

  5. 5.

    The correlation ratio, η 2, was first described by Karl Pearson in 1911 and 1923 and later by R.A. Fisher in 1925.

  6. 6.

    Technically, Pearson’s ϕ 2, Tschuprov’s T 2, Cramér’s V 2, and Pearson’s C are maximum-corrected measures of association under only certain highly restrictive conditions.

  7. 7.

    For a somewhat different organization using nominal, ordinal, and interval scales, see a 1983 book by A.M. Liebetrau on non-permutation Measures of Association.

References

  1. Agresti, A.: The effect of category choice on some ordinal measures of association. J. Am. Stat. Assoc. 71, 49–55 (1976)

    Article  Google Scholar 

  2. Anderson, A.B., Balilevsky, A., Hum, D.P.J.: Missing data. In: Rossi, P.H., Wright, J.D., Anderson, A.B. (eds.) Handbook of Survey Research, chap. 12, pp. 415–479. Academic Press, New York (1983)

    Chapter  Google Scholar 

  3. Berry, K.J., Mielke, P.W.: Extension of Spearman’s footrule to multiple rankings. Psychol. Rep. 82, 376–378 (1998)

    Article  Google Scholar 

  4. Berry, K.J., Mielke, P.W., Johnston, J.E.: Permutation Statistical Methods: An Integrated Approach. Springer-Verlag, Cham, CH (2016)

    Book  Google Scholar 

  5. Borgatta, E.F., Bornstedt, G.W.: Level of measurement—once over again. Sociol. Method Res. 9, 147–160 (1980)

    Article  Google Scholar 

  6. Bornstedt, G.W.: Measurement. In: Rossi, P.H., Wright, J.D., Anderson, A.B. (eds.) Handbook of Survey Research, chap. 3, pp. 69–121. Academic Press, New York (1983)

    Chapter  Google Scholar 

  7. Costner, H.L.: Criteria for measures of association. Am. Sociol. Rev. 30, 341–353 (1965)

    Article  Google Scholar 

  8. Cowles, M.: Statistics in Psychology: An Historical Perspective, 2nd edn. Lawrence Erlbaum, Mahwah, NJ (2001)

    MATH  Google Scholar 

  9. Everitt, B.: Chance Rules: An Informal Guide to Probability, Risk, and Statistics, 2nd edn. Springer–Verlag, New York (2008)

    Book  Google Scholar 

  10. Fernandes, P.: Don’t send us back to the closet. NY Times 166, A25 (11 May 2017)

    Google Scholar 

  11. Gaito, J.: Measurement scales and statistics: Resurgence of an old misconception. Psychol. Bull. 87, 564–567 (1980)

    Article  Google Scholar 

  12. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications. J. Am. Stat. Assoc. 49, 732–764 (1954)

    MATH  Google Scholar 

  13. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications, II: Further discussion and references. J. Am. Stat. Assoc. 54, 123–163 (1959)

    MATH  Google Scholar 

  14. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications, III: Approximate sampling theory. J. Am. Stat. Assoc. 58, 310–364 (1963)

    Google Scholar 

  15. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classifications, IV: Simplification of asymptotic variances. J. Am. Stat. Assoc. 67, 415–421 (1972)

    MATH  Google Scholar 

  16. Leik, R.K., Gove, W.R.: Integrated approach to measuring association. In: Costner, H.L. (ed.) Sociological Methodology, pp. 279–301. Jossey Bass, San Francisco, CA (1971)

    Google Scholar 

  17. Liebetrau, A.M.: Measures of Association. Sage, Beverly Hills, CA (1983)

    Book  Google Scholar 

  18. Lord, F.: On the statistical treatment of football numbers. Am. Psychol. 8, 750–751 (1953)

    Article  Google Scholar 

  19. Luce, R.D., Krantz, D.H., Suppes, P., Tversky, A.: Foundations of Measurement, vol. 3. Academic Press, New York (1990)

    MATH  Google Scholar 

  20. Mielke, P.W., Berry, K.J., Johnston, J.E.: Resampling probability values for weighted kappa with multiple raters. Psychol. Rep. 102, 606–613 (2008)

    Article  Google Scholar 

  21. Mortimer, I.: The Time Traveler’s Guide to Restoration Britain. Pegasus, New York (2017)

    Google Scholar 

  22. Mosteller, M., Tukey, J.W.: Data Analysis and Regression: A Second Course in Statistics. Addison–Wesley, Reading, MA (1977)

    Google Scholar 

  23. Pfanzagl, J.: Theory of Measurement. Wiley, New York (1968)

    MATH  Google Scholar 

  24. Stevens, S.S.: On the theory of scales and measurement. Science 103, 667–680 (1946)

    Article  Google Scholar 

  25. Stevens, S.S.: Mathematics, measurement, and psychophysics. In: Stevens, S.S. (ed.) Handbook of Experimental Psychology, chap. 1, pp. 1–49. Wiley, New York (1951)

    Google Scholar 

  26. Thomson, W.: Popular Lectures and Addresses. MacMillan, London (1889)

    Google Scholar 

  27. Vellman, P.F., Wilkinson, L.: Nominal, ordinal, interval and ratio typologies are misleading. Am. Stat. 47, 65–72 (1993)

    Google Scholar 

  28. Weiss, R.S.: Statistics in Social Research: An Introduction. Wiley, New York (1968)

    Google Scholar 

  29. Wilson, T.P.: Critique of ordinal variables. Social Forces 49, 432–444 (1971)

    Article  Google Scholar 

  30. Yule, G.U.: On the methods of measuring association between two attributes. J. R. Stat. Soc. 75, 579–652 (1912). [Originally a paper read before the Royal Statistical Society on 23 April 1912]

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Sociology, Colorado State University, Fort Collins, Colorado, USA

    Kenneth J. Berry

  2. Alexandria, Virginia, USA

    Janis E. Johnston

  3. Department of Statistics, Colorado State University, Fort Collins, Colorado, USA

    Paul W. Mielke Jr.

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  1. Kenneth J. Berry
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  2. Janis E. Johnston
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  3. Paul W. Mielke Jr.
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Berry, K.J., Johnston, J.E., Mielke, P.W. (2018). Introduction. In: The Measurement of Association. Springer, Cham. https://doi.org/10.1007/978-3-319-98926-6_1

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