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The Measurement of Association pp 577–626Cite as

Fourfold Contingency Tables, II

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Abstract

This chapter continues the discussion measures of association for 2×2 contingency tables initiated in the previous chapter, but concentrates on symmetrical 2×2 contingency tables. Included in this chapter are permutation statistical methods applied to Pearson’s ϕ 2, Tschuprov’s T 2, and Cramér’s V 2 coefficients of contingency, Pearson’s product-moment correlation coefficient, Leik and Gove’s \(d_{N}^{\,c}\) measure, Goodman and Kruskal’s t a and t b measures, Kendall’s τ b and Stuart’s τ c measures, Yule’s Y measure, and Cohen’s κ measure of inter-rate agreement.

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Notes

  1. 1.

    It was not too many years ago that while μ x and \(\sigma _{x}^{2}\) denoted the population mean and variance, respectively, \(\hat {\mu }_{x}\) and \(\hat {\sigma }_{x}^{2}\) denoted the unbiased sample-estimated population mean and variance. The American Psychological Association presently recommends using M for the sample mean instead of the conventional \(\bar {x}\).

  2. 2.

    The test is often called the Cochran–Mantel–Haenszel test as William Cochran presented essentially the same test in an earlier paper [5].

  3. 3.

    The symbol M for the Mantel–Haenszel test should not be confused with the symbol M for the number of possible, equally-likely arrangements of the observed data under the Fisher–Pitman permutation model.

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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). Fourfold Contingency Tables, II. In: The Measurement of Association. Springer, Cham. https://doi.org/10.1007/978-3-319-98926-6_10

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