Misunderstood and Unattributed: Revisiting M. H. Doolittle's Measures of Association, With a Note on Bayes’ Theorem

Timothy W. Armistead

The American Statistician, 2016, vol. 70, issue 1, 63-73

Abstract: In the 1880s, American scholars developed measures of association and chance for cross-classification tables that anticipated the more widely known work of Galton, Pearson, Yule, and Fisher. Three of the measures form the historical backdrop for the earliest known use of a joint probability measure that mirrored Bayes’ theorem long before the latter gained general interest among statisticians. The joint probability measure, which served as a foundational step in M. H. Doolittle's development of the first of the two “association ratios,” has not previously been reviewed in the statistical literature. It was reintroduced as if newly developed in a subfield of experimental psychology more than a century after Doolittle's work was published. It has flourished there, but it has not seen use in other academic venues. The article describes its properties and limitations and proposes that it be disseminated and debated beyond its current narrow application. The article notes that Doolittle's first association ratio can be expressed as another joint probability and that prior treatments in the literature are inconsistent with Doolittle's understanding of its purpose. The article also demonstrates that the equivalent of Cohen's kappa ( κ ) was developed by Doolittle in 1887, as his second association measure.[Received December 2014. Revised August 2015.]

Date: 2016
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DOI: 10.1080/00031305.2015.1086686

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