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I am interested in Freeman's coefficient of differentiation (theta) because it appears to be one of the few measures of effect size for an association between an ordinal variable and a nominal variable.

The statistic is mentioned in a fair number of articles, e.g. Agresti, 1981 (below) and is listed in the top ranked answer to this Cross Validated question.

The original calculations are in Freeman, 1965, Elementary Applied Statistics for Students in Behavioral Science.

There is also a description of calculations in Freeman, 1976 (below).

EDITED: To remove extraneous information and questions in light of my own answer below.

UPDATE, 2023:

A more complete list of references.

Freeman, L.C. 1965. Elementary Applied Statistics for Students in Behavioral Science. Wiley.

Freeman, L.C. 1976. A Further Note on Freeman's Measure of Association. Psychometrika 4(2) June, 273-275. https://www.researchgate.net/publication/24062209_A_further_note_on_freeman%27s_measure_of_association

Agresti, A. Measures of Nominal-Ordinal Association. 1981. Journal of the American Statistical Association 76 (375) Sept., 524-529. https://users.stat.ufl.edu/~aa/articles/agresti_1981.pdf.

Mangiafico, S. 2016. Measures of Association for Ordinal Variables. In Summary and Analysis of Extension Program Evaluation in R. https://rcompanion.org/handbook/H_11.html.

Mangiafico, S. 2023. freemanTheta(). [R package] In rcompanion: Functions to Support Extension Education Program Evaluation. https://CRAN.R-project.org/package=rcompanion.

Sal Mangiafico
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1 Answers1

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In honor of Russell's paradox (barber version), and the fact that there were no answers to my question, I'll add an answer to my own question.

The calculations for Freeman's theta are included in the Freeman (1965) reference cited in the question. I was able to order the book inexpensively, and the calculations were simple enough.

I added a function to calculate Freeman's theta to the rcompanion package in R, available on CRAN. The function is called freemanTheta.

Sal Mangiafico
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