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