Measures of Ordinal Association: A New Look at an Old Problem

Evidence shows that the gamma coefficient (Goodman & Kruskal, 1954) as a measure of association between two classifications either overestimated or underestimated the degree of association in the 2 × 2 case in most situations, underestimated the degree in the m × 2 ( m > 2) case, and was subject to restricted-range and fineness/coarseness effects. This study is to treat the degree of association as the extent to which the percentage of observations falling into a class on one classification can be increased by an increase from one class to another on the other classification. A statistic computing the relative magnitude of the percentage increase to its maximal increase, designated as C p , is ideal for measuring the degree without being contaminated by other factors. Moreover, the value of C p is accurate and stable across different portions of classification data and free from restricted-range and fineness/coarseness effects.