Consistent Small-Sample Variances for Six Gamma-Family Measures of Ordinal Association

Gamma-family measures are bivariate ordinal correlation measures that form a family because they all reduce to Goodman and Kruskal's gamma in the absence of ties (1954) Goodman, L. A. and Kruskal, W. H. 1954. Measures of association for cross classifications.. Journal of the American Statistical Association, 49: 732–764. Taylor &; Francis Online], Web of Science ®] , Google Scholar]. For several gamma-family indices, more than one variance estimator has been introduced. In previous research, the “consistent” variance estimator described by Cliff and colleagues produced more accurate confidence intervals (CIs) than 3 other types of variances. However, the Cliff consistent (CC) variance is available for only 4 of 10 gamma-family measures. In the present research, a CC variance is derived for the remaining 6 gamma-family measures, and CIs constructed with the CC variance are compared with CIs constructed using other available variance estimators. The CIs are evaluated and compared in simulations and illustrated with scores on the Disinhibition and Avoidance scales of the Schedule for Nonadaptive and Adaptive Personality. Computer code for calculating all 10 gamma-family measures and their CC variances (using the R program) is available on a Web site (http://www.artsci.wustl.edu/~cwoods/CCvarR.html).