In the Contingency platform, the Measures of Association option provides association statistics. See Example of the Measures of Association Option.
The Measures of Association report contains the value, standard error, and confidence intervals for the following statistics:
Gamma
A measure of ordinal association. Defined as the difference in probability of concordant and discordant pairs disregarding tied pairs. Takes values in the range -1 to 1.
Kendall’s Tau-b
Similar to Gamma with a correction for the number of ties. Takes values in the range -1 to 1.
Stuart’s Tau-c
Similar to Gamma with an adjustment for table size and a correction for ties. Takes values in the range -1 to 1.
Somers’ D
An asymmetric modification of Tau-b. Somers’ D uses a correction for ties only when the pair is tied on the independent variable. Takes values in the range -1 to 1.
– The C|R denotes that the row variable X is regarded as an independent variable and the column variable Y is regarded as a dependent variable.
– Similarly, the R|C denotes that the column variable Y is regarded as an independent variable and the row variable X is a dependent variable.
Note: Gamma, Kendall’s Tau-b, Stuart’s Tau-c, and Somers’ D are measures of ordinal association that consider whether the variable Y tends to increase as X increases. They classify pairs of observations as concordant or discordant. A pair is concordant if an observation with a larger value of X also has a larger value of Y. A pair is discordant if an observation with a larger value of X has a smaller value of Y. These measures are appropriate only when both variables are ordinal.
Lambda Asymmetric
Differs for C|R and R|C. Takes values in the range 0 to 1.
– For C|R, this measure is interpreted as the probable improvement in predicting the column variable Y given knowledge of the row variable X.
– For R|C, this measure is interpreted as the probable improvement in predicting the row variable X given knowledge about the column variable Y.
Lambda Symmetric
Loosely interpreted as the average of the two Lambda Asymmetric measures. Takes values in the range 0 to 1.
Uncertainty Coef
Differs for C|R and R|C. Takes values in the range 0 to 1.
– For C|R, this measure is the proportion of uncertainty in the column variable Y that is explained by the row variable X.
– For R|C, this measure is interpreted as the proportion of uncertainty in the row variable X that is explained by the column variable Y.
Uncertainty Coef Symmetric
Symmetric version of the two Uncertainty Coef measures. Takes values in the range 0 to 1.
Note: The Lambda and Uncertainty measures are appropriate for both ordinal and nominal variables.
For computational details about the measures of association statistics, see the FREQ Procedure chapter in SAS Institute Inc. (2022b). The following references also contain additional information:
• Brown and Benedetti (1977)
• Goodman and Kruskal (1979)
• Kendall and Stuart (1979)
• Snedecor and Cochran (1980)
• Somers (1962)