Publication date: 11/29/2021

The Measures of Association option provides association statistics.

Note: See also Example of the Measures of Association Option.

Gamma

Based on the number of concordant and discordant pairs and ignores tied pairs. Takes values in the range -1 to 1.

Kendall’s Tau-b

Similar to Gamma and uses a correction for ties. Takes values in the range -1 to 1.

Stuart’s Tau-c

Similar to Gamma and uses 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.

– The C|R denotes that the row variable X is regarded as an independent variable and the column variable Y is regarded as dependent.

– Similarly, the R|C denotes that the column variable Y is regarded as an independent variable and the row variable X is dependent.

Somers’ D differs from Tau-b in that it uses a correction for ties only when the pair is tied on the independent variable. It takes values in the range -1 to 1.

Lambda Asymmetric

Differs for C|R and R|C.

– For C|R, is interpreted as the probable improvement in predicting the column variable Y given knowledge of the row variable X.

– For R|C, is interpreted as the probable improvement in predicting the row variable X given knowledge about the column variable Y.

Takes values in the range 0 to 1.

Lambda Symmetric

Loosely interpreted as the average of the two Lambda Asymmetric measures. Takes values in the range 0 to 1.

Uncertainty Coef

– For C|R, is the proportion of uncertainty in the column variable Y that is explained by the row variable X.

– For R|C, is interpreted as the proportion of uncertainty in the row variable X that is explained by the column variable Y.

Takes values in the range 0 to 1.

Uncertainty Coef Symmetric

Symmetric version of the two Uncertainty Coef measures. Takes values in the range 0 to 1.

Notes:

• Each statistic appears with its standard error and confidence interval.

• 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.

• The Lambda and Uncertainty measures are appropriate for ordinal and nominal variables.

For computational details about the measures of association statistics, see the FREQ Procedure chapter in SAS Institute Inc. (2020b). 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)

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