Basic Analysis and Graphing - SAS

Chapter 6 Performing Contingency Analysis 199
Measures of Association
Table 6.11 Description of the Measures of Association Report (Continued)
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
Somer’s D
Similar to Gamma and uses an adjustment for table size and a correction for
ties. Takes values in the range -1 to 1.
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.
Somer’s 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 • 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.
Each statistic appears with its standard error and confidence interval. Note the following:
• Gamma, Kendall’s Tau-b, Stuart’s Tau-c, and Somer’s 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.