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Capabilities Index
Basic Analysis
•
Contingency Analysis
• Measures of Association
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Measures of Association
You can request several statistics that describe the association between the variables in the contingency table by selecting the
Measures of Association
option.
For details about measures of association, see the following references:
•
Brown and Benedetti (1977)
•
Goodman and Kruskal (1979)
•
Kendall and Stuart (1979)
•
Snedecor and Cochran (1980)
•
Somers (1962)
Description of the Measures of Association Report
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
•
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 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.
Related Information
•
Example of the Measures of Association Option