The CORR Procedure
- Overview
- Getting Started
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Syntax
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Details
Pearson Product-Moment Correlation Spearman Rank-Order Correlation Kendall’s Tau-b Correlation Coefficient Hoeffding Dependence Coefficient Partial Correlation Fisher’s z Transformation Polyserial Correlation Cronbach’s Coefficient Alpha Confidence and Prediction Ellipses Missing Values In-Database Computation Output Tables Output Data Sets ODS Table Names ODS Graphics
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Examples
Computing Four Measures of Association Computing Correlations between Two Sets of Variables Analysis Using Fisher’s z Transformation Applications of Fisher’s z Transformation Computing Polyserial Correlations Computing Cronbach’s Coefficient Alpha Saving Correlations in an Output Data Set Creating Scatter Plots Computing Partial Correlations
- References
| Kendall’s Tau-b Correlation Coefficient |
Kendall’s tau-b is a nonparametric measure of association based on the number of concordances and discordances in paired observations. Concordance occurs when paired observations vary together, and discordance occurs when paired observations vary differently. The formula for Kendall’s tau-b is
 |
where 
, 
, and 
. The 
is the number of tied 
values in the 
th group of tied values, 
is the number of tied 
values in the 
th group of tied values, 
is the number of observations, and 
is defined as
 |
PROC CORR computes Kendall’s tau-b by ranking the data and using a method similar to Knight (1966). The data are double sorted by ranking observations according to values of the first variable and reranking the observations according to values of the second variable. PROC CORR computes Kendall’s tau-b from the number of interchanges of the first variable and corrects for tied pairs (pairs of observations with equal values of X or equal values of Y).
Probability Values
Probability values for Kendall’s tau-b are computed by treating
 |
as coming from a standard normal distribution where
 |
and 
, the variance of 
, is computed as
 |
where
The sums are over tied groups of values where 
is the number of tied values and 
is the number of tied values (Noether 1967). The sampling distribution of Kendall’s partial tau-b is unknown; therefore, the probability values are not available.