The CORR Procedure
- Overview
- Getting Started
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Syntax
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DetailsPearson Product-Moment CorrelationSpearman Rank-Order CorrelationKendall’s Tau-b Correlation CoefficientHoeffding Dependence CoefficientPartial CorrelationFisher’s z TransformationPolychoric CorrelationPolyserial CorrelationCronbach’s Coefficient AlphaConfidence and Prediction EllipsesMissing ValuesIn-Database ComputationOutput TablesOutput Data SetsODS Table NamesODS Graphics
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ExamplesComputing Four Measures of AssociationComputing Correlations between Two Sets of VariablesAnalysis Using Fisher’s z TransformationApplications of Fisher’s z TransformationComputing Polyserial CorrelationsComputing Cronbach’s Coefficient AlphaSaving Correlations in an Output Data SetCreating Scatter PlotsComputing Partial Correlations
- References
Spearman Rank-Order Correlation
Spearman rank-order correlation is a nonparametric measure of association based on the ranks of the data values. The formula is
![\[ \theta =\frac{\sum _ i (\, (R_ i-\bar{R})(S_ i-\bar{S})\, )}{\sqrt {\sum _ i (R_ i-\bar{R})^2 \, \sum (S_ i-\bar{S})^2}} \]](images/procstat_corr0047.png){kind=small} |
where 
is the rank of 
, 
is the rank of 
, 
is the mean of the values, and 
is the mean of the values.
PROC CORR computes the Spearman correlation by ranking the data and using the ranks in the Pearson product-moment correlation formula. In case of ties, the averaged ranks are used.
![\[ t \, = \, {(n-2)}^{1/2} \, {\left(\frac{r^{2}}{1-r^{2}}\right)}^{1/2} \]](images/procstat_corr0044.png){kind=small}
