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Base SAS Procedures Guide: Statistical Procedures
 

The CORR Procedure

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 equals StartFraction sigma-summation Underscript i Endscripts left-parenthesis left-parenthesis upper R Subscript i Baseline minus upper R overbar right-parenthesis left-parenthesis upper S Subscript i Baseline minus upper S overbar right-parenthesis right-parenthesis Over StartRoot sigma-summation Underscript i Endscripts left-parenthesis upper R Subscript i Baseline minus upper R overbar right-parenthesis squared sigma-summation left-parenthesis upper S Subscript i Baseline minus upper S overbar right-parenthesis squared EndRoot EndFraction

where upper R Subscript i is the rank of x Subscript i, upper S Subscript i is the rank of y Subscript i, upper R overbar is the mean of the upper R Subscript i values, and upper S overbar is the mean of the upper S Subscript i 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.

Probability Values

Probability values for the Spearman correlation are computed by treating

t equals left-parenthesis n minus 2 right-parenthesis Superscript 1 slash 2 Baseline left-parenthesis StartFraction r squared Over 1 minus r squared EndFraction right-parenthesis Superscript 1 slash 2

as coming from a t distribution with left-parenthesis n minus 2 right-parenthesis degrees of freedom, where r is the sample Spearman correlation.

Last updated: April 10, 2023