PROC CORR: Spearman Rank-Order Correlation

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

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where $\text{[math]}$ is the rank of $\text{[math]}$ , $\text{[math]}$ is the rank of $\text{[math]}$ , $\text{[math]}$ is the mean of the $\text{[math]}$ values, and $\text{[math]}$ is the mean of the $\text{[math]}$ 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

$\text{[math]}$

as coming from a t distribution with $\text{[math]}$ degrees of freedom, where $\text{[math]}$ is the sample Spearman correlation.

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