The Spearman rank correlation coefficient, also known as Spearman's rho, is a nonparametric (distribution-free) rank statistic proposed by Spearman in 1904 as a measure of the strength of the associations between two variables (Lehmann and D'Abrera 1998). The Spearman rank correlation coefficient can be used to give an R-estimate, and is a measure of monotone association that is used when the distribution of the data make Pearson's correlation coefficient undesirable or misleading.
The Spearman rank correlation coefficient is defined by
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(1)
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where 
is the difference in statistical
rank of corresponding variables, and is an approximation to the exact correlation
coefficient
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(2)
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computed from the original data. Because it uses ranks, the Spearman rank correlation coefficient is much easier to compute.
The variance, kurtosis excess, and higher-order moments are
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(3)
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(4)
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(5)
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Student was the first to obtain the variance.
