Spearman Rank Correlation Coefficient
المؤلف:
Hogg, R. V. and Craig, A. T.
المصدر:
Introduction to Mathematical Statistics, 5th ed. New York: Macmillan
الجزء والصفحة:
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4-3-2021
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Spearman Rank Correlation Coefficient
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
 |
(1)
|
where 
is the difference in statistical rank of corresponding variables, and is an approximation to the exact correlation coefficient
 |
(2)
|
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
Student was the first to obtain the variance.
REFERENCES:
Hogg, R. V. and Craig, A. T. Introduction to Mathematical Statistics, 5th ed. New York: Macmillan, pp. 338 and 400, 1995.
Lehmann, E. L. and D'Abrera, H. J. M. Nonparametrics: Statistical Methods Based on Ranks, rev. ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 292, 300, and 323, 1998.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:Cambridge University Press, pp. 634-637, 1992.
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