R_CORRELATE

The R_CORRELATE function computes Spearman’s (rho) or Kendalls’s (tau) rank correlation of two sample populations X and Y. The result is a two-element vector containing the rank correlation coefficient and the two-sided significance of its deviation from zero. The significance is a value in the interval [0.0, 1.0]; a small value indicates a significant correlation.

where Rx_i and Ry_i are the magnitude-based ranks among X and Y, respectively. Elements of identical magnitude are ranked using a rank equal to the mean of the ranks that would otherwise be assigned.

This routine is written in the IDL language. Its source code can be found in the file r_correlate.pro in the lib subdirectory of the IDL distribution.

Examples

; Define two n-element sample populations:
X = [257, 208, 296, 324, 240, 246, 267, 311, 324, 323, 263, $
     305, 270, 260, 251, 275, 288, 242, 304, 267]
Y = [201, 56, 185, 221, 165, 161, 182, 239, 278, 243, 197, $
     271, 214, 216, 175, 192, 208, 150, 281, 196]
; Compute Spearman's (rho) rank correlation of X and Y. 
result = R_CORRELATE(X, Y)
PRINT, "Spearman's (rho) rank correlation: ", result
; Compute Kendalls's (tau) rank correlation of X and Y:
result = R_CORRELATE(X, Y, /KENDALL)
PRINT, "Kendalls's (tau) rank correlation: ", result

IDL prints:

Spearman’s (rho) rank correlation:   0.835967  4.42899e-006

Kendalls’s (tau) rank correlation:   0.624347  0.000118729

Syntax

Result = R_CORRELATE( X, Y [, D=variable] [, /KENDALL] [, PROBD=variable] [, ZD=variable] )

Return Value

Returns a two-element vector indicating the rank correlation coefficient and the significance of its deviation from zero.

Arguments

X

An n-element integer, single-, or double-precision floating-point vector.

Y

An n-element integer, single-, or double-precision floating-point vector.

Keywords

D

Set this keyword to a named variable that will contain the sum-squared difference of ranks. If the KENDALL keyword is set, this parameter is returned as zero.

KENDALL

Set this keyword to compute Kendalls’s (tau) rank correlation. By default, Spearman’s (rho) rank correlation is computed.

PROBD

Set this keyword to a named variable that will contain the two-sided significance level of ZD. If the KENDALL keyword is set, this parameter is returned as zero.

ZD

Set this keyword to a named variable that will contain the number of standard deviations by which D deviates from its null-hypothesis expected value. If the KENDALL keyword is set, this parameter is returned as zero.

Version History

4.0	Introduced

Resources and References

Numerical Recipes, The Art of Scientific Computing (Second Edition), Cambridge University Press (ISBN 0-521-43108-5).