## 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.

### Calling Sequence

Result = R_CORRELATE( X, Y )

### 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.

### Example

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, result

IDL prints:

[0.835967, 4.42899e-06]

Compute Kendalls's (tau) rank correlation of X and Y.

result = R_CORRELATE(X, Y, /KENDALL)

PRINT, result

IDL prints:

[0.624347 0.000118732]