The spearman operator computes a rank-based measure of association called Spearman's rho. Available only in the Enterprise Edition.

Synopsis

spearman(A,B);

Library

The spearman operator resides in the Linear Algebra library. Run the following query to load this library:

AFL% load_library('linear_algebra');

Summary

Spearman's rho, , or the Spearman rank correlation coefficient, is a non-parametric measure of dependence between two variables. Spearman's is defined as the Pearson correlation coefficient of the ranks of the two variables. For a sample population of size and two arrays and let :

where ties in rank are defined as the mean of the tied ranks had they been assigned sequentially, and

Then Spearman's is defined as

which reduces to

Example

Calculate Spearman's rho for the wikipedia example of 10 people's IQ's and the corresponding number of hours watching TV:

Create a vector of 10 IQ's:

AFL% store(build(<iq:double>[i=1:10; j=0:0],'[[106], [86],[100],[101],[99],[103],[97],[113],[112],[110]]',true),IQ);

The output is:

{i,j} iq
{1,0} 106
{2,0} 86
{3,0} 100
{4,0} 101
{5,0} 99
{6,0} 103
{7,0} 97
{8,0} 113
{9,0} 112
{10,0} 110

Create the coresponding vector of hours-per-week:

AFL% store(build(<hours:double>[i=1:10; j=0:0],'[[7],[0],[27],[50],[28],[29],[20],[12],[6],[17]]',true),HOURS);

The output is:

{i,j} hours
{1,0} 7
{2,0} 0
{3,0} 27
{4,0} 50
{5,0} 28
{6,0} 29
{7,0} 20
{8,0} 12
{9,0} 6
{10,0} 17

Calculate Spearman's rho between 'iq' and 'hours':
```
AFL% spearman(IQ, HOURS);
```
The output is:
```
{j1,j2} spearman
{0,0} -0.175758
```
This result suggests that the relationship between IQ and hours-of-TV/week is weak and should it exist, would be negatively correlated.