Kendall Tau Test Examples

The Kendall Tau test computes a correlation coefficient (tau) similar to Spearman's correlation coefficient by ranking all possible pairs of entries. A tau value of 1 implies that the data is ordered perfectly according to rank while a tau value of -1 implies that the data is reverse ordered according to rank. In the examples below we generate various sets of data and compute Kendall's tau.

1. Increasing function with low level noise.

To generate the data execute the following command:

Make wave1=x+gnoise(15)

Picture0

To compute Kendall's Tau for the data shown above execute the following command:

StatsKendallTauTest/T=1 wave1

The results are shown in the table:

N128
tau0.7618
svar0.00356
zscr12.753
pValue2.968e-37

Positive Tau as expected for a generally increasing function.

2. Increasing function with high level noise.

To generate the data execute the following command:

wave1=x+gnoise(35)

Picture1

StatsKendallTauTest/T=1 wave1

The results are shown in the table:

N128
tau0.5366
svar0.00356
zscr8.984
pValue2.598e-19

Positive Tau but smaller than the example above because the level of the noise high relative to the range of x.

3. Periodic function

wave1=sin(x/2)

Picture2

statsKendallTauTest/T=1 wave1

The results are shown in the table:

N128
au-0.0393701
svar0.00356791
zscr-0.659112
pValue0.509824

In this case Tau is close to zero becacuse the function is periodic so the ordering of ranks results in negligible Tau value with a sign that depends on the phase of the periodic signal.