You can test rank correlation of two waves using the operation StatsRankCorrelationTest. In the first example we consider the two random waves shown in the figure below

Picture0

To run the test execute the command:

StatsRankCorrelationTest/T=1/Q data1,data2

The results are displayed in the Rank-Correlation Test table:

n 100
sumDi2 165316
sumTx 0
sumTy 0
SpearmanR 0.0080048
Critical 0.196777

The Spearman rank correlation coefficient (SpearmanR) is smaller than the critical value so we accept H0, i.e., that there is no correlation between the two waves.

By comparison, you can run the parametric test using the command:

StatsLinearCorrelationTest/T=1/Q data1,data2

results in:

n 100
r -0.0377559
sr 0.100943
rc1 0.16543
rc2 0.196551
t_Value -0.374031
tc1 1.66055
tc2 1.98447
F 1.07847
Fc1 1.39644
Fc2 1.48927
Power1 0.0218772
Power2 0.00981472

Since F < Fc2 we accept H0 corresponding to no rank-correlation between data1 and data2.

The next example shows correlated waves:

Picture0

StatsRankCorrelationTest/T=1/Q data3,data4

The results are displayed in the Rank-Correlation Test table:

n 100
sumDi2 49716
sumTx 0
sumTy 0
SpearmanR 0.701674
Critical 0.196777

With SpearmanR > Critical value we clearly reject H0 and conclude that data3 and data4 are rank-correlated. If we now compare with the parametric test:

StatsLinearCorrelationTest/T=1/Q data3,data4

The results of the parametric test are:

n 100
r 0.728588
sr 0.0691906
rc1 0.16543
rc2 0.196551
t_Value 10.5302
tc1 1.66055
tc2 1.98447
F 6.36887
Fc1 1.39644
Fc2 1.48927
Power1 1
Power2 1

In this case F > Fc2 and we again reject H0 (no correlation) and conclude that the two waves are correlated.

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