The Wheeler-Watson tests the hypothesis H₀: the samples came from the same population.

1. Testing two waves

The following waves represent angles in radians. Both are centered about pi/6.

To test the hypothesis H₀, execute:

StatsWheelerWatsonTest/T=1/Q data1,data2

The results are displayed in the Wheeler-Watson Test table:

Since the test statistic W is greater than the critical value, H₀ is rejected.

2. Testing more than two waves (Mardia's method)

The additional sample is in the wave data3:

Again, H₀ corresponds to the samples being from the same distribution. To run the test execute:

StatsWheelerWatsonTest/T=1/Q data1,data2,data3

The results are displayed in the Wheeler-Watson Test table:

This time the test statistic is smaller than the critical value and H₀ can't be rejected. This result may be explained, in part, by the fact that the wave data3 was constructed intentionally to have circular dispersion between that of data1 and data2. This can be seen by comparing the results of StatsCircularMoments for the three waves: