Watson's U2 Test

The following three waves contain angular data in radians.

data1data2data3
0.8071470.8050690.868458
0.8335860.8649310.908372
0.823210.7989630.882047
0.8525880.7376890.826652
0.8032170.8360120.871351
0.8017260.8252480.838512
0.8023020.8582590.862167
0.6856510.7341240.816303
0.8561090.7494090.871654
0.841990.7653440.999934
0.7849850.7390250.855328
0.8459090.7992170.912431

Testing the hypothesis H0: data1 and data2 are samples from the same distribution. To run the test execute:

StatsWatsonUSquaredTest/T=1/Q data1,data2

The results are displayed in the Watson U2 Test table:

Total_Points24
Watson_U20.1386
Critical_Tiku0.18524
Approx_P0.130043
Critical0.186238

In this case the U2 statistic is smaller than the critical value and so H0: (the two samples came from the same distribution) can't be rejected. Note that although we don't really need the Tiku approximation in this case, it appears to be pretty close to the exact critical value.

Applying the same test to data1 and data3:

StatsWatsonUSquaredTest/T=1/Q data1,data3

The results are displayed in the Watson U2 Test table:

Total_Points24
Watson_U20.20370
Critical_Tiku0.18524
Approx_P0.03405
Critical0.18623

The test statistic is larger than the critical value so we reject H0 (at the 0.05 significance).