This example covers four tests that are available in the StatsCircularTwoSampleTest operation. All tests are used to compare two samples of circular data which represent either raw data or means of data (second order analysis).

For the first two examples we use the waves Sample1, Sample2 and Sample3:

Sample1

 Angle Radius 2.07109 1.05535 2.20479 1.11541 1.6637 1.12639 2.14861 1.01445 2.3785 0.990459 2.0421 0.985494 2.14861 1.02701 1.98404 0.944105 1.87446 0.986208 1.97171 0.888526 1.81322 0.976384

Sample2

 Angle Radius 2.09745 0.925728 1.86866 1.03347 1.95995 1.00445 2.01705 0.932245 2.04559 1.06179 2.04506 0.999727 2.42668 1.0344 2.03605 1.0751 2.33602 1.0398 2.18839 0.935943 1.92262 1.03721

Sample3

 Angle Radius 1.81504 0.925728 1.93231 1.03347 1.84001 1.00445 1.8353 0.932245 1.85639 1.06179 1.81432 0.999727 1.93607 1.0344 1.89947 1.0751 1.57929 1.0398 1.84727 0.935943 1.86696 1.03721

### Non-Parametric Paired-Sample Test

To test if the pairs represented by corresponding rows in Sample1 and Sample2 are the same (H0) execute the command:

`StatsCircularTwoSampleTest/Q/T=1/NPR Sample1,Sample2`

The results of the test are summarized in the table:

 numPairs 11 Rp 0.350962 Critical 1.04402 P-Value 0.739203

Since the statistic Rp is smaller than the critical value we can't reject H0 that the two paired distributions are the same.

### Parametric Paired-Sample Test

To test if the pairs represented by corresponding rows in Sample1 and Sample2 are the same (H0) execute the command:

`StatsCircularTwoSampleTest/Q/T=1/PPR Sample1,Sample2`

The results of the test are summarized in the table:

 numPairs 11 xBar -0.0520224 yBar -0.0247836 F 0.246806 Critical 4.25649 P-Value 0.786411

As expected the parametric test results in the same conclusion that H0 can't be rejected. To repeat the test and compare Sample1 to Sample3 execute the command:

`StatsCircularTwoSampleTest/Q/T=1/PPR Sample1,Sample3`

The results of the test are summarized in the table:

 numPairs 11 xBar 0.170992 yBar 0.0770423 F 4.62463 Critical 4.25649 P-Value 0.0415419

In this case the pair-wise equality of the samples is rejected.

### Two-Sample Parametric Second Order Test

Suppose you have two samples of means of circular data contained in Sample4 and Sample5 as shown below.

Sample4

 Angle Radius 1.95156 0.998453 2.02499 0.966636 1.923 0.900775 1.93213 0.952201 2.11902 0.980929 1.90744 0.993908 2.09811 0.999118 2.03358 0.901898

Sample5

 Angle Radius 1.86072 0.994223 1.74222 0.930861 1.98412 0.90284 1.66055 1.0654 1.94668 1.00991 2.03487 1.02034 1.83005 0.957592 1.79043 0.956647 1.68544 0.973875 1.62441 0.944371 2.05969 1.02666

To test if the means of the populations from which the two samples were taken are equal (H0), execute the following command:

`StatsCircularTwoSampleTest/Q/T=1/PSOA Sample4,Sample5`

The results of the test are summarized in the table:

 Samples1 8 xBar1 -0.398434 yBar1 0.872187 r1 0.958885 a1 1.99931 Samples2 11 xBar2 -0.25697 yBar2 0.935076 r2 0.969743 a2 1.83899 F 4.03807 Critical 3.63372 P-Value 0.0380423

Since the F statistic is greater than the critical value we reject H0.

### Two-Sample Non-Parametric Second Order Test

To test the same data using a non-parametric test, execute the command:

`StatsCircularTwoSampleTest/Q/T=1/NSOA Sample4,Sample5`

The results of the test are summarized in the table:

 Total_Points 19 Watson_U2 0.202153 Critical_Tiku 0.184557 Approx_P 0.0345285 Critical 0.184103

Clearly the Watson_U2 statistic is greater than the critical value and H0 (equality of the means) must be rejected.

Forum

Support

Gallery