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:

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 reusults of the test are summarized in the table:

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 reusults of the test are summarized in the table:

As expected the parameteric 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 reusults of the test are summarized in the table:

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.

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 reusults of the test are summarized in the table:

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 reusults of the test are summarized in the table:

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