The Watson-Williams test for the equality of the means of two or more samples. In this example we consider the following 3 samples where the numerical values represent angles in radians:

First, we test the equality of the means of data1 and data2. To execute the test, execute the following command:

The results are given in the Watson-Williams Test table.

In this case the test provides both the F and the T statistics together with their critical values. It is evident that the critical values are much larger than the two test statistics so H₀ (equality of means) can't be rejected. The remaining test results, include the population mean angle (in radians) as well as the weighted value rw and the correction factor K used in both the F and T statistics calculations.

You can use this operation with more than two waves as in the following example. To execute the test, execute the following command:

The results are given in the Watson-Williams Test table.

Here, again, H₀ can't be rejected. By contrast, we have to reject H₀ in the following test:

Note: the Watson-Williams test applies to data from a von Mises distribution where the different samples have the same dispersions. If these assumptions are invalid, you should consider using one of the non-parametric tests. See, for example Wheeler-Watson Test.