The Hodges-Ajne test provides a non-parametric measure for the angular uniformity of the data.

Uniform angular distribution

We create the distribution using the following command:

Make/O/N=30 data1=mod(2*pi*(1+enoise(1))/2,2*pi)

The data are displayed in the polar graph below.

To run the test execute the command:

The results are shown in the Hodges-Anje Stats table:

This means that the least number of data that can be found on one side of any diameter of this circle is 10. Since the critical value is 6, H₀ of uniformity is accepted with a P-value 0f 0.559632. Note that in this case m must exceed the critical value to accept H₀.

Working with a non-uniform distribution

We create the non-uniform distribution by executing the command:

Make/O/N=30 data2=mod(pi*(1+enoise(1))/3,2*pi)
StatsHodgesAjneTest/T=1/Q data2

In this case the operation found a diameter where there were no data on one side. This is a clear violation of uniformity and H₀ must be rejected.

Testing uniformity against a specific direction alternative

Using data2 from above we first test against an alternative with mean direction pi/8. To execute the test enter the command below:

StatsHodgesAjneTest/T=1/Q/SA=(pi/8) data2

The results are shown in the Hodges-Anje Stats table:

In this case the test for uniformity indicates that we must reject H₀ in favor of the alternative. If we execute:

StatsHodgesAjneTest/T=1/Q/SA=(pi/3) data2

We observe that there is an even stronger rejection of H₀ in favor of the alternative concentration about pi/3.