# non-parametric circular statistics

I am working on a research question of color preference (which can be represented in a circular space).

I have divided the circular space into 16 equally spaced bins and done a pairwise comparison amongst them to understand preference. So I have a total of 120 comparisons.

I am interested to see how these preferences change after experimental intervention. So I have a PRE and POST condition of time. You can see an example of this below.

Here the graph shows the number of times an image was picked. Note this is frequency and not a strength parameter like Bradley Terry. An item can be picked maximum of 15 times and a minimum of 0.

My question to you is how to tell 1. if there was any difference between the PRE and the POST. 2. If so, how much was the difference and 3. In what direction?

Are traditional circular statistics valid here? The data, while evenly spread, is not evenly distributed (only 16 possible angles). In addition, the measurements are counts.

What tests can be done to answer these questions? Is it best to convert the data into a ranked list? (however, that means I lose information about circularity).

Thanks in advance for your help.