# Test for, and compare means of folded normal distribution

I have two datasets of absolute distances to a single point in a 2D space. I have reasons to expect that if I had the sign and magnitude of these distances, my datasets would be normally distributed with a mean of zero.

Think of the datasets to be the absolute distances from the Bull's eye in a game of darts. I have a set of these distances for two different players, and I would like to compare the performance of the two players (both players had to aim for the Bull's eye).

I think the 'folded normal distribution' applies to my dataset. Since I would like to compare the two datasets, I need to answer the following questions.

• How can I verify that I indeed have a 'folded normal distribution'?
• How can I compare the (means of) these two datasets in this distribution? For example, am I allowed to use ANOVA?

Thank you!

Multiply each data point by $+1$ or $-1$, taken independently with equal probabilities. If your datasets are indeed samples from folded normal distributions, you will now have normal distributions with mean $0$, and you can use any of the tools appropriate thereto.
$$p(x) = \frac{2}{\sqrt{\pi}\sigma}\exp\left(-\frac{x^2}{2\sigma^2}\right)$$
You'd need to use a $\sigma$ parameter, that you could perhaps empirically find using a normal fit from the ±1 approach above, or play around with the parameter if you just want to get a feel for the distribution.