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.