# Statistics when the data is a list of angles

I’m a biologist and my data is the measurement of a specific parameter which is an angle (so the units are degrees). I have wild-type (WT) and then four different treatments (T1, T2, T3, and T4). Within each measurement, I measure 20 individuals, so I have 20 angles for WT, 20 for T1 etc. I then repeat the whole process three times, and I’m planning to represent the data as a circular histogram using coord_polar in ggplot. I have two questions about analyzing this data.

1. Since these measurements are angles, does that change the analysis in any way compared to if they were simply lengths? In some sense, I think no, because both measures are continuous and could in theory be any value above 0. But part of me feels like there is something inherently different about angles that may require attention. For instance, does it change the statistical test I should perform to test whether the WT is different from the treatments?
2. My histogram shows the spread of data amongst the 20 individuals per replicate quite nicely. But I also want to represent the fact that the experiment includes 3 biological replicates (and so there are 60 values to plot overall). Is the best way to simply show all three histograms on top of each other (maybe in a slightly different shade of color) or to just group all 60 values into a single histogram? The former looks quite messy/confusing but the latter doesn’t give the sense that the experiment has biological replicates. I don’t want to average the 20 readouts for the three repeats and plot those because then there’s only three points and the histogram doesn’t work.

Any thoughts are appreciated.

EDIT: Based on some questions below, here is a bit more information about the experimental set up:

The angles are in theory anything between 0 and 360 and each one would be taken as a different result; none of them are the same thing. In practice, the different treatments cause them to group in certain areas (e.g. WT is 70-110), T1 is (110-130), T2 is around 180 etc.

I’m measuring embryos from a intercross of Drosophila. The Drosophila lay many eggs; I take 20 and leave untreated (what I called WT before), then I treat 20 with drug 1, 20 with drug 2 etc. So all the embryos in this experiment are from the same parents on the same day. I then do two more repeats of the whole thing on a different day from a different set of embryos. Thus, the embryos from each experiment are more related to each other (siblings) than they are between repeats (because those have different parents). I’m considering each batch of embryos as different biological repeats and each embryo within a batch as a kind of technical repeat.

submitted by /u/microMe1_2