[![enter image description here][1]][1]You may have many more data points, but scrutiny of a quick plot suggests

1. The observed range of angles is very limited, which often implies that you don't really need circular statistics. It is not even given that angle is the best way to record direction: sine or cosine may be closer to the underlying problem. Some kind of regression on angle or sine or cosine may suffice, with perhaps parameterisation so that $-90^\circ$ defines an intercept. (Perhaps you should just add $90^\circ$.) 

2. There may well be hard limits in practice on what angles are possible or likely, and if so knowing them is very important to guide what makes scientific and statistical science.

3. The question of whether radius is significantly different from zero is hard to understand. First off, whatever is called a radius is usually a positive quantity, and if your definition implies otherwise, please explain. Second off, all reported values in the example are positive, so a significance test appears pointless for that reason. Perhaps you mean something more like "are radius and angle related?" to which the answer appears to be yes. Assuming that radius must be positive, analysis in terms of its logarithm seems indicated to me. 

4. It makes quite a difference to analysis whether the angle is in some sense given and the radius is the outcome to be explained (which with problems like this is often true) -- or the opposite -- or neither. 

5. Given the small subsamples I have not attempted an analysis in terms of treatments but the plot suggests that (e.g.) treatment 1 at least is quite distinctive. 

Good statistical advice is very hard to give with no context whatsoever on what the numbers represent (other than something in polar coordinates).

EDIT Given more information and the full dataset, I can try a little more. 

*Disclaimer. I don't understand the science here and I don't even understand what kind of statistical problem this is. So why say more? I have some experience with circular data, which many statistical people don't have at all, so perhaps something a little helpful can be said.*

The full dataset is 315 observations on 66 treatments, the latter represented by 5 observations in most instances, but only 3 or 4 in some (thus that's why not 330). 

I can readily imagine that this represents a great deal of hard experimental work, but unfortunately from a statistical point of view 3, 4 or 5 observations is a very small sub-sample size for saying much reliably about individual treatments. 

Circular plots may seem natural given the outcome space, but there can be a chicken and egg question that you have to look at several before you can think easily about any one (unless perhaps you already have some experience of thinking in and about that space, as is often true of compass direction). 
That aside, I have found that linear plots can be very helpful too, which runs a little contrary to the advice in circular statistics texts and reviews. 

A plot of the full data shows that they too seem limited, but now to half the circle. Is there any sense in which $90^\circ = -90^\circ$, because that would be an important detail? It affects what kind of test might make sense, but "typical" theta, however measured, is a long way from zero. 

Another plot plots all of the data repeatedly, but a little arbitrarily picks out 4 treatments as extreme in either median or median absolute deviation on radius, theta or both. That's cherry-picking and nothing to do any formal testing. 

As before, logarithmic scale for radius might help. 

[![enter image description here][2]][2] 


  [1]: https://i.sstatic.net/bMSbI.png
  [2]: https://i.sstatic.net/ZIfST.png