Is there any difference between degrees, radians, trigonometric parameters and so on for statistical tests like ANOVA or non-parametric tests?
There should not be difference by just changing the unit.
However, traditionnal methods are not suited for angles because of the periodicity (that is, 360 ° is closest to 0° than to 270° for instance). You should used special methods for that: search for « circular statistics ». I never had to use such methods (never worked with angles so far), so I can't help more...
There's a linear relationship between radians and angles, so choosing one over the other doesn't matter. Remember that if you're calculating averages of angles that also have lengths associated with them that you'll need to change from an (r, theta) co-ordinate system to an (x, y), do the averaging and then back-transform to (r, theta).
If you're doing any regression modelling, make sure you use a basis that is periodic, as Emmanuel has pointed out. You can use sums of sin and cos waves or a periodic spline basis.
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