The two variables I am testing are:
Indep: Class size
Dep: Performance (like test scores)
The relationship between the variables appears to be nonlinear and the data is interval.
Am I correct in thinking that I should be using a parametric test?
What correlation test would you guys recommend using?
I'd look very closely at whether your test scores are truly interval scaled, or merely ordinal. They might be interval, but in the German academic system with grades 1-6 (1-4 is passing), there sometimes seems to be a dichotomy between the best grade 1 and everything else, as in "everything less than 1 means I'll start arguing with the teacher" - in which case I think one can make a convincing argument that the scale is in fact ordinal.
If your scores are truly interval, then you can try transforming either scores or class size to get a roughly linear relationship, then try pearson-r.
If your scores are ordinal, or you simply can't get a linear relationship, try spearman-rho or kendall-tau. I personally prefer Kendall's $\tau$, simply because I like the rationale with concordant and discordant pairs better, but to a degree, the choice between Spearman and Kendall is one of taste. Consider looking at our relevant question Kendall Tau or Spearman's rho? for inspiration.
