Hypothetically let's say I'm doing a study in which the data on both variables are likely to be quite positively skewed, but the sample size is potentially quite large.
In this research context using significance tests on Pearson's r is the most common technique and it would be useful if I could use it. It's less desirable for me to use the Spearman correlation because of the audience this study is pitched at.
I know from this question that Pearson's r doesn't "assume normality" per se, but that I may not be able to trust the p-values if I have non-normal data and a small sample size.
Clearly the right way to proceed will depend on how non-normal my data are and how large my sample is. Are there any rules of thumb I can usefully apply?