# Understanding the p-value in Spearman's rank correlation

I have some pairs of datasets (n=200 or thereabouts), of samples which are non-negative and not normally distributed. I think these pairs of variables are related, probably linearly.

Calculating Spearman's rank correlation on these datasets gives some strange results. The correlation coefficients show that the pairs of variables are weakly, positively correlated (e.g. rho of around 0.4), but the p-values are very low (e.g. 4.1e-10).

My vague understanding of this is that the variables are weakly, positively correlated but the probability of unrelated variables producing the same correlation is very low. Does this mean we can be reasonably certain that a positive correlation exists or have I misunderstood?

• 0.4 isn't a weak correlation, In Cohen's terms (often used in social sciences) a large correlation is 0.5, medium is 0.3 and small is 0.1. – Jeremy Miles Apr 5 '13 at 23:47
• WHat you call 'weak' depends on circumstances. Your association is so unlikely to have occurred just by random variation that it would be reasonable to conclude that it must be due to some other cause. If the assumptions hold, you're left with concluding some level of monotonic association is present. – Glen_b Apr 6 '13 at 1:40