# Probability of getting a certain correlation by random chance

Say I have two different binary vectors (containing only 0s and 1s) with 20,000 observations in each and find the correlation between them. I'm interested in finding out if a very high correlation (.9-1.0) could have just been caused by chance and is possibly a fluke. I want to find the probability of two vectors having a specific high correlation (say a perfect 1.0 correlation) by random chance?

Would this just entail using the p-value/critical values for Pearson's r ? Would that tell me the probability of getting this correlation by chance?

If not, I would appreciate it if someone could point me in the right direction!

Also, what effect does binary data have on the accuracy of using Pearson's correlation and basing how strong/reliable my correlation is from probability values calculated from Pearson's correlation?

• Not an answer, but I recommend you to look for Cohen's Kappa and other related statistics. – Firebug May 20 '16 at 18:29
• When you say "by chance" do you mean in the case that the population correlation is 0? – Glen_b -Reinstate Monica May 21 '16 at 1:44
• Yes, which is why I figured using the p-value would work since that would be the probability of getting that specific p-value given that the population correlation is actually 0. – Megan May 23 '16 at 12:45
• With two binary vectors, why not look at the contingency table and use at the chisquare test? If you insist on Pearson correlation, you could use bootstrapping. – kjetil b halvorsen Sep 27 '18 at 20:21