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?