What is the minimum number of data pairs in computing for correlation coefficient?

Ωthunderpantz: What is the minimum number of data pairs in computing for correlation coefficient?
It would be better if you can please cite your references.. Thanks!

Answers and Views:

Answer by Matteh
2

For there to be correlation there needs to be a relation between data points. The most simple relation is between two points.

However the correlation for two points would simply be a straight line.

hope that helps

Answer by 1ofU
Depends on how tight of a confidence factor you need. I assume you’re talking about Pearson’s coefficient, which is based on his chi-square work and can be performed with only 1 degree of freedom, but with only 2 data pairs you have no idea if there’s a normal distribution. In order to assume and preferably test for normal distribution, the rule of thumb I’ve heard quoted most often (my line of work is biology-ecology) is a bare minimum of 30 pairs to do any parametric testing, and that’s limited to normally distributed variables. If you’re working with some kind of oddball distribution such as Poisson in a linear model, Manly et al. (2002) suggest at least 100 replicates.

Demonstrating correlation can be achieved with as few as three pairs (you could even argue 2 pairs) using non-parametric tests such as Mann-Whitney, but if you want a reliable coefficient, the more the better.