Interpret correlation results

Question

[anamaria]

Hi,

What can we say for the results, if they are correlated or no when we have: r=0.49, p=1.3x10^-6

Thanks Ana

Answer 1

[Jean-Karim Heriche]

The Pearson's correlation coefficient (which I assume is what we're talking about here) measures the strength of the linear relationship between two variables. You should have a look at the plot of the two variables because if you can't see a sign of a linear relationship there (i.e. there's no relationship or it is not linear or there are outliers), the correlation coefficient is meaningless. A correlation of ~0.5 is often considered to indicate a weak/moderate linear relationship but there's no hard threshold. It depends on what you want to do with the information that this provides. The p-value is associated with the null hypothesis that the population correlation coefficient is 0. The p-value is the chance of observing this or a stronger correlation if the population correlation is 0 (and NOT the chance that the correlation is 0 given the data).

[anamaria]

Thank you so much for this elaborate explanation!