How to interpret low but statistically significant correlation I am doing an analysis on whether older planes would lead to higher delays. However, when I run correlation tests between delays and age of the planes, it shows that the sample correlation is 0.005 with p-value < 2.2e-16, implying it is significant. However, this correlation is so low that it seems irrelevant at all. How do i interpret this?

Assume you use scipy.stats.pearsonr, it models the distribution of $correlation$ values with a beta distribution which uses $n/2 -1$ as the distribution's shape parameter, where $n$ is the size of your data. If your $n$ is large, then the distribution will be very sharp at $correlation = 0$, making even $abs(correlation)>=0.005$ a very very small chance ($=2.2 \times 10^{-16}$). If you are fine with such model assumption, then the interpretation is just as you think - that the correlation is significant (meaning it is not 0), and the size of that correlation is 0.005 (which happens to be quite small).
