# 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?

• It is unlikely that a sample correlation coefficient for these data would follow any distribution routinely used to compute a p-value. (Delays are not independent and the association between planes and delays is not one-to-one.) You need to describe your data and the method you have used to compute the p-value. Even better, why not ask for suitable methods to analyze your data, rather than pursuing an analysis whose results might be meaningless or even deceptive?
– whuber
Jan 22, 2022 at 15:57
• Thank you for the reply. What do you think is a suitable method to analyze the association between delays and the age of the plane? Mar 22, 2022 at 15:36
• It would begin with a consideration of what data you could use. Ideally, you would have other variables to control for spurious correlations and confounding. For instance, if older planes are given lower priorities at airports or are assigned to often-delayed routes, you could find a strong association between age and delay but you would misinterpret it. Look for ways to control for all other variables besides age.
– whuber
Mar 22, 2022 at 16:28

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).