How to Interpret a Correlation Coefficient

The sign tells you which way the relationship moves. A positive r means higher values of one variable tend to appear with higher values of the other. A negative r means higher values of one variable tend to appear with lower values of the other.

The sign does not tell you whether the relationship is useful, causal, or statistically reliable. It only tells you the direction of the linear or monotonic pattern being measured.

The absolute value of r shows strength. As a rough starting point, |r| around 0.10 is weak, around 0.30 is moderate, around 0.50 is strong, and 0.70 or higher is very strong.

Those cutoffs are only conventions. A weak correlation can matter in public health or finance when scaled across many people, while a strong-looking correlation can be unimportant if the outcome is trivial.

The p-value asks whether the observed correlation is hard to explain by random sampling if the true population correlation were zero. It does not ask whether the relationship is large enough to matter.

For example, r = 0.08 can be statistically significant in a huge sample, but it explains very little variation. Conversely, r = 0.70 in a tiny sample can look impressive while still being unstable.

A correlation coefficient can be distorted by outliers, curved patterns, restricted ranges, mixed subgroups, or non-independent observations. Always inspect a scatter plot when raw data is available.

If the relationship is monotonic but not linear, Spearman or Kendall may describe it better than Pearson. If one variable is binary and the other is continuous, point-biserial correlation is usually the cleaner interpretation.