# Correlation - Negligible correlation but statistically significant... Do the 2 variables have a significant relationship?

I run Pearson correlation for 2 variables and the results say that r = .16, signifying a negligible correlation. However, the p-value is significant p = .05

Do the 2 variables have a significant relationship?

You are using 'significant' in two different ways. The term is a common source of confusion.

p < 0.05 is called statistically significant by convention. But p < 0.05 does not necessarily mean that a relationship is strong or practically significant. The correlation coefficient of 0.16 is telling you that the relationship is weak (and positive).

This is commonly encountered when analysing large datasets. Having a lot of data means that you have more power, and so even weak relationships may be statistically significant.

It's worth reading more about what p-values are exactly before you proceed. These threads may be a useful place to start:

What is the meaning of p values and t values in statistical tests?

Practical vs Statistical significance

• And since "statistically significant" means almost nothing and is often a low bar for correlations to pass, concentrate more on a confidence interval for the correlation using Fisher's $z$-transform. Commented Jun 27, 2023 at 10:58