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?
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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?
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3$\begingroup$ 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. $\endgroup$ Commented Jun 27, 2023 at 10:58