A correlation coefficient equals 0. Can we claim that the samples are independent? Why?

A correlation coefficient of 0 means that there is no linear dependence between the two samples. However, this does not guarantee that the samples are independent overall.

Dependence can be nonlinear or more complex, and the correlation coefficient may not detect it. Therefore, a zero correlation coefficient is only an indication of the absence of a linear relationship, but not proof of complete independence of the samples.

To test independence, other methods should be used, such as independence tests or mutual information analysis.