The expectation of the sampling distribution of Pearson's correlation

[Ad VanderVen]

TL;DR

The shape of the sampling distribution of the Pearson product moment correlation coefficient depends on the size of the sample. Is the expectation of the sampling distribution of the Pearson product moment correlation coefficient always equal to the population correlation coefficient, regardless of the sample size?

The shape of the sampling distribution of the Pearson product moment correlation coefficient depends on the size of the sample. Is the expectation of the sampling distribution of the Pearson product moment correlation coefficient always equal to the population correlation coefficient, regardless of the sample size?

 

[Stephen Tashi]

The shape of the sampling distribution of the Pearson product moment correlation coefficient depends on the size of the sample.

Doesn't it also depend on the joint distribution of the variables involved?

Is the expectation of the sampling distribution of the Pearson product moment correlation coefficient always equal to the population correlation coefficient, regardless of the sample size?

No, not according to the first paragraphs of https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2403&context=jmasm. However, I haven't read the entire article.

 

[Office_Shredder]

Consider the case of a sample of 2 data points.