A The expectation of the sampling distribution of Pearson's correlation

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The expectation of the sampling distribution of the Pearson product moment correlation coefficient is not always equal to the population correlation coefficient, particularly when sample sizes are small. The shape of this distribution is influenced by the sample size and the joint distribution of the variables involved. For very small samples, such as those with only two data points, the correlation may not accurately reflect the population correlation. This highlights the importance of considering both sample size and distribution characteristics when interpreting correlation coefficients. Overall, the relationship between sample size and the accuracy of the correlation estimate is crucial in statistical analysis.
Ad VanderVen
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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?
 
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Ad VanderVen said:


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?

Ad VanderVen said:
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.
 
Consider the case of a sample of 2 data points.
 
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