The expectation of the sampling distribution of Pearson's correlation

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SUMMARY

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 sampling distribution is influenced by the sample size and the joint distribution of the variables involved. A sample size of 2 data points can significantly affect the accuracy of the correlation estimate. This indicates that researchers must consider both sample size and variable distribution when interpreting correlation coefficients.

PREREQUISITES
  • Understanding of Pearson product moment correlation coefficient
  • Knowledge of sampling distributions in statistics
  • Familiarity with joint distributions of variables
  • Basic statistical inference concepts
NEXT STEPS
  • Research the implications of sample size on correlation estimates
  • Study the properties of sampling distributions in statistics
  • Explore the relationship between joint distributions and correlation coefficients
  • Investigate statistical methods for small sample sizes
USEFUL FOR

Statisticians, data analysts, researchers in social sciences, and anyone involved in correlation analysis and interpretation of statistical data.

Ad VanderVen
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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?
 
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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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