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The effects of sample size and variability on the correlation coefficient

B T Bates1, S Zhang, J S Dufek

  • 1Department of Exercise and Movement Science, University of Oregon, Eugene, USA. btbates@oregon.uoregon.edu

Medicine and Science in Sports and Exercise
|March 1, 1996
PubMed
Summary

High variability significantly reduces shared variance, impacting the Pearson correlation coefficient (PCC). Sample size affects PCC reliability, not the mean value, highlighting the importance of considering variability in correlation analysis.

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Analysis

Background:

  • The Pearson product-moment correlation coefficient (PCC) is widely used to measure the linear relationship between two variables.
  • Understanding factors influencing PCC accuracy is crucial for reliable data interpretation in various scientific fields.

Purpose of the Study:

  • To investigate how variability and sample size affect the Pearson product-moment correlation coefficient (PCC).
  • To assess the impact of these factors on shared variance under the assumption of a perfect relationship.

Main Methods:

  • A computer model was developed to simulate and demonstrate the effects of sample size and variability on PCC.
  • The model was utilized to analyze selected examples from existing scientific literature.

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Main Results:

  • Variability exceeding 10% of the range for a variable led to a mean reduction of shared variance by 50% or more.
  • While sample size did not alter the mean PCC, it significantly impacted extreme percentile values, compromising result reliability.
  • Low PCC values can be an artifact of excessive data variability.

Conclusions:

  • Researchers must exercise caution when interpreting the relationship between variables solely based on PCC, especially without considering associated variabilities.
  • Variability is a critical factor that can distort correlation findings, necessitating its assessment alongside PCC.