Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using...

Area of Science:

• Psychological statistics
• Quantitative psychology
• Correlation analysis

Background:

• The Pearson product-moment correlation coefficient (r) and Spearman rank correlation coefficient (r) are frequently employed in psychological research.
• Assessing the performance of these correlation coefficients under various data conditions is crucial for accurate statistical inference.

Purpose of the Study:

• To compare the Pearson (r) and Spearman (r) correlation coefficients based on variability, bias, and outlier robustness.
• To determine the optimal correlation coefficient for psychological research, particularly concerning data distribution characteristics.

Main Methods:

• Simulations were conducted across sample sizes from N=5 to N=1,000 using normally and highly kurtotic distributions.
• A sampling study analyzed a psychometric dataset with light tails and two Likert-type survey datasets (light-tailed and heavy-tailed).

Main Results:

• For normally distributed variables, Pearson (r) and Spearman (r) showed similar expected values, but Pearson's r exhibited higher variability, especially with strong correlations.
• With high kurtosis or heavy-tailed distributions (common in survey data), Spearman's r demonstrated lower variability and often a more accurate estimate of the population Pearson correlation (R) compared to Pearson's r.
• Using Spearman's r instead of Pearson's r reduced variability by approximately 20%, whereas doubling the sample size reduced variability by 41%.

Conclusions:

• Pearson's r is suitable for light-tailed distributions.
• Spearman's r is preferable for heavy-tailed distributions or when outliers are anticipated, which is frequent in psychological research.
• Spearman's r offers a more robust and stable estimate in non-ideal data conditions prevalent in psychological studies.