Comparative Performance Between Spearman’s Rho and Pearson’s R Correlation Coefficient in Measuring Statistical Relationships at Different Population Distribution

In many correlational studies, Pearson’s correlation coefficient (r) is commonly used to assess bivariate distributions. However, this statistic is inappropriately applied when variables are highly skewed, whereas Spearman’s Rho (ρₛ) is better suited. This study used a Monte Carlo simulation to compare the accuracy and stability of Pearson's r and Spearman's rho across three population distributions that differed in skewness, kurtosis, and the presence of outliers (normal, uniform, exponential), at sample sizes ranging from n = 10 to n = 1,000, and at population associations of ρₛ = 0 (no relationship) and ρₛ = .50 (moderate monotonic relationship). Bivariate samples were generated using a Gaussian copula so that the rank-order dependence structure was held constant while the marginal distributions were manipulated. Each condition was replicated 3,000 times. Results showed that under the symmetric distributions (normal, uniform), Pearson's r was slightly more efficient (lower sampling variability) than Spearman's rho, consistent with classical asymptotic relative efficiency theory. Under the skewed exponential distribution, this pattern reversed: Spearman's rho showed consistently lower variability and, at larger sample sizes, lower root-mean-square error than Pearson's r, with the variance ratio favoring Spearman's rho by as much as 1.6:1 at n = 1,000. Both coefficients were approximately unbiased under the null hypothesis of no association, regardless of distributional shape. These findings indicate that no single coefficient is uniformly superior: Pearson's r is preferable for approximately symmetric, light-tailed data, whereas Spearman's rho offers a more robust and often more efficient estimate of association when data are skewed.

Pearson’s correlation, Spearman’s correlation, bivariate distribution, Monte Carlo simulation

1. Alshangiti, A. M., Gemeay, A. M., Bakr, M. E., Yousuf, A. M., El-Qurashi, M. A., Balogun, O. S., ... & Hammad, A. T. (2025). New robust estimator for handling outliers and multicollinearity in gamma regression model with application to breast cancer data. Scientific Reports, 15(1), 38436. [Google Scholar] [Crossref]

2. Bocianowski, J., Wrońska-Pilarek, D., Krysztofiak-Kaniewska, A., Matusiak, K., & Wiatrowska, B. (2024). Comparison of Pearson’s and Spearman’s correlation coefficients for selected traits of Pinus sylvestris L. Biometrical Letters, 61(2), 115-135. [Google Scholar] [Crossref]

3. Ceritoğlu, F. (2026). Systematic Undercoverage in Bootstrap Confidence Intervals for Xi Correlation Coefficient: A Simulation Study. Mathematics, 14(12), 2136. [Google Scholar] [Crossref]

4. Dazong, R. H., & Terrang, A. U. (2026). Investigating the Relationship between Pearson’s and Spearman Rank Correlation Mathematically and through Simulation. KolaDaisi University Journal of Applied Sciences, 3, 29-34. [Google Scholar] [Crossref]

5. Díaz, H., Teixeira, A. P., & Soares, C. G. (2022). Application of Monte Carlo and Fuzzy Analytic Hierarchy Processes for ranking floating wind farm locations. Ocean Engineering, 245, 110453. [Google Scholar] [Crossref]

6. Harary, M. (2024). Efficient algorithms for the sensitivities of the Pearson correlation coefficient and its statistical significance to online data. arXiv preprint arXiv:2405.14686. [Google Scholar] [Crossref]

7. Hopkins, V., Kagalwala, A., Philips, A. Q., Pickup, M., & Whitten, G. D. (2024). How do we know what we know? Learning from Monte Carlo simulations. The Journal of Politics, 86(1), 36-53. [Google Scholar] [Crossref]

8. Hurley, L. (2025). Completing and studentising Spearman's correlation in the presence of ties. arXiv preprint arXiv:2512.23993. [Google Scholar] [Crossref]

9. Ji, X. (2023). Multivariate extreme wind loads: copula-based analysis. Journal of Engineering Mechanics, 149(1), 04022082. [Google Scholar] [Crossref]

10. Lo, A. A. P., & Christian, C. (2026). Behavioural Predictors of Forward Head Posture Risk: A Correlation, Machine Learning, and Clustering Analysis. Journal of Applied Informatics and Computing, 10(1), 398-405. [Google Scholar] [Crossref]

11. Okoye, K., & Hosseini, S. (2024). Correlation tests in R: pearson cor, kendall’s tau, and spearman’s Rho. In R programming: Statistical data analysis in research (pp. 247-277). Singapore: Springer Nature Singapore. [Google Scholar] [Crossref]

12. Rahaman, A. (2026). Comprehensive classification of statistical methods: A hierarchical taxonomy from foundations to research frontiers. Available at SSRN 6604119. [Google Scholar] [Crossref]

13. Sathyanarayana, S., & Mohanasundaram, T. (2025). Correlation methodologies revisited: From classical statistics to contemporary residual diagnostics. Asian Journal of Economics, Business and Accounting, 25(11), 86-103. [Google Scholar] [Crossref]

14. Soltani, A., & Imani, M. A. (2024). Overcoming implementation barriers to renewable energy in developing nations: A case study of Iran using MCDM techniques and Monte Carlo simulation. Results in Engineering, 24, 103213. [Google Scholar] [Crossref]

15. Ventura-León, J., Peña-Calero, B. N., & Burga-León, A. (2023). The effect of normality and outliers on bivariate correlation coefficients in psychology: A Monte Carlo simulation. The Journal of General Psychology, 150(4), 405-422. [Google Scholar] [Crossref]

16. Zrelak, P. A. (2026). Inferential Statistics and the Pitfalls of Nonrandomized Sampling in Nursing Research. Nursing Research, 75(1), 63-69. [Google Scholar] [Crossref]

• A Comparative Study on the Thermal and Electrical Conductivity of Common Materials
• Thickness Dependent Thermoelectric Properties of Pb0.4In0.6Se Thin Films Deposited by Physical Evaporation Technique
• Optimization of a Patch Antenna Using Genetic Algorithm
• Kinematic Constraints On Brown Dwarf Atmospheric Variability And Evidence For Bimodal Formation From Multi-Survey Analysis
• Reservoir Characterization through the Application of Petrophysical Evaluation of Well Logs of Animaux Field, Niger Delta Basin, Nigeria