Cross-Sectional Analysis of Methods of Computing Partial Correlation Coefficients: A Self-Explained Note With R Syntax

Timothy A. Ogunleye, Kehinde K. Adesanya, Oluwatosin J. Akinsola, Godwill I. Wilcox


This paper examines four different methods of computing partial correlation coefficients. These include conventional method, variance-covariance matrix approach, regression residual’s approach, and OLS method. Each of these is fully illustrated with practical examples as well as R syntax. Applicability of each of the methods is discussed in our illustrations. Strength and weakness of each method are extensively detailed. It’s, however, discovered that none of the basic assumptions of partial correlation: linearity, normality, and non-existence of outliers is violated after performing statistical checks on the datasets used. The study, therefore, recommends the best method(s) of computing partial correlation coefficients when at least one variable is held constant, thereby adding more invaluable knowledge to the existing literatures. Finally, the study further recommends the best method in each scenario with illustrative examples as evidences. 


Conventional method; OLS method; Partial correlation; Regression residual’s approach; Variance-covariance matrix method

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Akoglu, H. (2018). User’s guide to correlation coefficients. Turkish Journal of Emergency Medicine, 18(3), 91-93.

Aloe, A.M. (2013). The synthesis of partial effect sizes. Journal of the Society for Social Work and Research, 4(4), 390-405.

Bishara, A.J., & James B.H. (2017). Confidence intervals for correlations when data are not normal. Behavior Research Methods, 49(1), 294-309. Retrieved from

Egozcue, J. J., Pawlowsky-Glahn, V., & Gloor, G. B. (2018). Linear association in compositional data analysis. Austrian Journal of Statistics, 47 (1), Pp. 3-31.

Fieller, E. C., Herman, O. H., & Egon, S. P. (1957). Tests for rank correlation coefficients I. Biometrika, 44(3/4), 470- 81. Retrieved from

Fisher, R.A. (1924). The distribution of the partial correlation coefficient. Metron, 3(3-4), 329-332.

Guilford, J.P., & Fruchter, B. (1973). Fundamental statistics in psychology and education. McGraw-Hill, Kogakusha, Ltd.

Ha, M.J., & Sun, W. (2014). Partial correlation matrix estimation using ridge penalty followed by threshold and re-estimation. Biometrics, 70(3), 762-770.

Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2018). Applied statistics for the behavioral sciences (8th ed.). Boston: Houghton Mifflin.

Horwitz, B., & Rapoport, S. I. (1988). Partial correlation coefficients approximate the real intrasugject correlation pattern in the analysis of interregional relations of cerebral metabolic activity. Journal of Nuclear Medicine, 29(3), 392-399.

Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3-4), 321-377. doi:10.1093/biomet/28.3- 4.321. JSTOR 2333955.

Kenett, D. Y., Huang, X., Vodenska, I., Havlin, S., & Stanley, E. (2015). Partial correlation analysis: application for financial market. Journal of Quantitative Finance, 15(4), 569-578.

Kynčlová, P., Hron, K., & Filzmoser, P. (2017). Correlation between compositional parts based on symmetric balances. Mathematical Geosciences, 49, 777-796.

Langfelder, P., & Steve, H. (2012). Fast R functions for robust correlations and hierarchical clustering. Journal of Statistical Software, 46(11). Retrieved from

Lonas, E. (2020). Partial correlations in compositional data analysis. Applied Computing and Geosciences, 6, 100026.

Merrian-webster dictionary (2020). Definition of correlation. Available from https://www.merriam- Downloaded on 10th January, 2020.

Mukaka, M. M. (2012). A guide to appropriate use of correlation coefficient in medical research. Malawi Medical Journal, 24(3), 69-71.

Pedhazur, E. J. (1982). Multiple regression in behavioural research: Explanation and prediction (2nd ed.). New York: Holt, Rinehart Winston.

R Core Team (2020). R: A language and environment for statistical computing Vienna, Austria: R foundation for statistical computing. Retrieved from

Roverato, A., & Castelo, R. (2017). The networked partial correlation and its application to the analysis of genetic interactions. Journal of the Royal Statistical Society: Applied Statistics., Series C, 66(3), 647-665.

Serlin, R. C., & Harwell, M. R. (2007). An empirical study of 8 tests of partial correlation coefficients. Communication in Statistics-Simulation and Computation, 22(2), 545-567.

Waliczec, T. M. (1996). A primer on partial correlation coefficients. A paper presented at the annual meeting of the Southwest Educational Research Association, New Orleans, January.

Yule, G. U. (1907). On the theory of correlation for any number of variables treated by a new system of notation. Roy. Soc. Proc. A. LXXIX, 182-193.



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