# Which Correlation Coefficient Should Be Used for Investigating Relations between Quantitative Variables?

## Keywords:

correlation coefficient, type I error, test power, simulation, robust methods## Abstract

Since the purpose of many studies is to describe and summarize the relations between two or more variables, the correlation analysis has been become one of the most fundamental statistical concepts for many researchers. There are different correlation coefficients have been developed and proposed for different cases. In this stage, it is extremely important to aware of which correlation coefficient(s) is more appropriate to use based on the measurement levels, type of the variables, distribution of the variables, type of relations between the variables, and presence of outliers or not in dataset. In this study, nine different correlation coefficients have been compared in terms of Type I error rate and test power under different experimental conditions. As a result, it has been possible to produce information about which correlation coefficient is more appropriate to use in which situations. Results of this simulation study showed that the performances of these correlation coefficients are affected by sample size and effect size rather than the distribution shape. When both the type I error and test power estimates are evaluated together, the Pearson's correlation, Winsorized, Spearman Rank, and Kendall-Tau correlation coefficients are seem to be the most appropriate coefficients for many experimental conditions.

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*American Scientific Research Journal for Engineering, Technology, and Sciences*,

*85*(1), 265–277. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/7326

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