The identification of the dependence between variables is a common task in Psychology. The most common approaches to this task are Pearson’s, Spearman’s, and Kendall correlation coefficients. A...Show moreThe identification of the dependence between variables is a common task in Psychology. The most common approaches to this task are Pearson’s, Spearman’s, and Kendall correlation coefficients. A clear limitation of those coefficients is that they can only identify linear and monotonic relationships. In recent years, several methods to identify nonmonotonic associations have been developed. Nevertheless, there is not a clear answer to which method should be used when facing unknown conditions in research as is often the case in Psychology. In this study, we aimed to identify which dependence test performs the best under conditions that can be found in psychological research. Method: A simulation was performed to compare nine dependence tests through hypothesis testing. The conditions assessed were sample size, type of relationship, and noise. Three approaches were employed to summarize the statistical power and analyse the results: complete class, average power, and Maximin. Results: There was not a uniformly most powerful test across all conditions. However, several nonmonotonic tests presented a good performance in terms of power for most conditions. Moreover, Mutual Information (MI) estimated through Kernel Density Estimation with the Epanechnikov kernel and the Sheater-Jones plugin bandwidth outperformed all other methods in terms of the analysis approaches of this study. Conclusion: For the evaluated conditions we recommend the use of MI estimated through the defined settings. Nevertheless, other modern tests should not be immediately discarded as their difference in performance with MI is small and could be due to the design of this specific simulation.Show less
