Testing for Zero Correlation between Two Uncorrelated Non-Linearly Dependent Random Variables: A Cautionary Note

Abstract

A simulation study was performed to analyze the effects of violations of the normality assumption on the t-test of the Pearson correlation coefficient when the variables are not independent, even though the population correlation is zero. Large effects for violations of normality were found. The Type I error rate can be either inflated or deflated with respect to the assumed error rate. A recommendation is made that the use of the t-test be avoided where there are good reasons to believe that a nonlinear relationship exists between the variables.