It was recently demonstrated that performing median splits on both of two predictor variables could sometimes result in spurious statistical significance instead of lower power. Not only is the conventional wisdom that dichotomization always lowers power incorrect, but the current article further demonstrates that inflation of apparent effects can also occur in certain cases where only one of two predictor variables is dichotomized. In addition, we show that previously published formulas claiming that correlations are necessarily reduced by bivariate dichotomization are incorrect. While the magnitude of the difference between the correct and incorrect formulas is not great for small or moderate correlations, it is important to correct the misunderstanding of partial correlations that led to the error in the previous derivations. This is done by considering the relationship between partial correlation and conditional independence in the context of dichotomized predictor variables.
On conditional independence and log-convexity
