Considerable prior statistical work has criticized replacing a continuously measured variable in a general linear model with a dichotomy based on a median split of that variable. Iacobucci, Posovac, Kardes, Schneider, and Popovich (2015-in this issue) defend the practice of "median splits" using both conceptual arguments and simulations. We dispute their conceptual arguments, and we have identified technical errors in their simulations that dramatically change the conclusions that follow from those simulations. We show that there are no real benefits to median splits, and there are real costs in increases in Type II errors through loss of power and increases in Type I errors through false-positive consumer psychology. We conclude that median splits remain a bad idea.