Inversions Everywhere: when "It Depends" Does not Amount to Simple Contingent Relationships

Theories in management are often subjects to potential inversion in the nature of the effect described. We explore three canonical possible inversions: the max/min point in a quadratic regression model; the point of intersection and the change of slope in a moderated regression model. The inquiry explores the motivation for considering such inversions, considers typical common situations where inversions are misinterpreted empirically (both type I and type II errors), and proposes a methodological approach to conduct more in depth exploration. We illustrate those situations by simulated examples and computations conducted in R.