Response surface analysis (RSA) enables researchers to test complex psychological effects, for example, whether the congruence of two psychological constructs is associated with higher values in an outcome variable. RSA is increasingly applied in the personality and social psychological literature, but the validity of published results has been challenged by some persistent oversimplifications and misconceptions. Here, we describe the mathematical fundamentals required to interpret RSA results, and we provide a checklist for correctly identifying congruence effects. We clarify two prominent fallacies by showing that the test of a single RSA parameter cannot indicate a congruence effect, and when there is a congruence effect, RSA cannot indicate whether a predictor mismatch in one direction (e.g., overestimation of one’s intelligence) is better or worse than a mismatch in the other direction (underestimation). We hope that this contribution will further enhance the validity and strength of empirical studies that apply this powerful approach.