Improving the probability of reaching correct conclusions about congruence hypotheses: Integrating statistical equivalence testing into response surface analysis.

Abstract

Many psychological theories imply that the degree of congruence between two variables (e.g., self-rated and objectively measured intelligence) is related to some psychological outcome (e.g., life satisfaction). Such congruence hypotheses can be tested with response surface analysis (RSA), in which a second-order polynomial regression model is estimated and suitably interpreted. Whereas several strategies exist for this interpretation, they all contain rationales that diminish the probability of drawing correct conclusions. For example, a frequently applied strategy involves calculating six auxiliary parameters from the estimated regression weights and accepting the congruence hypothesis if they satisfy certain conditions. In testing the conditions, a nonsignificant null-hypothesis test of some parameters is taken as evidence that the parameter is zero. This interpretation is formally inadmissible and adversely affects the probability of making correct decisions about the congruence hypothesis. We address this limitation of the six-parameter strategy and other RSA strategies by proposing that statistical equivalence testing (SET) be integrated into RSA. We compare the existing and new RSA strategies with a simulation study and find that the SET strategies are sensible alternatives to the existing strategies. We provide code templates for implementing the SET strategies. (PsycInfo Database Record (c) 2025 APA, all rights reserved).