Statistical Evaluation of Tests for Suppression As a Case of Inconsistent Mediation

Introduction: This research explores tests of suppression. Suppression is a statistical phenomenon whereby the magnitude of an effect becomes larger when adjusted for a suppressor variable. From a causal perspective, suppression occurs when there is inconsistent mediation or negative confounding (MacKinnon et al., 2001). One example of suppression is, workers’ intelligence is positively related to boredom which is positively related to making errors on an assembly line task, but workers’ intelligence is negatively related to making errors (McFatter, 1979). Another example uses verbal and mechanical ability to predict pilot performance (Horst, 1941). In that study, the relationship between mechanical ability and pilot performance increased when verbal performance was included in the regression equations. Gignac (2018) applied a test for suppression that hypothesizes if the zero-order and partial correlations differ by 1-2%, then there is evidence for suppression (Velicer, 1978). Several different approaches for testing suppression are evaluated conceptually and in a statistical simulation study where we impose conditions of inconsistent mediation. In particular, a statistical test of suppression based on work by Velicer (1978) was compared to tests based on the change in magnitude of regression coefficients based on tests for mediation.

Method: The multivariate delta method was used to derive the variance of the Velicer test of suppression (Dorfman, 1938; Velicer, 1978). Bootstrap methods were also evaluated. Simulation conditions varied sample size, path coefficients, and size of correlations between variables so that we could evaluate the results of the statistical tests. We then check if these tests detect suppression under conditions where a suppressor effect is present or not present. We evaluate the suppression tests for empirical power and empirical Type I error rates.

Results: The derived standard error for the Velicer test for suppression was similar to the simulated standard error indicating that our derivation was correct. The Velicer test did not perform as well as the general test for mediation. We describe cases of suppression/inconsistent mediation in prevention research.

Conclusions: In general, the Velicer test for suppression did not perform as well as other methods in suppression detection. General methods for testing inconsistent mediation in prevention science are recommended for testing for suppression.