Three Approaches to Testing for Statistical Suppression

Suppression effects are important for theoretical and applied research because these effects occur when there is an unexpected increase in an effect when it is adjusted for a third variable. This paper investigates three approaches to testing for statistical suppression. The first test was proposed in 1978 and is based on the relationship between the zero-order and semi-partial correlations. The second test comes from a condition that is necessary for suppression proposed in 1997. The third test is an extension of the test for the inconsistent mediated effect. We derive standard errors for the Velicer, and Sharpe and Roberts tests, conduct a statistical simulation study, and apply all three tests to two real data sets and several published correlation matrices. In the simulation study, the test based on inconsistent mediation had the best properties overall. For the data examples, when raw data were available, we constructed bootstrap confidence intervals to assess significance, and for correlations, we compared each test statistic to the normal distribution to assess statistical significance. Each test gave consistent results when applied to the example data sets. Analytical work demonstrated conditions where each test gave conflicting results. The mediation test of suppression based on the sign of the product of the mediated effect and the direct effect had the best overall performance.