Figure 1

Comparison of marginal and conditional tests. Comparison of conditional and marginal tests for two models. Under (a), where T has a direct effect on g₂, T ⊥̸ ⊥g₂and T ⊥̸ ⊥g₂ | g₁, but the conditional test will generally have greater power than the marginal test, since using g₁as a regressor will explain some proportion of g₂’s variation. Under (b), where T does not have a direct effect on g₂, T ⊥̸ ⊥g₂but T ╨ g₂ | g₁. Hence the conditional null hypothesis holds, and the Type II error of the conditional test is less than α, the Type I error of the test. In contrast, the marginal hypothesis is more likely to be rejected, and the Type II error is inflated.