Resolution:
## 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 g_{2}, T ⊥̸ ⊥g_{2}and T ⊥̸ ⊥g_{2} | g_{1}, but the conditional test will generally have greater power than the marginal test,
since using g_{1}as a regressor will explain some proportion of g_{2}’s variation. Under (b), where T does not have a direct effect on g_{2}, T ⊥̸ ⊥g_{2}but T ╨ g_{2} | g_{1}. 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.
Edwards |