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 Tg2 | 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.

Edwards et al. BMC Bioinformatics 2012 13:167   doi:10.1186/1471-2105-13-167
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