Differentiating the Cochran-Armitage Trend Test and Pearson's χ² Test: Location and Dispersion

In genetic case-control association studies, a standard practice is to perform the Cochran-Armitage (CA) trend test with 1 degree-of-freedom (d.f.) under the assumption of an additive model. However, when the true genetic model is recessive or near recessive, it is outperformed by Pearson's χ² test with 2 d.f. In this article, we analytically reveal the statistical basis that leads to the phenomenon. First, we show that the CA trend test examines the location shift between the case and control groups, whereas Pearson's χ² test examines both the location and dispersion shifts between the two groups. Second, we show that under the additive model, the effect of location deviation outweighs that of the dispersion deviation and vice versa under a near recessive model. Therefore, Pearson's χ² test is a more robust test than the CA trend test, and it outperforms the latter when the mode of inheritance evolves to the recessive end.