The size of the Cochran–Armitage trend test in 2×C2×C contingency tables

Although a number of studies showed that the Cochran–Armitage trend test does not preserve the nominal level, it is applied to only small sample cases, because the studies were conducted in small samples by simulation. Little is known about maintenance of the nominal level in infinite samples. Theoretical proof is needed to extend the results in small samples obtained by simulation into those in infinite samples. The purpose of this study is to investigate the sizes and the type I error rates of the Cochran–Armitage trend test, theoretically and numerically. Especially, we showed that the size (the supremum of the type I error rates over the nuisance parameter space) of the Cochran–Armitage trend test in large samples is always greater than or equal to the nominal level. That is, we proved limn⟶∞sup0