Rules, in particular the requirement of a minimum cell expectation of 5, have long been available for determining whether the classic chi-square test with the correction for continuity can be suitably applied to the data of a single fourfold table. A similar kind of rule is proposed for the Mantel-Haenszel chi-square test for independence in several fourfold tables. That rule, applicable also in applying a non-central variant of the Mantel-Haenszel procedure, requires that there be a potential variation of at least 5 on each side of the expected total across the tables for a particular cell entry. Thus, if the entry in that cell for table i is A1, its lowest possible value (A1)L and its highest possible value (A1)U, while its expectation under a specified value for the odds ratio, Zo, is E(A1)∣(Zo), the requirement is that min [(σE(A1∣Zo) − σ(A1)L), (σ(A1)U − σE(A1∣Zo))] ≥ 5. With this requirement met, there is sufficient variation for the continuity corrected chi-square test of the hypothesis Z = Zo to be reasonably valid. It is further proposed that a short-cut test can be made relative to a hypothetical σE(A1)o without specifying the value of Zo giving rise to that expectation. This is accomplished through use of a simply calculated upper bound on the variance of σA1 based on the hypothesized σE(A1)o.