In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($χ^2$), thus allowing the new test to be used in place of or as a complement to $χ^2$ testing for purposes of distinguishing a larger class of deviations from uniformity. We establish that the proposed max-gap test has the same sequential and parallel computational complexity as $χ^2$ and thus is applicable for Big Data analytics and integrity verification.