We examine a set of specific criteria designed to test hypotheses about the membership of observations to the uniform law. We studied the distribution of statistics of criteria and their power relative to various competing hypotheses. We identified advantages and disadvantages of the various criteria. It has been shown that a significant part of the criteria traditionally used when testing hypotheses about uniformity, is ectopic relative to a certain type of competing hypotheses. It is stressed that the special criteria for testing uniformity have no obvious advantages over non-parametric agreement criteria used for checking uniformity.