Abstract

Studied the theoretical underpinnings of Gatlin's tests of randomness, D -sub(n), by examining interrelationships of D-sub(n ) and classical tests of frequency bias and of serial dependence. D-sub(n ) is statistically equivalent to some of the tests studied for all sample sizes and, for all practical purposes, equivalent to the other tests for large sample sizes. The asymptotic distribution of D-sub(n ) is shown to be chi square. Methods for computing the exact small-sample distribution are discussed. It is concluded that there is little or no basis for preference of D-sub(n ) over any of the other tests in terms of statistical power; however, some readers may find D-sub(n ) a conceptually preferable test because of its basis in information theory. (19 ref)