NCJ Number
84549
Date Published
Unknown
Length
22 pages
Annotation
This assessment of a simple rank-based omnibus test for differences in distribution suggests that the test is about equal in power to the familiar omnibus test of Kolgomorov and Smirnov.
Abstract
This study proposes a rank-based omnibus test for differences in distribution that, like the familiar test of Kolmogorov and Smirnov, aims at sensitivity to all kinds of differences rather than those of particular form. The test is is both conceptually simple and easy to use. The study derives the asymptotic distribution of its key statistic and presents simulated comparisons of its power versus both the Kolgomorov-Smirnov and some specialized tests. The simulation results identify some circumstances in which the proposed test is more powerful than its Kolgomorov-Smirnov counterpart. On balance, however, the two tests seem about equally matched; they reached the same conclusion in the overwhelming majority of simulated cases. The proposed test may be preferred to the Kolgomorov-Smirnov test, however, because it involves less calculation; the reasoning behind it is more transparent to nonstatisticians; and it is more directly informative about how two distributions differ. Examples of the use of the test in criminal justice are to determine how the distribution of prison sentences are related to particular offender in the distributions of time until rearrest after release for similar cohorts of offenders subject to different correctional programs. Mathematical equations and three references are provided.