A detailed investigation of the statistical procedure of W. Stout (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary response data from a psychological test is presented. One finding is that DIMTEST may fail to perform as desired in the presence of guessing when coupled with many high-discriminating test items. A revision of DIMTEST is proposed to overcome this limitation. Also, an automatic approach is devised to determine the size of the assessment subtests. Further, an adjustment is made on the estimated standard error of the statistic on which DIMTEST depends. These three refinements result in an improved procedure that is shown in simulation studies to adhere closely to the nominal level of significance while achieving considerably greater power. Finally, DIMTEST is validated on real data sets from the Armed Services Vocational Aptitude Battery (1,984 and 1,961 examinees) and the American College Testing program (2,491 and 2,494 examinees). Seven tables present analysis results, and 46 references are included. (Author/SLD)