The theoretical differences between the traditional definition of dimensionality and the more recently defined notion of essential dimensionality are presented. Monte Carlo simulations are used to demonstrate the utility of W. F. Stout's procedure to assess the essential unidimensionality of the latent space underlying a set of terms. The traditional definition of dimensionality makes no distinction between major and minor dimensions. It is desirable to count only dominant dimensions in psychometric assessment of dimensionality of a latent space. Stout (1987, 1988) has provided a definition known as essential dimensionality and has developed a statistical test to assess the essential unidimensionality of a set of items. Monte Carlo simulation studies with two examinee sizes, n=750 and n=2,000, were generated with item parameters resembling those of real tests. Both simulations exhibited good performance in assessing essential unidimensionality. Since applications of item response theory techniques are becoming increasingly popular in most educational assessment, procedures to assess unidimensionality accurately will greatly facilitate the use of item response theory. Four tables provide data from the simulations. (SLD)