The capability of the DIMTEST statistical test to assess essential dimensionality of the model underlying item responses of real tests as opposed to simulated tests was investigated. A variety of real test data from difference sources was used to assess essential dimensionality. Based on DIMTEST results, some test data are assessed as fitting an essential unidimensional model, while others are not. Essential unidimensional test data, as assessed by DIMTEST, are then combined to form two-dimensional test data. The power of Stout's statistic T is examined for the two-dimensional data. It is shown that the results of DIMTEST on real tests replicate findings from simulated tests in that the statistic T discriminates well between essential unidimensional and multidimensional tests and is also highly sensitive to major abilities while being insensitive to relatively minor abilities influencing item responses. Five tables present analysis results, and 38 references are included. (Author/SLD)