The major goal of this study is to apply the essential unidimensionality statistic of W. Stout and the corresponding computer program (DIMTEST) to a hierarchical level mathematics achievement data set and to determine the extent to which the undimensional assumption can be accurately applied to mathematics achievement data. The study also ascertains if the unidimensionality assumption is more tenable when applied to specific subsets of items than to broader categories of items. A comparison of the essential unidimensionality structure across cultures is also performed. Results indicate that in the Japanese and U.S. data form the Second International Mathematics Study (SIMS), there are several subscales in SIMS mathematics tests, and that individual scores should be calibrated on each subscale rather than on a total score in the SIMS test. Essential unidimensionality estimates for the four tests were not the same in the two countries, calling into question the equivalence of dimensionality of the four tests. Either items on the test are more unidimensional in Japan, or the ability spaces among Japanese students are more homogeneous than for U.S. students. Eleven tables are included. (Contains 10 references.) (Author/SLD)