Factor analysis is the traditional method for studying the dimensionality of test data. However, under common conditions, the factor analysis of tetrachoric correlations does not recover the underlying structure of dichotomous data. The purpose of this paper is to demonstrate that the factor analyses of tetrachoric correlations is unlikely to yield clear support for unidimensionality even when the data are generated to be unidimensional. This result is caused by a failure of the item data to meet the assumptions of the tetrachoric correlation. For this study, item true score distributions were generated assuming a normal latent trait and a variety item characteristic curve (ICC) forms for the items. In every case, these distributions were nonnormal, and the bivariate distribution did not match the bivariate normal. The principal component analysis of data generated according to these ICC's yielded a highly complex solution, most likely a result of the violation of the assumptions of the tetrachoric correlations that form the basis of the analysis. Further research is needed on new methods of factor analysis of dichotomous test data generated by a variety of ICC forms. (BS)