The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA typically consist of Pearson correlations. In this study, the authors matched the type of random data matrix to the type of input matrix. Analyses were conducted on both polychoric and Pearson correlation matrices, and random matrices of the same type (polychoric or Pearson) were generated for the PA procedure. PA based on random Pearson correlations was found to perform at least as well as PA based on random polychoric correlations, for nearly all of the conditions studied. (Contains 1 table and 1 figure.)