Determining the number of dimensions underlying many variables in the data or many items in the test is a crucial process prior to performing exploratory factor analysis. Failure to do so leads to serious consequences concerning construct validity. Parallel analysis (PA) has been found to be useful to determine the number of dimensions (i.e., components or factors) in many conditions. As computational power of computers is much advanced, novel procedures have been developed to improve the accuracy of PA. Authors of a number of previous studies have investigated the use of parallel analysis with scale data (e.g., questionnaires). However, little research has been conducted on the performance of PA when applied to existing real test data. This present study, therefore, compared the consistency of PA and other criteria (i.e., minimum average partial, broken stick, average root and modified average roots, imbedded error, and indicator function) in extracting the number of dimensions from large existing real test data at the population level (approximately 400,000 cases) based on these studied variables: sample size, factor structure, number of randomly generated data sets, threshold, and type of input correlation matrices. R scripts in the R program were written to repeatedly sample from a population's data in a Monte Carlo simulation procedure and to run the analyses. Consistent methods yielding precise results under most studied conditions were: MAP, IND, PA[subscript COR95] (i.e., PA using the original correlation matrices with 1s on the diagonal) with the 95th percentile as a threshold and 100 randomly generated data sets, and MAR[subscript 1.4] (i.e., 1.4*Average Root), respectively. When practitioners have small sample sizes of at least 100, MAP is recommended for use. PA performed consistently with sample sizes of at least 200. However, MAP and PA are not incorporated in commercial statistical software (e.g., SPSS, SAS). Therefore, alternative methods are recommended for use in place of or in conjunction with recommended methods to compare the results. IND and MAR[subscript 1.4] are recommended for use with sample sizes of at least 200 and 300, respectively. However, BS and IE are not recommended due to large errors and unvaried results of other than one dimension when n [greater than or equal to] 100, respectively. In general, a sample size of 100 is not recommended for use because it is not sufficient to yield precise results. Sample sizes of 200, 300, and 400 are recommended to be minimum, acceptable, and desirable sample sizes to yield consistent results. In this study, an unbalanced factor structure (i.e., unequal numbers of items in each dimension) showed a negative impact on the precision of the factor extraction results. Tutorials on how to perform PA and the other five criteria with examples were presented. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]