Thesis (M.S.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

One of the most important decisions to make when performing an exploratory factor or principal component analysis regards the number of factors to retain. Parallel analysis is considered to be the best course of action in these circumstances as it consistently outperforms other factor extraction methods (Zwick & Velicer, 1986). Even so, parallel analysis could benefit from further research and refinement to improve its accuracy. Characteristics such as factor loadings, correlations between factors, and number of variables per factor all have been shown to adversely impact the effectiveness of parallel analysis as a means of identifying the number of factors (Pearson, Mundfrom, & Piccone, 2013). Critically, even the choice of criteria on which to evaluate factors (such as the eigenvalue at the 50th or 95th percentile) can have deleterious effects on the number of factors extracted (Peres-Neto, Jackson, & Somers, 2004). One area of parallel analysis yet to be researched is the magnitude of the difference between the actual eigenvalue and the random data-based eigenvalue. Currently, even if the margin between the actual eigenvalue and the random data-based eigenvalue is nominal, the factor is considered to be meaningful. As such, it may behoove researchers to enforce a higher standard, such as a greater margin between the two eigenvalues than just a simple difference. Accordingly, the purpose of this study was to evaluate the efficacy of a 10% margin criterion as compared to an absolute margin. These margins were evaluated in conjunction with the 50th, 90th, 95th, and 99th percentile eigenvalue criteria on a population correlation matrix designed to engender underextraction. Previous research (Matsumoto & Brown, 2017) explored the same conditions on a population correlation matrix designed to elicit overextraction. They found that the most stringent standard (99th percentile eigenvalue plus a 10% margin) was the most accurate. For the present study however, it was hypothesized that the most accurate results would be obtained from a standard less stringent than the 99th percentile eigenvalue plus a 10% margin. The results suggest that when a correlation matrix has properties which may illicit underextraction, the use of less stringent criteria may lead to greater accuracy in identifying the number of factors and that the incorporation of an additional margin criterion may not improve the accuracy of the analysis.