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ERIC Number: ED251510
Record Type: RIE
Publication Date: 1984-Aug
Reference Count: 0
A Comparison of Five Rules for Determining the Number of Components in Data Sets.
Zwick, William R.; Velicer, Wayne F.
A common problem in the behavioral sciences is to determine if a set of observed variables can be more parsimoniously represented by a smaller set of derived variables. To address this problem, the performance of five methods for determining the number of components to retain (Horn's parallel analysis, Velicer's Minimum Average Partial (MAP), Cattell's SCREE, Bartlett's Chi-Square test, and Kaiser's eigenvalue greater than unity rule) was investigated across seven systematically varied factors (sample size, number of variables, number of components, component saturation, equal or unequal numbers of variables per component, and the presence or absence of unique and complex variables). Five sample correlation matrices were generated at each of two levels of sample size from the 48 known population correlation matrices representing six levels of component pattern complexity. The performances of the parallel analysis and the MAP methods were generally the best across all situations. The SCREE test was generally accurate but variable. Bartlett's test was less accurate and more variable than the SCREE test. Kaiser's method tended to severely overestimate the number of components. Recommendations concerning the conditions under which each of the methods are accurate are discussed, along with the most effective and useful methods combinations. (Author/BW)
Publication Type: Speeches/Meeting Papers; Reports - Research
Education Level: N/A
Authoring Institution: N/A
Identifiers: Cattell (Raymond B); Chi Square Test (Bartlett); Eigenvalue Greater Than Unity Rule (Kaiser); Minimum Average Partial Rule (Velicer); Parallel Analysis (Horn); Scree Test
Note: Paper presented at the Annual Meeting of the American Psychological Association (92nd, Toronto, Ontario, August 24-28, l984).