ERIC Number: EJ1201550
Record Type: Journal
Publication Date: 2019-Feb
Abstractor: As Provided
Proportion of Indicator Common Variance Due to a Factor as an Effect Size Statistic in Revised Parallel Analysis
Xia, Yan; Green, Samuel B.; Xu, Yuning; Thompson, Marilyn S.
Educational and Psychological Measurement, v79 n1 p85-107 Feb 2019
Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic--the proportion of common variance (PCV)--into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues [(mathematical characters omitted)] overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as [mathematical characters omitted], even with a relatively large sample size of 5,000. Finally, we investigated the use of [mathematical characters omitted] in combination with R-PA and concluded that practitioners can gain additional information from [mathematical characters omitted] and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.
Descriptors: Effect Size, Factor Analysis, Hypothesis Testing, Psychometrics, Statistics, Statistical Bias
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
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