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The rejection of the hypothesis of complete independence prior to conducting a factor analysis
Reddon, John R.
Reddon, John R.
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1990
Type
Article
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Keywords
Psychology,Article,Factorial analysis,Human,Independence,Mental test,Theoretical study
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Citation
Reddon, J. R. (1990). The Rejection of the Hypothesis of Complete Independence Prior to Conducting a Factor Analysis. Multivariate Experimental Clinical Research, 9(3), 123-129. https://doi.org/10.62704/10057/17669
Abstract
Two tests of complete independence were compared in terms of relative power efficiency on 50 equi-correlation matrices and 26 published data sets. Λ1 a test based on Fisher's tanh-1 (r) transformation had greater power efficiency than, Λ0 a test based on -log|R| with finite sample corrections. Consequently, sample size requirements for rejecting P=I should be determined from Λ1 instead of Λ0. In addition, Baggaley's estimate of Q=-log|R|/k from the average absolute off-diagonal correlation was compared with a root mean square estimate of Q. The root mean square estimate was preferable but also demonstrated considerable bias. Because of the bias in estimating Q from the off-diagonal correlations, because Λ1 has greater relative power efficiency for P=I than ?0, and because the test statistic for Λ1 can be approximated from the root mean square off-diagonal correlation, it is preferable to tabulate power results for Λ1 as a function of the average correlation instead of Λo.
Table of Contents
Description
Publisher
Wichita State University, Department of Psychology
Journal
Book Title
Series
Multivariate Experimental Clinical Research
v.9 no.3
v.9 no.3
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0147-3964