Factor Analysis, Random Data, and Patterned Results

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Abstract
Multivariate statistical techniques such as factor analysis are capable of producing patterned results with most, if not all, data matrices. This paper demonstrates that patterned results are obtainable when principal component analysis is applied to a random data set. It is suggested that Bartlett's test for the statistical significance of a correlation matrix be employed in deciding whether a factor analysis of the matrix is justified.