A NOTE ON HORN'S TEST FOR THE NUMBER OF FACTORS IN FACTOR ANALYSIS

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Abstract
To examine the statistical sampling distributions of Horn's test for the number of factors, 100 sample correlation matrices at each of three sample sizes were generated from a structured population correlation matrix and an unstructured (identity) population correlation matrix of the same order. Each of the 600 sample matrices was submitted to principal components, SMC, image, and Harris rescaled farings. Two variations of the Horn test (which differed in the number of sets of unstructured Eigen-values averaged for the comparison) were applied to each factoring of each structured sample matrix. It was found that the 2 variations were not significantly different but that the type of factoring did have a significant effect. It was also found that the test tended to fail to give an estimate of the number of factors in many samples following the SMC and image factorings.

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