Cattell's Scree Test In Relation To Bartlett's Chi-Square Test And Other Observations On The Number Of Factors Problem.

It is demonstrated that Cattell's scree test and Bartlett's chi-square test for the number of factors are both based on the same rationale, so the former reflects statistical (subject sampling) variability and the latter usually involves psychometric (variable sampling) influences. If the alpha-level (implicit in the scree test) is set the same, the two tests should lead to the same conclusions. Analyses with some examples suggest that if the alpha-level for the Bartlett test is set (explicitly) in the neighborhood of .0003 for sample Ns of 100 to 150, the results from applications of this test will indicate approximately the same number of factors as estimated on the basis of a scree test determined on a much larger (N ≃ 600) sample. Used in this way, the Bartlett test may yield fairly good "population" estimates of the number of factors. Relationships between the Bartlett test, hence the scree test, and tests for a common factor model and for the significance of a correlation matrix are explicated.