Which statement is true regarding the use of eigenvalues in factor analysis?

• A. Factors with eigenvalues greater than .05 are retained
• B. Factors with eigenvalues equal to or less than 0 are retained
• C. All factors should always be retained regardless of eigenvalue
• D. Eigenvalues are not used in factor analysis

Answer: (A)

The correct assertion regarding the use of eigenvalues in factor analysis is that factors with eigenvalues greater than 1 are typically retained, as these eigenvalues indicate that the factor accounts for more variance than a single observed variable would. This criterion is based on the idea that a factor should capture substantial information from the data set; using an eigenvalue of 1 as a cut-off is standard practice, rather than the suggested threshold of .05, which is not a conventional criterion in factor analysis.

In factor analysis, each factor that is extracted will have an associated eigenvalue, which measures the amount of variance that the factor explains. Factors with eigenvalues greater than 1 are considered significant enough to warrant retention because they reflect underlying structures in the data that can contribute meaningfully to the modeling process.

The other choices do not correctly reflect standard practices in factor analysis. Specifically, retaining factors with eigenvalues equal to or less than zero would suggest that those factors explain no variance or are superfluous, while the idea that all factors should be retained regardless of their eigenvalues disregards the importance of understanding which factors are truly useful. Furthermore, the statement that eigenvalues are not used in factor analysis is false, as they are critical to evaluating the meaningfulness of