The author notes that Bartlett's test of sphericity is often significant in practice, leading to questions about its practical utility. Which option best captures this view?

The author notes that Bartlett's test of sphericity is often significant in practice, leading to questions about its practical utility. Which option best captures this view?

• A. The test is widely accepted as essential in practice.
• B. The test often yields non-significant results, supporting utility.
• C. The test tends to yield significant results, which may limit its practical utility.
• D. The test is never used in multivariate analysis.

Answer: (C)

Bartlett's test of sphericity checks whether the observed correlation matrix differs from an identity matrix, which would indicate that the variables are related enough to justify a factor-analytic approach. A significant result suggests there is some correlation structure to explore. But in practice, the test often comes out significant, especially with large samples or many variables. That frequent significance doesn’t necessarily tell you about the number of meaningful factors or how strong the relationships are, so it can limit its usefulness as a practical gatekeeper for proceeding with factor analysis. So the best fit is that the test tends to be significant, which may limit its practical utility.

Bartlett's test of sphericity checks whether the observed correlation matrix differs from an identity matrix, which would indicate that the variables are related enough to justify a factor-analytic approach. A significant result suggests there is some correlation structure to explore. But in practice, the test often comes out significant, especially with large samples or many variables. That frequent significance doesn’t necessarily tell you about the number of meaningful factors or how strong the relationships are, so it can limit its usefulness as a practical gatekeeper for proceeding with factor analysis. So the best fit is that the test tends to be significant, which may limit its practical utility.