BRIEF REPORT: BARTLETT'S TEST OF SPHERICITY AND CHANCE FINDINGS IN FACTOR ANALYSIS.

Area of Science:

• Multivariate statistics
• Psychometrics

Background:

• Factor analysis is a common statistical technique used to identify underlying structures in data.
• Assessing the suitability of a correlation matrix for factor analysis is a critical preliminary step.
• Bartlett's test of sphericity is a statistical test used to evaluate the null hypothesis that the correlation matrix is an identity matrix.

Purpose of the Study:

• To evaluate the effectiveness of Bartlett's test of sphericity in detecting chance correlations.
• To emphasize the importance of conducting Bartlett's test prior to factor extraction.

Main Methods:

• Bartlett's test of sphericity was applied to a correlation matrix.
• The correlation matrix was computed using random normal deviates, as reported by Armstrong and Soelberg (1968).
• A chi-square value was obtained from the test.

Main Results:

• The Bartlett's test yielded a chi-square value suggesting the correlation matrix could originate from a population with zero correlations.
• This outcome indicates a sensitivity of the test in identifying matrices that may produce spurious factor structures.

Conclusions:

• The findings reinforce the necessity of performing Bartlett's test of sphericity before proceeding with factor extraction.
• Consistent with previous research, Bartlett's test is a sensitive indicator for detecting chance findings in correlation matrices.