A Monte Carlo simulation was conducted to examine the Type I error rates and power of the tests by Bartlett; Brien, Venables, James, and Mayo; Kullback; and Steiger of the null hypothesis that a correlation matrix equals the identity matrix. Such tests are often recommended as preliminary procedures before performing factor analysis or evaluating the hypothesis of equal correlations. The Brien et al. procedure was found to be the most powerful test while maintaining stable empirical alpha values.
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