Correlation coefficients are frequently reported in educational and psychological research. The robustness properties and optimality among practical approximations when phi does not equal 0 with moderate sample sizes are not well documented. Three major approximations and their variations are examined: (1) a normal approximation of Fisher's Z,…

A maximum likelihood approach to correlational outlier identification is introduced and compared to the Mahalanobis D squared and Comrey D statistics through Monte Carlo simulation. Identification performance depends on the nature of correlational outliers and the measure used, but the maximum likelihood approach is the most robust performance…

The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…