Measures of Association for the Component Analysis of Likert Scale Data

This study involved an investigation of the use of Pearson r, tetrachoric r, Φ, Φ/Φmax, and Kendall Tau-B coefficients as measures of association for the incomplete principal components analysis of simulated Likert scale attitudinal data, based on a known factor pattern and possessing different types of severe departures from normality. The results suggested that in addition to being based on few assumptions, Tau-B was most robust, with respect to distributional distortion, with large or small samples, and this coefficient was followed by the Pearson r. The measures based on 2 x 2 tables–tetrachoric r, Φ, and Φ/Φmax—tended to be less robust and were seen to be adversely affected by uneven marginal splits, a condition generally present with Likert scale data.