Attenuation of the Squared Canonical Correlation Coefficient Under Varying Estimates of Score Reliability
Description: Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability. Monte Carlo simulation methodology was used to fulfill the purpose of this study. Initially, data populations with various manipulated conditions were generated (N = 100,000). Subsequently, 500 random samples were drawn with replacement from each population, and data was subjected to canonical correlation analyses. The canonical correlation results were then analyzed using descriptive statistics and an ANOVA design to determine under which condition(s) the squared canonical correlation coefficient was most attenuated when compared to population Rc2 values. This information was analyzed and used to determine what effect, if any, the different conditions considered in this study had on Rc2. The results from this Monte Carlo investigation clearly illustrated the importance of score reliability when interpreting study results. As evidenced by the outcomes presented, the more measurement error (lower reliability) present in the variables included in an analysis, the more attenuation experienced by the effect size(s) produced in the analysis, in this case Rc2. These results also demonstrated the role between and within set correlation, variable set size, and sample size played in the attenuation levels of the squared canonical correlation coefficient.
Date: August 2010
Creator: Wilson, Celia M.