Comparison of Different Shrinkage Formulas in Estimating Population Multiple Correlation Coefficients

Abstract

Five different shrinkage formulas were compared to see which most accurately reduced the positive bias in sample R ² values as estimators of the squared population multiple correlation coefficient (ρ²). Artificial populations of known parameters were constructed and "Monte Carlo" sampling was done with a computer. The following parameters were examined: number of independent variables (5 and 15), sample size (400, 200, 100, 50, 25, and 10), and ρ² (.2, .4, .6, and .8). On the basis of the data collected, one formula was eliminated and the conditional use of two others was recommended.