COMPARISON OF DIFFERENT SHRINKAGE FORMULAS IN ESTIMATING POPULATION MULTIPLE CORRELATION-COEFFICIENTS

Five different shrinkage formulas were compared to see which most accurately reduced the positive bias in sample R2 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. © 1979, Sage Publications. All rights reserved.