The Precision Efficacy Analysis for Regression Sample Size Method

The general purpose of this study was to examine the efficiency of the Precision Efficacy Analysis for Regression (PEAR) method for choosing appropriate sample sizes in regression studies used for precision. The PEAR method, which is based on the algebraic manipulation of an accepted cross-validity formula, essentially uses an effect size to determine the subject-to-variable ratio appropriate for the squared multiple correlation expected in a given study. An effort was made to determine how appropriate the sample sizes calculated by the PEAR method are for use with stepwise regression. A Monte Carlo analysis of precision efficacy rates was performed, manipulating effect sizes, predictors, and multicollinearity conditions, and using Turbo Pascal procedures to generate sample data. The PEAR method recommended sample sizes that provided reliable regression coefficients. Higher precision efficacy levels provided more stable coefficients. The use of the PEAR method in stepwise regression analyses proved less conclusive. For orthogonal predictors, the PEAR method did not fail, but as multicolinearity increased, the results were less impressive. Results suggest that for less multicolinear data, precision efficacy levels do not drop dramatically for stepwise analysis. Four appendixes contain figures illustrating the discussion. (Contains 11 tables and 56 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document. Running Head: PEAR Method PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY 1 TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) PEAR Method 1 U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDU ATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. The Precision Efficacy Analysis for Regression