Bootstrap Standard Error of the Corrected Correlation Coefficient Under Various Types of Range Restriction

• In Event: Roundtable Session 41
  In Roundtable Session: Simulation Studies

Abstract

We propose a method for correcting the correlation coefficient (rc) and calculating its standard error under direct (DRR) and indirect (IRR) range restriction. The bootstrap standard error (SEb) of rc, the bootstrap percentile interval (BPI), univariate bootstrap percentile interval (UBPI), and the bias-corrected and accelerated (BCa) interval, are examined. The restricted size (n), selection ratio (π), and the population correlations (ρ) are manipulated, and each has 1000 Monte Carlo replications with 2000 bootstrap iterations. Comparing percentage biases (PB) of SEb, r, and rc, coverage probabilities (CP) of the intervals about ρ and the null-hypothesis ρ =0, and interval lengths, we find which intervals are optimal per condition. We further discuss the negative PB of rc and its inherent power issues.

Authors

• Brett Loren Chaney, University of Oklahoma

• Jorge L. Mendoza, University of Oklahoma