Revisiting Case IV: a reassessment of bias and standard errors of Case IV under range restriction

In 2004, Hunter and Schmidt proposed a correction (called Case IV) that seeks to estimate disattenuated correlations when selection is made on an unmeasured variable. Although Case IV is an important theoretical development in the range restriction literature, it makes an untestable assumption, namely that the partial correlation between the unobserved selection variable and the performance measure is zero. We show in this paper why this assumption may be difficult to meet and why previous simulations have failed to detect the full extent of bias. We use meta-analytic literature to investigate the plausible range of bias. We also show how Case IV performs in terms of standard errors. Finally, we give practical recommendations about how the contributions of Hunter and Schmidt (2004) can be extended without making such stringent assumptions.