Schmidt & Hunter Approach to r Artifact Corrections

Statistical Artifacts Extraneous factors that influence observed effect –Sampling error* –Reliability* –Range restriction* –Computational error –Dichotomization of variables *Addressed in the analysis

Psychometric Meta-Analysis Disattenuation for reliability Correction for both Correction for IV Correction for DV Suppose r xy =.30, r xx = r yy =.80. Then:

Range Restriction/Enhancement These are examples of direct RR.

Direct Range Restriction/enhancement Suppose r xy =.33, SD 1 =12, SD 2 = 20. Then: Can also invert by u X = 1/U X

Indirect RR Reliability of IV in restricted sample (job incumbents in I/O validation study). Reliability of IV in unrestricted sample (job applicants in I/O validation study). Ratio of SD of true scores; analogous to u X. You will need u T AND r xxi for INDIRECT range restriction correction. You will need r xxa for DIRECT range restriction correction.

Meta-Analysis of corrected r If information is available can correct r for each study Compute M-A on the corrected values Can also be done with assumed distributions, but I don’t recommend it.

Steps (1) Record data (N, r, artifact values r xx, etc.) Compute the corrected correlation for each study: Note r o is observed and r C is corrected. If there is only 1 kind of artifact, disattenuation is simple: Where a is the disattenuation factor. If there is range restriction, things are tricky. If INDIRECT range restriction, then use Ut instead of Ux and disattenuate for reliability before adjusting for range restriction. Use reliabilities from the restricted group. If DIRECT range restriction, adjust for r yy, then range restriction, then r xx, but r xxa, the reliability in the unrestricted group.

Steps (1b) Compute sampling variance of uncorrected r: Note this is sampling variance for one study. For each study, compute compound attenuation factor:

Steps (2) Compute sampling variance of disattenuated r: If there is range restriction, then do the following 2 steps. Compute adjustment for range restriction: Adjust sampling variance of disattenuated r: Compute weights: Note A is the compound attenuation factor.

Steps (3) Compute the weighted mean: Compute the weighted variance: Compute average corrected r sampling error: Compute variance of rho:

Psychometric M-A data StudyNiNi rr xxi r yy UxUx Mean We’ve already done the bare-bones analysis of these data. Now we’ll analyze 3 ways: (1) just criterion reliability, (2) all artifacts with INDIRECT RR, (3) all artifacts DIRECT rr.

Correct r yy only (1) Study 1 r =.20, r xx =.90, r yy =.80, Ux = 1.5 Disattenuation r yy : r C =.2/sqrt(.8) = Compound attenuation factor A =.20/ =.894. Suppose we only wish to correct for criterion unreliability.

Correct r yy only (2) Study rArCrC NV1V1 V2V

Correct r yy only (3) StudyrCrC ANiNi wiwi wirCwirC Sum

Correct r yy only (4) StudyrCrC wiwi W i [r C -rbar C ] 2 V2V2 wV Sum

Correct r yy only (5) Bare- Bones r yy corrected M V(r) SDrho CRlow CRup.40.41

All corrections, Indirect RR StudyNiNi rr xxi r yy UxUx Mean Already know bare-bones mean.

Indirect RR (2) Study roro r xxi r yy UxUx uxux r xxa UTUT

Indirect RR (3) Study roro r xxi r yy UTUT r c1 rcrc A

Indirect RR (4) Study NiNi rcrc Awiwi wr c Sum

Indirect RR (5) StudyNiNi rcrc Awiwi V1V1 V2V2 a rr V3V3 wV Sum

Indirect RR (6) Bare- Bones r yy corrected Full indirect correction M V(r) SDrho CRlow CRup

Direct Range Restriction (1) Study roro r xxi r yy UxUx r xxa r c1 r c2 rcrc

Direct RR (2) Study roro rcrc A NiNi wwr c Sum

Direct RR (3) Study rcrc w Sum

Direct RR (4) StudyNiNi rcrc Awiwi V1V1 V2V2 a rr V3V3 wV Sum

Direct RR (5) Bare- Bones r yy corrected Full indirect correction Full direct correction M V(r) SDrho CRlow CRup