Fig 1.
Missing data patterns under range restriction.
(a) Direct range restriction scenario (selection on X), and (b) indirect range restriction scenario (selection on Z). The shaded areas in Y represent the location of the missing values in the dataset.
Table 1.
Design of the intercorrelation matrix of the correlation coefficients for direct range restriction (DRR) and indirect range restriction (IRR).
Table 2.
Results of the preliminary study: Root mean square errors of the correlation estimates using m = 5, 20, and 50 imputations for 70%, 50%, and 30% missing values (DRR scenario, N = 500, 1000 iterations).
Fig 2.
Direct range restriction (DRR): Root mean square error (RMSE) of the estimates of the predictive validity ( and
).
is the estimate of the biserial correlation coefficient for an artificially dichotomous criterion variable, and
is the estimate of the point-biserial correlation coefficient for a naturally dichotomous criterion variable.
Fig 3.
Indirect range restriction (IRR): Root mean square error (RMSE) of the estimates of the predictive validity ( and
).
is the estimate of the biserial correlation coefficient for an artificially dichotomous criterion variable, and
is the estimate of the point-biserial correlation coefficient for a naturally dichotomous criterion variable.
Fig 4.
Direct range restriction (DRR): Effects of a weak, moderate, and strong predictive validity on the root mean square error (RMSE) of the estimates of the predictive validity ( and
).
is the estimate of the biserial correlation coefficient for an artificially dichotomous criterion variable, and
is the estimate of the point-biserial correlation coefficient for a naturally dichotomous criterion variable.
Fig 5.
Indirect range restriction (IRR): Effects of a weak, moderate, and strong predictive validity on the root mean square error (RMSE) of the estimates of the predictive validity ( and
).
is the estimate of the biserial correlation coefficient for an artificially dichotomous criterion variable, and
is the estimate of the point-biserial correlation coefficient for a naturally dichotomous criterion variable.
Fig 6.
Indirect range restriction (IRR): Effects of a weak, moderate, and strong relationship between predictor X and selection variable Z on the root mean square error (RMSE) of the estimates of the predictive validity ( and
).
is the estimate of the biserial correlation coefficient for an artificially dichotomous criterion variable, and
is the estimate of the point-biserial correlation coefficient for a naturally dichotomous criterion variable.
Table 3.
Mean errors (ME) of the correlation estimates.
Table 4.
F-ratio of the correlation estimates when correcting with multiple imputation by chained equations and Thorndike’s formulas.
Table 5.
Accuracy of the estimate of the base rate of success when correcting via multiple imputation by chained equations (MICE).