In validating a selection test (x), complete test-criterion (y) scores are typically not available for all cases. Given this incomplete xy data set, one can estimate the population correlation using either the uncorrected correlation (computed using the data only from the selected group) or the so-called corrected correlation. Although the uncorrected value is always more biased than the corrected value, the former can have a substantially smaller expected mean square error when sample sizes are small, selection is extreme, and the population correlation is low.
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