FISHER TRANSFORMATIONS FOR CORRELATIONS CORRECTED FOR SELECTION AND MISSING DATA

The validity of a test is often estimated in a nonrandom sample of sel ected individuals. To accurately estimate the relation between the pre dictor and the criterion we correct this correlation for range restric tion. Unfortunately, this corrected correlation cannot be transformed using Fisher's Z transformation, and asymptotic tests of hypotheses ba sed on small or moderate samples are not accurate. We developed a Fish er r to Z transformation for the corrected correlation for each of two conditions: (a) the criterion data were missing due to selection on t he predictor (the missing data were MAR); and (b) the criterion was mi ssing at random, not due to selection (the missing data were MCAR). Th e two Z transformations were evaluated in a computer simulation. The t ransformations were accurate, and tests of hypotheses and confidence i ntervals based on the transformations were superior to those that were not based on the transformations.