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Biased Sampling and Statistical Prediction

Horst, Paul
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Prediction, Regression (Statistics), Sampling, Statistical Bias


In many cases, the optimal weights (least square) determined for the prediction variables in one sample are to be applied to other samples in which the variances of the variables differ systematically from those in the original sample. Therefore, regression weights from samples that are not representative of the population from which persons are to be selected may be justified. Two types of selection would not be expected to affect the regression coefficients. The first is where direct selection takes place on one or more of the prediction variables. There is also the case where selection takes place on a group of variables that are not used for prediction; but correlated with the criterion and predictor variables. The second type of selection problem has been discussed by Pearson for the two variable case. This report is concerned with the effect of selection on the intercorrelations among the selected variables themselves. Incidental effects of selection on variances and covariances are discussed, as are direct effects of selection on covariances. Then a look is taken at how the deviation score regression weights behave when restriction is placed on some of the variables. Under specified conditions of selection, the deviant score regression weights are invariant except for a proportionality constant. (SGK).

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