Restriction of Range

Restriction of range is the term applied to the case in which observed sample data are not available across the entire range of interest. The most common case is that of a bivariate correlation between two normally distributed variables, one of which has a range less than that commonly observed in the population as a whole. In such cases the observed correlation in the range restricted sample [Page 1279]will be attenuated (lower) than it would be if data from the entire possible range were analyzed.

The context in which restriction of range is discussed most often is that of criterion-related validity evidence of predictors in a selection context such as employee selection or educational institution admissions. For instance, common cases include those in which job applicants take a test of some type, and then only a subset of those applicants is hired. When the selection decision is based on the test scores, the range of the sample will be restricted.

How Range Restriction Affects Correlation Coefficients

Figure 1 illustrates the effect of restriction of range on observed correlations. In Figure 1(a), data for 50 persons appears for both a predictor and a criterion. With this full sample, the correlation is .82. Figure 1(b) illustrates the effect of restriction of range on the predictor. Such a scenario is a common one in validation research that uses predictive validity designs in which there is a large pool of job or college applicants, yet only a subset of applicants with the highest scores on the predictor is selected. In this example, only persons with the top 15 scores on the predictor were selected. Thus criterion data would be available only for these persons. The observed correlation is attenuated from .82 in the full sample to .58 in the range-restricted sample.

Conversely, Figure 1(c) illustrates the effect of restriction of range on the criterion in which only the 15 persons with the highest criterion scores are included. Such a scenario is often encountered in validation research in which a concurrent validation design is employed. In such a design, current employees are given a predictor measure of interest and the correlation between predictor scores and the criterion is assessed. In this case, poorly performing employees likely would have been fired or would have quit their jobs, thus restricting the range of the performance criterion. In this example, the observed correlation is .51.

Figure 1 Effects of Restriction of Range