Abstract
In discussions of range-restricted correlation coefficients, two situations are most often addressed. The first is the case where restriction has occurred directly on one of the two variables of interest. The other is termed indirect range restriction to designate the situation where direct restriction has occurred on some third variable. The Thorndike (1947) Case 3 formula provides a means of correcting correlations that have arisen in this latter case when information on the third variable is available. Bryant and Gokhale (1972) gave a formula for correcting such indirectly restricted correlations when no information is available on the third (directly restricted) variable. This note shows that the Bryant and Gokhale (1972) formula is accurate only in one special instance of indirect range restriction. The more general correction formula is given and demonstrated. Throughout the discussion, r' and S' will refer to the range-restricted correlation and standard deviation, and r and S to their unrestricted counterparts. Consider the trivariate normal X-Y-Z distribution where the correlation of
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