Correcting Correlations of Personality Scales for Spurious Effects of Shared Items

Budescu and Rodgers (1981) noted that zero-order correlations of scales which have items in common have spurious components due to the overlapping elements. They proposed a method of adjusting these correlations, to eliminate the spurious component, and applied this method to correct the normative zero-order correlations of the nine original Minnesota Multiphasic Personality Inventory (MMPI) clinical scales. This article draws attention to the fact that Budescu and Rodgers' reliability-corrected formulae were derived under an assumption which is rarely tenable in the context of personality measurement; namely, that scores on two overlapping scales can be viewed (for purposes of the derivation) as sums of standardized scores of subsets of shared items, and of subsets of items uniquely present in each scale. The assumption generally implies new scales that are not linearly related to the original personality scales, and results in reliability-corrected correlations that are not relevant to the original scales. In particular, the assumption cannot be justified with respect to MMPI scales. Reliability-corrected formulae are derived which do not make this assumption. These formulae are equivalent to explicitly defined or implied special cases of Bashaw and Anderson's (1967) "General Linear Case" formula.