“Evaluating the Effect of Inadequately Measured Variables in Partial Correlation Analysis”, 1936 (; backlinks; similar):
It is not generally recognized that such an analysis [using regression] assumes that each of the variables is perfectly measured, such that a second measure X’i, of the variable measured by Xi, has a correlation of unity with Xi. If some of the measures are more accurate than others, the analysis is impaired [by measurement error]. For example, the sociologist may have a problem in which an index of economic status and an index of nativity are independent variables. What is the effect, if the index of economic status is much less satisfactory than the index of nativity? Ordinarily, the effect will be to underestimate the [coefficient] of the less adequately measured variable and to overestimate the [coefficient] of the more adequately measured variable.
If either the reliability or validity of an index is in question, at least two measures of the variable are required to permit an evaluation. The purpose of this paper is to provide a logical basis and a simple arithmetical procedure (a) for measuring the effect of the use of 2 indexes, each of one or more variables, in partial and multiple correlation analysis and (b) for estimating the likely effect if 2 indexes, not available, could be secured.