True scores, latent variables, and constructs

This paper comments on an article by Schmidt and Hunter [Intelligence 27 (1999) 183.], who argue that the correction for attenuation should be routinely used in theory testing. It is maintained that Schmidt and Hunter's arguments are based on mistaken assumptions. We discuss our critique of Schmidt and Hunter in terms of two arguments against a routine use of the correction for attenuation within the classical test theory framework: (1) corrected correlations do not, as Schmidt and Hunter claim, provide correlations between constructs, and (2) corrections for measurement error should be made using modern test theory models instead of the classical model. The arguments that Schmidt and Hunter advance in favor of the correction for attenuation can be traced to an implicit identification of true scores with construct scores. First, we show that this identification confounds issues of validity and issues of reliability. Second, it is pointed out that equating true scores with construct scores is logically inconsistent with the classical test theory model itself. Third, it is argued that the classical model is not suited for detecting the dimensionality of test scores, which severely limits the interpretation of the corrected correlation coefficients. It is concluded that most measurement problems in psychology concern issues of validity, and that the correction for attenuation within classical test theory does not help in solving them.