The correction for attenuation due to measurement error: clarifying concepts and creating confidence sets

The correction for attenuation due to measurement error (CAME) has received many historical criticisms, most of which can be traced to the limited ability to use CAME inferentially. Past attempts to determine confidence intervals for CAME are summarized and their limitations discussed. The author suggests that inference requires confidence sets that demarcate those population parameters likely to have produced an obtained value--rather than indicating the samples likely to be produced by a given population--and that most researchers tend to confuse these 2 types of confidence sets. Three different Monte-Carlo methods are presented, each offering a different way of examining confidence sets under the new conceptualization. Exploring the implications of these approaches for CAME suggests potential consequences for other statistics.