This study provides a methodological critique of major quality assessments in U.S. higher education over the last 70 years, through an examination of their taxonomy, unit of analysis, frame of reference, and definition of quality. Many quantitative indicators currently used in assessments have a weak theoretical link to quality and have serious methodological drawbacks. The study offers recommendations for continued improvements to assessments indicators, so that institutions may better assert their own voices in debates over higher education quality.