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“Reliability theory” is reinterpreted as a theory regarding the adequac with which one can generalize from one observation to a universe of observations. If the observation is randomly sampled from the universe—whether or not the universe consists of equivalent observations—the intraclass correlation provides an approximate lower bound to the expected value of the desired coefficient of generalizability.
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British Journal of Statistical Psychology
University of Illinois Urbana-Champaign
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Cronbach et al. (Fri,) studied this question.