Reliability formulas for independent decision data when reliability data are matched

A distinction is made between reliability data and decision data. Each of these sets of data may be matched or independent, depending on whether the same instruments (tests, judges, etc.) are applied to every individual in the group or the instruments to be applied to each individual are selected independently for him. Reliability formulas are developed (for both single observations and for composites ofk observations) for the case where reliability data are matched but decision data are independent. Formulas previously reported in the literature are inappropriate for this case.This paper was prepared under USPHS Grant M-1839, in which the author is associated with Lee J. Cronbach and Goldine C. Gleser, and is an outgrowth of a more comprehensive conceptualization of reliability being developed in that study. The author is indebted to Dr. Frederic M. Lord for numerous suggestions.An unpublished paper prepared in 1958 entitled A generalization of Kuder-Richardson reliability formula 21.