The calculation of reliability from a split-plot factorial design

This paper treats the question, "How should one estimate the reliability of school (or classroom) means when persons are nested within schools (or classrooms)? " We begin by reviewing the use of variance components in the estimation of reliability from a ran-domized block (RB) design. Then we extend this rationale to the es-timation of reliability (or generalizability) coefficients in a split-plot factorial (SPF) design with persons nested within schools. Through the use of variance components from the SPF design, we derive estimates of reliability for schools and for persons within schools. Then we compare the reliability for persons within schools from a SPF design with the reliability for persons from a RB design. Finally, we compare the reliability for schools from a SPF design with the reliability for school means from a RB design