Lower Bounds for the Reliability of the Total Score on a Test Composed of Non-Homogeneous Items: II: A Search Procedure to Locate the Greatest Lower Bound
- 1 December 1977
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 42 (4) , 579-591
- https://doi.org/10.1007/bf02295980
Abstract
Finding the greatest lower bound for the reliability of the total score on a test comprising n non-homogenous items with dispersion matrix Σx is equivalent to maximizing the trace of a diagonal matrix ΣE with elements θI, subject to ΣE and ΣT=Σx − ΣE being non-negative definite. The cases n=2 and n=3 are solved explicity. A computer search in the space of the θi is developed for the general case. When Guttman's λ4 (maximum split-half coefficient alpha) is not the g.l.b., the maximizing set of θi makes the rank of ΣT less than n − 1. Numerical examples of various bounds are given.Keywords
This publication has 2 references indexed in Scilit:
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- A Basis for Analyzing Test-Retest ReliabilityPsychometrika, 1945