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 |
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Authors: | Brian Woodhouse Paul H Jackson |
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Institution: | (1) Department of Statistics, University College of Wales, Aberystwyth, Dyfed, Wales |
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Abstract: | Finding the greatest lower bound for the reliability of the total score on a test comprisingn non-homogenous items with dispersion matrix Σ
x
is equivalent to maximizing the trace of a diagonal matrix Σ
E
with elements θ
I
, subject to Σ
E
and Σ
T
=Σ
x
− Σ
E
being non-negative definite. The casesn=2 andn=3 are solved explicity. A computer search in the space of the θ
i
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 θ
i
makes the rank of Σ
T
less thann − 1. Numerical examples of various bounds are given.
Present affiliation of the first author: St. Hild's College of Education, Durham City, England. |
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Keywords: | reliability bounds non-homogeneous composites search procedure trace minimization with constraints |
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