Reliability Formulas that do not Assume Experimental Independence

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Abstract
Tautologies are established for the reliability coefficient ρ2t of the sum of n part scores. It is not assumed that the part scores are experimentally independent of each other nor that the parts are equivalent to each other. The tautologies show the exact role played by experimental dependence and nonequivalence of parts, respectively, in the reliability of the sum. The formal algebra is appropriate to reliability in the sense of repeated trials of the same test, as well as in the sense of a universe of parallel tests, although the empirical meanings are different. Emphasis is on practical formulas that require information from only a single experiment (or test). These can take the form only of lower bounds to ρ2t, four of which are developed.

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