The restrictive assumption of classical parallelism for the Spearman-Brown formulas makes them obsolete when the two-part alpha and coefficient alpha formulas can be used. The alpha coefficients require the less restrictive assumption of essential tau-equivalence. Even small reliability differences produced by the Spearman-Brown and alpha coefficient formulas on the same data can result in large applied differences.
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Richard A. Charter (2001) studied this question.
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