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The SAGE Encyclopedia of Social Science Research Methods

Michael S. Lewis-Beck & Alan Bryman & Tim Futing Liao

Pub. date: 2004 | DOI:

Print ISBN: 9780761923633 | Online ISBN: 9781412950589

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Encyclopedia Entry

Spearman-Brown Formula

Karen J. Long

Developed independently by Charles Spearman (1910) and William Brown (1910), this formula estimates the reliability of multi-item measures or indexes, and provides an important foundation for the statistical theory of measurement. The Spearman-Brown formula also calculates expected increases in reliability if more indicators of the same trait are available. In both capacities, the Spearman-Brown formula is used frequently in the social sciences, especially in sociology, psychology, and education, where multi-item indexes are commonly employed. To illustrate, following Brown (1910), let x 1 and x 2 be two measurements of a particular characteristic x , together comprising a “test” in which x 1 and x 2 are given equal weight. x ′ 1 and x ′ 2 are two other measurements of the same trait and, in combination, provide a parallel test of characteristic x . Suppose that all of the measurements are equally reliable, or that ...

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