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Spearman–Brown prediction formula
The Spearman–Brown prediction formula, also known as the Spearman–Brown prophecy formula, is a formula relating psychometric reliability to test length and used by psychometricians to predict the reliability of a test after changing the test length. The method was published independently by Spearman (1910) and Brown (1910).〔Stanley, J. (1971). Reliability. In R. L. Thorndike (Ed.), ''Educational Measurement''. Second edition. Washington, DC: American Council on Education〕〔Wainer, H., & Thissen, D. (2001). True score theory: The traditional method. In H. Wainer and D. Thissen, (Eds.), ''Test Scoring''. Mahwah, NJ:Lawrence Erlbaum〕
==Calculation==
Predicted reliability, , is estimated as:
:
where ''n'' is the number of "tests" combined (see below) and is the reliability of the current "test". The formula predicts the reliability of a new test composed by replicating the current test ''n'' times (or, equivalently, creating a test with ''n'' parallel forms of the current exam). Thus ''n'' = 2 implies doubling the exam length by adding items with the same properties as those in the current exam. Values of ''n'' less than one may be used to predict the effect of shortening a test.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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