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Spearman–Brown Prophecy Formula

Charles Spearman and William Brown separately derived a formula to predict the reliability of a test when its length was altered by the addition or subtraction of parallel items. Each presented their formula in 1910 in Volume Three of The British Journal of Psychology. Because their articles were published at the same time, the formula is known as the Spearman–Brown prophecy formula.

The basic premise of classical test theory is that an observed test score consists of the sum of the following two components: true score and error score. For any individual examinee, the two cannot be separated, but for a group of examinees, the variance attributed to each source can be estimated. Test reliability, which is an important characteristic of test score quality, is ...

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