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). 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). Predicted reliability, ρ x x ′ ∗ {displaystyle { ho }_{xx'}^{*}} , is estimated as: where n is the number of 'tests' combined (see below) and ρ x x ′ {displaystyle { ho }_{xx'}} 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.