Spearman–Brown prediction formula

The Spearman - Brown formula is used to calculate the reliability of a psychological test, after having changed its length (length = number of items). For this, the reliability ( Rel) of the original test is required. The Spearman - Brown formula is as follows:

Where k is the factor by which the extended test ( or shortened ) was; Rel is the reliability. Rel (k · l) is the new reliability, after changing the test length. The formula can be used, for example, to calculate how much more would be a test in order to increase its reliability to a certain value.

Application

In the extension of a test to the original length it is also mathematically related to an increase in the reliability of the test. This increase in reliability can be detected by the Spearman -Brown formula.

Let X be a test that is divided into two equally long, parallel halves Y and Z. The reliability test of the two halves Rel usually calculated by their correlation R ( Y, Z) and R ( Z, Y). The reliability of the total test X is now given by the following expression:

If the reliability of the total test were calculated in this way, it is called split- half reliability.

Spearman Brown formula is used for calculating the SPSS reliability. The corresponding coefficient can be found at Cronbach's alpha.