An empirical study of the validity of the Spearman-Brown formula as applied to the Purdue rating scale.

Abstract

When the same test is given at different times to the same persons, the correlation between the resulting scores gives a measure of the reliability of the test used. It is a well known fact that the reliability of a test is increased as its length is increased, but for some time there was no way of foretelling just how much the reliability would be increased in its length. There was need for a formula that would predict the reliability of a test n times as long as a given test. In 1911 William Brown published a formula which promised to meet this need. It was found to be only a special case of an earlier formula of Spearman's for finding the correlation between the sums or averages of scores. This revised formula is now in current use and is known as the Spearman-Brown prediction formula. If r,t is the coefficient of reliability of a test, then r», the coefficient of reliability of a test n times as long, is given by the formula: