Reliability of Composite Measurements Based on the m Highest of n Equivalent Components

Abstract

Under the assumptions of classical measurement theory and the condition of normality, a formula is derived for the reliability of composite scores based onm highest ofn equivalent components. The formula represents an extension of the Spearman-Brown formula to the case of truncated data. The results of a simulation study indicate that errors encountered in the use of the said formula for projection purposes are confined largely to the second decimal.