The paradoxical attenuation effect in tests based on classical test theory: mathematical background and practical implications for the measurement of high abilities

The aim of this paper is to demonstrate the dramatic consequences the application of cut‐off points can have in the practice of identifying gifted individuals. The paradoxical attenuation effect describes the frequent situation in which measurements of the gifts and talents individuals possess are lower than their true values. However, in assessing the results of a measurement, one should suspect that the talent being measured is in actuality even lower than the score representing it. The practical implications of the paradoxical attenuastion effect are taken under discussion, including how high α errors and β errors are for specific IQ cut‐off points. For example, among persons with IQs of 130 and above, and using reliabilities of .80, most of the persons measured to be gifted are actually not gifted at all.