Maximum validity of a test with equivalent items

Abstract

It is assumed that a scale of true scores on a function exists and that the probability of answering an item correctly is a curve of the type of the integral of the normal curve. The product moment correlation between the test score and true score is derived for a normal distribution of subjects and a test composed of equivalent items. Numerical examples demonstrate that the maximum correlation between test scores and true scores occurs for a one hundred item test when the point correlation between items is less than three tenths.