Estimation of Cronbach's alpha coefficient in the context of item response theory

Abstract

Cronbach's alpha coefficient is an index of reliability for the total score of a set of measurements. The alpha takes a value of 1.0 when the total score variance is perfectly attributable to the common factors running through the test items. In this research, a method of estimating Cronbach's coefficient alpha is proposed for the case where the parameters of dichotomous item response model arc known and the ability distribution of subjects is given. In addition, the case of polytomous response model where the item parameters are estimated by graded response model (Samejima, 1969) is also considered, and a method of estimating the alpha coefficient is proposed for that case.