Estimating the Reliability of a Test from a Single Test Administration

In the first part a review of existing indices is given, supplemented with two heuristics to approximate Guttman's ) ..4 and a new similar coefficient. Special attention is given to the greatest lower bound, to its meaning as well as to the problems in computing it. In the second part the relation between Cronbach's a and the reliability is studied by means of a factorial model for the item scores. This part gives some useful formulae to appreciate the amount with which the reliability is underestimated when a is used as its estimand. In the last part, the sampling distribution of the indices is investigated by means of two simulation studies, showing that the indices exhibit severe bias, the direction of which depends partly on the factorial structure of tht test. For three indices the bias is modeled. The model describes the bias accurately for all cases studied in the simulation studies. It is shown how this bias correction may be applied in the case of a single data set.