Reliability of True Cutting Scores for Rasch Calibrated Items

This paper provides formulas for expected true-score measures and reliability of binary items as a function of their Rasch difficulty parameters when the trait distribution is normal or logistic. With the proposed formula, one can evaluate the theoretical values of classical reliability indexes for norm-referenced and criterion-referenced interpretations without information about raw-score or trait scores of persons from the target population. This is achieved by representing the theoretical (marginalized) values of the true-score components of reliability indexes as functions of the item difficulty parameter. As the analytic forms of such functions are developed for individual items (and then "summarized" at test level), one can know the population values of true-score measures and reliability for a set of Rasch calibrated binary items prior to their administration. An example for the application of the proposed formulas and their empirical validation is also provided. (Contains 2 tables, 2 figures, and 31 references.) (Author) Reproductions supplied by EDRS are the best that can be made from the original document