Reliability and true-score measures of binary items as a function of their Rasch difficulty parameter

This article provides formulas for expected true-score measures and reliability of binary items as a function of their Rasch difficulty when the trait (ability) distribution is normal or logistic. The proposed formulas have theoretical value and can be useful in test development, score analysis, and simulation studies. Once the items are calibrated with the dichotomous Rasch model, one can estimate (without further data collection) the expected values for true-score measures (e.g., domain score, true score variance, and error variance for the number-right score) and reliability for both norm-referenced and criterion-referenced interpretations. Thus, given a bank of Rasch calibrated items, one can develop a test with desirable values of population true-score measures and reliability or compare such measures for subsets of items that are grouped by substantive characteristics (e.g., content areas or strands of learning outcomes). An illustrative example for using the proposed formulas is also provided.