Robustness of Lord’s Formulas for Item Difficulty and Discrimination Conversions Between Classical and Item Response Theory Models

  • Teresa Dawber University of Alberta
  • W. Todd Rogers University of Alberta
  • Michael Carbonaro University of Alberta

Abstract

Lord (1980) proposed formulas that provide direct relationships between IRT discrimination and difficulty parameters and conventional item statistics. The purpose of the present study was to determine the robustness of the formulas beyond the initial and restrictive conditions identified by Lord. Simulation and real achievement data were employed. Results from the simulation study indicate that the item discrimination parameters were recovered quite well for low to moderately discriminating items regardless of ability distribution, and the difficulty parameters were recovered quite well for the range typically found for achievement tests. Results of the real data were consistent with those found for the simulation study.

Author Biographies

Teresa Dawber, University of Alberta
Teresa Dawber works as a psychometrician in the United States. Her primary responsibilities include operational work on state contracts for several K12 testing programs.
W. Todd Rogers, University of Alberta
Todd Rogers is a professor and faculty member in the Centre for Research in Applied Measurement and Evaluation. His research interests are in psychometrics, large-scale assessments, and ethics in testing.
Michael Carbonaro, University of Alberta
Michael Carbonaro is a professor and faculty member in Educational Technology. His research interests are in learning and cognition, cognitive science, connectionist computer modeling, and technology use in teaching and learning.