Approximate Functional Relationship between IRT and CTT Item Discrimination Indices: A Simulation, Validation, and...

Area of Science:

• Psychometrics
• Educational Measurement
• Psychological Statistics

Background:

• Classical Test Theory (CTT) and Item Response Theory (IRT) are fundamental measurement paradigms.
• Lord (1980) proposed a conceptual equation linking CTT and IRT discrimination indices.
• Existing methods lack practical utility and empirical validation for this linkage.

Purpose of the Study:

• To modify Lord's (1980) conceptual equation for practical application.
• To develop an empirical function relating CTT and IRT discrimination indices.
• To incorporate item difficulty and corrected item-total correlation into the linkage.

Main Methods:

• Simulation of over 768 trillion item responses to determine a best-fitting empirical function.
• Modification of Lord's (1980) equation to include item difficulty.
• Validation using real-world data from 16 diverse workforce and educational tests.

Main Results:

• The modified equation demonstrates shifted functional asymptotes, slopes, and points of inflection.
• The empirical function provides good prediction accuracy under standard psychometric assumptions (e.g., normal ability distribution, moderate difficulty).
• The proposed modification offers greater precision compared to Lord's (1980) original formula.

Conclusions:

• The refined equation provides a practical and empirically validated method for relating CTT and IRT discrimination indices.
• This advancement enhances the practical utility of psychometric linkage for test developers and researchers.
• The findings support the use of the modified function in educational and workforce assessment contexts.