What is item response theory?

Item response theory (IRT) represents an important innovation in the field of psychometrics. While now 50 years old – assuming the “birth” is the classic Lord and Novick (1969) text – it is still underutilized and remains a mystery to many practitioners. So what is item response theory, and why was it invented?

Classical test theory (CTT) is approximately 100 years old, and still remains commonly used because it is appropriate for certain situations, and it is simple enough that it can be used by many people without formal training in psychometrics. Most statistics are limited to means, proportions, and correlations. However, its simplicity means that it lacks the sophistication to deal with a number of very important measurement problems. Here are just a few.

• Sample dependency: Classical statistics are all sample dependent, and unusable on a different sample; results from IRT are sample-independent within a linear transformation (that is, two samples of different ability levels can be easily converted onto the same scale)
• Test dependency: Classical statistics are tied to a specific test form, and do not deal well with sparse matrices introduced by multiple forms, linear on the fly testing, or adaptive testing
• Weak linking/equating: CTT has a number of methods for linking multiple forms, but they are weak compared to IRT
• Measuring the range of students: Classical tests are built for the average student, and do not measure high or low students very well; conversely, statistics for very difficult or easy items are suspect
• Lack of accounting for guessing: CTT does not account for guessing on multiple choice exams
• Scoring: Scoring in classical test theory does not take into account item difficulty.
• Adaptive testing: CTT does not support adaptive testing in most cases.

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