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Item Response Theory: The Backbone of Modern Psychometrics

Item response theory (IRT) is the modern psychometric paradigm. It facilitates stronger equating, fairer scores, better item analysis, and enables the algorithms for computerized adaptive testing. Our experts can help you easily implement IRT – or, download our user-friendly software and implement it yourself!

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What is Item Response Theory?

Item response theory (IRT) is more than just another way to analyze test questions. It is a complete psychometric paradigm that changes how you look at the interaction of examinees with tests or items. You fit machine learning models based on logistic regression, then use those to do a whole bunch of useful things in assessment.

Why use IRT?


How does item response theory work?

Item response theory starts with the analysis of test data to fit item response functions for each item (or each response, in the case of polytomous models).  These follow a logistic curve, like you see in the examples here.  The x-axis is examinee ability or knowledge and the y-axis is the probability of correct response; we expect the top examinees to have near 100% probability but the lower students to have a much lower probability (e.g., 25% if there is guessing on a 4-option multiple choice item).

Items can differ in the shape of this curve, which defines their difficulty, discrimination, and guessing parameters.  This allows psychometricians and test developers to truly understand how the item operates – and if it is not operating well, how we can improve it.

Moreover, these IRFs are then used in solving deeper questions in assessment.  How do we design multiple test forms that are truly equivalent?  How can we link this year’s scores to last year’s to track growth?  How can we personalize the assessment for each student?

How can Assessment Systems help you improve online exams?

User-Friendly Analytics Software

Our industry-leading software, Xcalibre, not only makes it easy to implement IRT – it automatically creates a draft Tech Report in Word for you!

Expert Consulting

Our expert psychometricians can help you apply IRT to improve your assessments.

Item Banking and Online Assessment

Leverage our cloud-based platforms to drive the entire test development cycle, including delivery with adaptive testing and multistage testing.

Xcalibre: Item Response Theory made simple

You don’t need to know how to code if you want to implement IRT.  If you’re interested in applying it yourself rather than hiring us, feel free to download our industry-leading platform Xcalibre.

Why Xcalibre?


Trusted Psychometric Experts

Our team of PhD psychometricians can help your organization implement item response theory.

Digital Assessment Platforms with IRT and CAT off-the-shelf

Item response theory is about much more than just occasionally running a statistical analysis.  It serves as the paradigm for most assessment procedures, including test publishing and scoring.  Our cloud-based platforms can help you easily implement item response theory for delivery – regardless of what analysis software you utilize.

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