# How can you implement an Angoff cutscore on a test scored with item response theory?

The modified-Angoff method is arguably the most common method of setting a cutscore on a test.  The Angoff cutscore is legally defensible and meets international standards such as AERA/APA/NCME, ISO 17024, and NCCA.  It also has the benefit that it does not require the test to be administered to a sample of candidates first; methods like Contrasting Groups, Borderline Group, and Bookmark do so.

There are, of course, some drawbacks to the Angoff cutscore process.  The most significant is the fact that the subject matter experts (SMEs) tend to overestimate their conceptualization of a minimally competent candidate, and therefore overestimate the cutscore.  Sometimes to the point that the expected pass rate is zero!

Another drawback is that the Angoff cutscore process only works in the classical psychometric paradigm – the recommended cutscores are on the number-correct metric or percentage-correct metric.  If your tests are developed and scored in the item response theory (IRT) paradigm, you need to convert the classical cutscore to the IRT theta scale.  The easiest way to do that is to reverse-calculate the test response function (TRF) from IRT.

## The Test Response Function

The TRF (sometimes called a test characteristic curve) is an important method of characterizing test performance in the IRT paradigm.  The TRF predicts a classical score from an IRT score, as you see below.  Like the item response function and test information function (item response and test information function ), it uses the theta scale as the X-axis.  The Y-axis can be either the number-correct metric or proportion-correct metric.

In this example, you can see that a theta of -0.4 translates to an estimated number-correct score of approximately 7.  Note that the number-correct metric only makes sense for linear or LOFT exams, where every examinee receives the same number of items.  In the case of CAT exams, only the proportion correct metric makes sense.

## Angoff cutscore to IRT

So how does this help us with the conversion of a cutscore?  Well, we hereby have a way of translating any number-correct score or proportion-correct score.  So any Angoff-recommended cutscore can be reverse-calculated to a theta value.  If your Angoff study (or Beuk) recommends a cutscore of 7 out of 10 points, you can convert that to a theta cutscore of -0.4 as above.  If the recommended cutscore was 8, the theta cutscore would be approximately 0.7.

Because IRT works in a way that it scores examinees on the same scale with any set of items, as long as those items have been part of a linking/equating study.  Therefore, a single Angoff study on a set of items can be equated to any other linear test form, LOFT pool, or CAT pool.  This makes it possible to apply the classically-focused Angoff method to IRT-focused programs.

Nathan Thompson, PhD, is CEO and Co-Founder of Assessment Systems Corporation (ASC). He is a psychometrician, software developer, author, and researcher, and evangelist for AI and automation. His mission is to elevate the profession of psychometrics by using software to automate psychometric work like item review, job analysis, and Angoff studies, so we can focus on more innovative work. His core goal is to improve assessment throughout the world.

Nate was originally trained as a psychometrician, with an honors degree at Luther College with a triple major of Math/Psych/Latin, and then a PhD in Psychometrics at the University of Minnesota. He then worked multiple roles in the testing industry, including item writer, test development manager, essay test marker, consulting psychometrician, software developer, project manager, and business leader. He is also cofounder and Membership Director at the International Association for Computerized Adaptive Testing (iacat.org). He’s published 100+ papers and presentations, but his favorite remains https://scholarworks.umass.edu/pare/vol16/iss1/1/.

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