An Inexpensive Retrospective Standard Setting Method Based on Item Facilities

Abstract

Background
Standard setting is one of the most challenging aspects of assessment in high-stakes healthcare settings. The Angoff methodology is widely used, but poses a number of challenges, including conceptualisation of the just-passing candidate, and the time-cost of implementing the method. Cohen methodologies are inexpensive and rapid but rely on the performance of an individual candidate. A new method of standard setting, based on the entire cohort and every item, would be valuable.

Methods
We identified Borderline candidates by reviewing their performance across all assessments in an academic year. We plotted the item scores of the Borderline candidates in comparison with Facility for the whole cohort and fitted curves to the resulting distribution.

Results
It is observed that for any given Item, an equation of the form
y ≈ C.eFx
where y is the Facility of Borderline candidates on that Item, x is the observed Item Facility of the whole cohort, and C and F are constants,
predicts the probable Facility for Borderline candidates over the test, in other words, the cut score for Borderline candidates. We describe ways of estimating C and F in any given circumstance, and suggest typical values arising from this particular study: that C = 12.3 and F = 0.021.

Conclusions
C and F are relatively stable, and that the equation
y = 12.3.e0.021x
can rapidly be applied to the item Facility for every item. The average value represents the cut score for the assessment as a whole. This represents a novel retrospective method based on test takers.
Compared to the Cohen method which draws on one score and one candidate, this method draws on all items and candidates in a test. We propose that it can be used to standard set a whole test, or a particular item where the predicted Angoff score is very different from the observed Facility.