Item Response Theory

Item Response Theory (IRT) assumes that there is a correlation between the score gained by a candidate for one item/test (measurable) and their overall ability on the latent trait which underlies test performance (which we want to discover). Critically, the 'characteristics' of an item are said to be independent of the ability of the candidates who were sampled.
Item Response Theory comes in three forms: IRT1, IRT2, and IRT3 reflecting the number of parameters considered in each case.

- For
**IRT1**, only the**difficulty**of an item is considered,

(*difficulty*is the level of ability required to be more likely to correctly answer the question than answer it wrongly). - For
**IRT2**,**difficulty and discrimination**are considered,

(*discrimination*is how well the question is at separating out candidates of similar abilities). - For
**IRT3**,**difficulty, discrimination and chance**are considered,

(*chance*is the random factor which enhances a candidates probability of success through guessing.

IRT can be used to create a unique plot for each item (the Item Characteristic Curve - ICC). The ICC is a plot of Probability that the Item will be answered correctly against Ability. The shape of the ICC reflects the influence of the three factors:

- Increasing the
*difficulty*of an item causes the curve to shift right - as candidates need to be more able to have the same chance of passing. - Increasing the
*discrimination*of an item causes the gradient of the curve to increase. Candidates below a given ability are less likely to answer correctly, whilst candidates above a given ability are more likely to answer correctly. - Increasing the
*chance*raises the baseline of the curve.

This simple simulation allows the user to investigate the factors governing the shape of the Item Characteristic Curve. All three well known IRT models are represented (referred to as IRT1, IRT2 and IRT3) and Item Characteristic Curves can be super-imposed on one another to see how they relate.

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this page was last updated December 2nd 2004 :CM

(thanks to Mhairi McAlpine of SQA for help with terminology)

© 2003 Jelsim Partnership

(thanks to Mhairi McAlpine of SQA for help with terminology)

© 2003 Jelsim Partnership