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Developing a Common Metric in Item Response Theory IRT SAT

Stocking, Martha L.; Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Data Analysis, Equated Scores, Item Analysis, Item Response Theory (IRT), Scaling, SAT, Test Theory


A common problem arises in scale transformation when independent estimates of item parameters from two separate data sets must be expressed in the same metric. These item parameter estimates will be different because the metric or scale defined by each independent calibration of the items is different. The problem is frequently confronted in studies of horizontal and vertical equating and in studies of item bias. The nature of scale transformation from one metric to another is discussed, and the use of mean and sigma method is reviewed. A new method is presented which uses more information from item calibrations to yield an estimated item response function or item characteristic curve. Using data from 12 separate administrations of the Scholastic Aptitude Test, the mean and sigma transformation and characteristic curve method are shown to work well in the verbal data and most of the mathematical data. When the mean and sigma method was unsatisfactory, the information content of the characteristic curve method worked better. In particular, the characteristic curve method produced a much better transformation for the item discriminations. (CM). (39pp.)

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