Developing the polytomous BW aberrant indices by person and item facets

[Speaker] Huang, Tsai-wei:1
[Co-author] Chih-ming, Lu:1
1:National Chiayi University (Taiwan)

This study extended the dichotomous BW family indices (Huang, 2012; Huang & Wu, 2013), which measured the aberrant/normal levels in a response pattern, to be the polytomous ones. Supposed the person i earned a score of xi on a sj credit of the item j, then the person exhibited a correct rate of xi/sj on the item. If the person obtained a total score of Ti in a K-item test, then his/her total score fell within the (JTi) item and the (JTi+1) item according to the item difficulties ranked from easy to hard. Based on the dichotomous logic, the four polytomously person-facet BW family indices (W, B, C, M) can measure the degree of carelessness, guess, mastery, and misconception for a student, respectively. Symmetrically, the four item-facet indices (w, b, c, m) can be derived to measure the degree of hint, disturbance, power, and easiness for an item, respectively.
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