Wednesday, January 5, 2011

Item Characteristic Curve

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An item characteristic curve (ICC) displays the probability of a right mark, or the portion of each group of students, with the same ability, to make a right mark. The raw scores, ranging from 15 to 24, are from the Total Score column in Winsteps Table 17.1, Person Statistics.

A student with a raw score of 15 missed Item 8 for an observed average score of zero on Winsteps Table 29.8. Individual students with raw scores of 16, 17, and 18 marked correctly had observed average scores of 1.0. A group of 6 students had average raw score of 19, 4 right:2 wrong or 4/6 or 0.67 observed average score. The ten groups plotted on Table 29.8 are circled on PUP Table 3.  
The Ministep graph, Expected Score and Empirical ICC, 8.8, displays the same information as in Table 29.8. The Model ICC, in Table 29.8, changes from a series of dots to a flowing line in the ICC graph.

The ten student ability groups found for Item 8 also hold for all the other items. An ICC defines item difficulty using student test scores. The standard reference point of zero logit and 0.5 probability or 50% expected test score is also marked on this graph.

On this test, the students were more able than the questions were difficult. This was either an easy test or the students were well prepared. Item 8 was a central performer (difficulty of 83%) on a test with an average score of 84%. The person and item locations for estimated measures on the horizontal axis correspond to their series of ogives on a 1-parameter IRT model.

A test characteristic curve (TCC) is developed by combining all of the ICCs. Persons with high ability fall to the right and those with low ability fall to the left (negative). Difficult items fall to the right and easy items fall to the left (negative). The consequence is that all along this line, student ability equals item difficulty (the ratio that Dr. Rasch discovered). The two highest ability students answered all questions correctly. The three easiest questions were answered correctly by all students.

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