Thursday, November 25, 2010

Item Discrimination

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PUP Table 3 is re-tabled using three levels of item discrimination as PUP Table 3a. Mastery/Easy items survey student knowledge and provide a positive adjustment to the test score. Discriminating items divide the class into groups of students who know and who do not know. A change in instruction or special attention may be needed. Unfinished items reflect a problem in instruction, learning and/or testing.

Three easy items show how item discrimination works. Item 14 shows negative discrimination (ND) as only one high scoring student missed it. Item 11 shows positive discrimination (B) as only one low scoring student missed it. Item 20 shows the maximum positive value (A) as only the bottom two students missed it. This is an example of perfect item performance, a  Guttman pattern: a string of all correct marks followed by all wrong marks.

Although discrimination is not a part (a parameter) of the Rasch model, it is such an important descriptive statistic in managing the Rasch model that it is printed, in several forms, in both the person and the item statistics. Ministep therefore prints discrimination values rather then levels (A, B, C, and D) as printed by PUP. PUP and Winsteps calculate the same corrected point biserial r (pbr) when the “PTBISERIAL = Yes” control variable is used. PUP only prints the descriptive item or question pbr statistic.

These differences reflect the different optimization in the software. Winsteps maximizes the production of stable efficient tests. PUP optimizes easy to use data for instruction, testing and student counseling.

Items that tend to fit the Rasch model best also tend to be discriminating. Items 5, 6, 7, and 8, with a range of difficulty from 71% to 88% (average difficulty = 84%), will be used as common items to link two tests.

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