A Statistical Analysis of Independent Test Items

by Chwan-Chin Song and Chin-Chuan Lu.

Abstract: Based on the classical test theory, a probability method is proposed to develop the computational formulas of difficulty index and discrimination index for independent test items. This method takes the performance of the middle group into account and may provide more information about these two indexes. By using probability generating functions, an efficient computing algorithm is also provided for obtaining both index values. A real data is given for empirical study and the results are compared with those obtained by the classical method. Discrepancies between these two methods are also discussed in this study.

Key Words: : Independent test items, Difficulty index, Discrimination index, Probability generating function

Chwan-Chin Song, ccsong@math.nccu.edu.tw
Chin-Chaun Lu, cclu@math.nccu.edu.tw
Jann-Huei Jinn, jinnj@gvsu.edu

Editor: Ravi Khattree, khattree@oakland.edu

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