點二系列相關試題鑑別指數之值譜分析及其在IRT上之應用

Spectral Analysis and Application of Point-Biserial Correlation Item Discrimination Index

劉湘川(Hsiang-Chuan Liu)

《測驗統計年刊》 8期 (2000/12) Pp. 1-20

https://doi.org/10.6773/JRMS.200012.0001

摘要

原有之高低試題鑑別指數為27%高低試題鑑別指數D27，受試者人數須為100或37的倍數，只適合在測驗預試時使用，常用之25%高低試題鑑別指數D25，受試者人數仍須為4的倍數，本文建議之50%高低試題鑑別指數D50，則只須為偶數即可。試題鑑別指數之優劣，除受試者人數限制之適用性考慮外，原無客觀量化準則，本文藉諸光譜學之值譜學分析概念，引進能客觀反應試題鑑別指數之鑑別能力的值譜數之量化率則及其系列有關性質，在可比較受試者人數之情況下，證明了50%高低鑑別試題指數D50，不僅在實用上受試者人數限制較少，且其鑑別能力的量化比較值，約為前二者之兩倍。而點二系列相關鑑別指數R，除無前述受試者人數之限制外，只要受試者之測驗得分有多於三個相異值時，其鑑別能力的量化比較值，恒優於任何高低鑑別指數，包括本文前所建議之50%高低試題鑑別指數D50，本文進而指出藉由導出之系列性質可廣泛應用於試題反應理論之相關專題，並舉二例以供參閱。其一，改進核平滑化無參數試題特徵曲線及選項分析之能力值譜。其二，發展出兼顧知識量之核平滑化與參數試題特徵曲線及選項分析之能力值譜分析。

關鍵字

值譜數 ； 值譜數列 ； 試題鑑別指數 ； 核平滑化無參數試題特徵曲線 ； 核平滑化無參數試題選項分析

並列摘要

The purpose of this study was to provide a comparable quantitative criterion of the power of differentiation for item discrimination indices. Using this criterion, spectrum size, and under the same comparable number of examinees, we pointed out that the power of differentiation of the 50% upper- lower item discrimination index, D50, is more powerful than which of the 27% upper-lower item discrimination index, D27, and the 25% upper-lower item discrimination index, D25. Moreover, We derived a serial properties to prove that if there are more than three different test scores of examinees, then the power of differentiation of point-biserial correlation item discrimination index, R, is more powerful than which of D50, D27, D25 and any other upper-lower item discrimination index. Finally, We suggested two very useful applied examples about improving kernel smoothing nonparametric item options analysis.

並列關鍵字

spectrum size ； spectrum sequence ； discrimination index ； kernel smoothing nonparametric item options analysis ； kernel smoothing nonparametric item characteristic curve