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題名：模擬與實徵試題差異功能之指標效能分析:IRT法及CFA法之比較
作者：何宗岳
作者(外文)：Zong-Yue Her
校院名稱：國立嘉義大學
系所名稱：教育學系研究所
指導教授：李茂能
學位類別：博士
出版日期：2010
主題關鍵詞：試題反應理論（IRT）；驗證性因素分析（CFA）；試題差異功能（DIF）；Item Response Theory（IRT）；Confirmatory Factor Analysis（CFA）；Differential Items Functioning（DIF）
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本研究旨在比較試題反應理論（IRT）與驗證性因素分析（CFA）二種不同取向試題差異功能（DIF）檢測之效能及其應用於實證研究上之結果。研究設計分兩部分，研究一為模擬實驗，比較六種檢測法在各種條件下之DIF檢測效能以及三種檢測模式之應用效果。研究二為實徵分析，針對97年第一次基測數學科做性別DIF分析。研究主要結論摘要如下：
一、IRT取向檢測法較適用於二元資料，CFA取向檢測法較適用於多元資料。
二、IRT取向與CFA取向各檢測法之統計考驗力與第Ⅰ類型錯誤比率皆是隨樣 本數增加而提高。
三、二元資料型態下，CFA取向之CFA-λ對一致性、雙重性DIF較不靈敏，CFA取向之MIMIC與IRT取向之SIBTEST則對非一致性、雙重性DIF較不靈敏。多元資料型態下，CFA取向之CFA-λ對一致性、雙重性DIF較不靈敏，CFA取向之MACS、 MIMIC與IRT取向之SIBTEST、DFIT則對非一致性DIF較不靈敏。
四、 IRT取向與CFA取向各檢測法之統計考驗力與第Ⅰ類型錯誤比率皆是隨DIF比率增加而提高。
五、二元資料型態下，小樣本及低DIF比率時，「未修正臨界值一般檢測法」檢測效能較佳；大樣本及高DIF比率時，「修正臨界值迭代檢測法」檢測效能較佳。多元資料型態下，在各種不同樣本及不同DIF比率情況下，「修正臨界值迭代檢測法」檢測效能皆較佳。
六、97年第一次國中基測數學科試題之性別差異，雖在統計檢測上顯示部份試題具有DIF，但在質性分析中則未見試題內容具有偏誤之情形。
The main goal of the study was to examine the CFA-based and IRT-based indices power and robustness in detecting DIF via both simulated and empirical data. First, six indices（CFA-λ、MACS、MIMIC & LRT、SIBTEST、DFIT） were compared in a Monte Carlo study with regard to their ability to detect DIF. The moderating effects of number of response categories、sample size、number of DIF items、DIF seriousness、type of DIF were also investigated under 3 testing models. Second, the empirical data from the 2007 Mathematics Basic Competency Tests for Junior High School Students（BCTEST）were investigated for gender DIF using the well-performed DIF indices.
The main conclusions of this study were summarized as follows.
1、IRT-based indices were more powerful in detecting dichotomously scored DIF items, but as the number of possible scores for an item increased, the CFA-based indices performed better in detecting DIF items.
2、Both IRT-based and CFA-based Procedures for DIF, the index power of DIF detectability and typeⅠerror increased as the sample size increased .
3、With dichotomous items, the IRT-based CFA-λ indices were not sensitive to identifying the uniform or mixed DIF items, and neither were the CFA-based MIMIC、IRT-based SIBTEST procedure with the nonuniform DIF items. With polytomous items, the CFA-λ procedure were not sensitive to to identifying the uniform or mixed DIF items, neither were the CFA-based MACS、MIMIC and IRT-based SIBTEST、DFIT procedure with the nonuniform DIF items.
4、Both IRT-based and CFA-based Procedures for DIF, the power of DIF detectability and typeⅠerror increased as the number of DIF items in a test increased .
5、With dichotomous items, indices with the general procedure using the uncorrected critical α value performed better in detecting DIF items than the general procedure or the iterative procedure using the corrected critical α value under small samples and lower percentage of DIF items, while the iterative procedure using the corrected critical α value has better performace than the other two procedures under large samples and higher percentage of DIF items. With polytomous items, indices with the iterative procedure using the corrected critical α value performed better in detecting DIF items than the general procedure using the uncorrected or the corrected critical α value under all conditions.
6.、Regarding to gender DIF analysis on the 2007 BCTEST math test, several items were flagged as a DIF item in the statistical analyses, but none of them revealed bias in the substantive analyses .
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