本研究旨在比較HGLM、MH、LR、SIBTEST在DIF分析的差異，同時藉由實徵資料與模擬資料瞭解四種方法的一致性，並藉由模擬資料計算不同方法的型一誤差率、型二誤差率及整體精確性。以HGLM分析DIF的最大特色在於可加入不同變項解釋偵測到的DIF試題。
實徵資料以HGLM、LR、MH三種方法進行DIF分析，並針對偵測到的DIF試題，在HGLM的二階與三階模式中加入個人變項：個人社經地位、試題位置，及組織變項：學校、縣市、地理區域，以瞭解各個變項對DIF試題的解釋情形。此外，並分析男女生在不同數學內容領域的DIF差異。其次，利用根據實徵資料所產生的模擬資料，比較在不同測驗長度、樣本數、DIF比率、試題參數下，HGLM、MH、LR、SIBTEST四種方法分析之精確性及對DIF分析的影響。
主要發現如下：
一、實徵資料結果顯示HGLM、MH、LR檢定結果及DIF效果量分類皆呈現良好一致性。
二、HGLM分析中加入的解釋變項皆能降低DIF比率，且在高中部分最為顯著。在組織階層的三個變項中，發現學校所能解釋DIF情形最為顯著。
三、在數學內容領域中，並未發現某一領域對男生或女生特別有利，但年級間DIF比率最高的內容領域並不相同。
四、模擬資料中結果顯示，HGLM與LR精確度最高。樣本大小、DIF強度對偵測率有顯著的影響，而在試題參數方面，a參數對偵測DIF試題的影響大於b參數。

The purposes of this study are to compare the differences of four DIF methods: HGLM, MH, LR, and SIBTEST. Empirical and simulated data were employed to understand the consistency of four methods. First, HGLM, LR, MH three DIF methods were used to analyze the empirical data from a large-scale mathematics assessment to compare the consistency. Several variables, like SES, location of item block, school, county-city, and region were added into the HGLM to see whether they can provide interpretation for DIF items. Secondly, given the item parameters calibrated from the empirical data, a simulated data was generated under different test length, sample size, DIF ratio, item parameters, and DIF strength. The accuracy rate, type I error rate, and type II error rate were calculated for the four methods to see the effects of detecting DIF items as well as the influence of different conditions on DIF analysis.
The main findings are the following:
1.The results from empirical data showed that HGLM, MH, and LR methods in detecting DIF items and DIF items classifications had very high consistency.
2.All variables adopted in this study, SES, location of item block, school, county-city, and region could reduce the DIF items effectively, especially for senior high students. Among the three organizational variables, the interpretation of school was most powerful.
3.The results didn’t show any gender difference in five math sub-contents, but the sub-contents with having most DIF items for each grade were different.
4.The simulation study showed that HGLM and LR had the highest accuracy. Sample size and DIF strength could have some impact on the detection of DIF. It also showed that a parameter had more impact than b parameter on the detection of DIF.

中 文 摘 要 ………………………………………………………… i
英 文 摘 要 ………………………………………………………… ii
誌 謝 ………………………………………………………… iii
目 次 ………………………………………………………… iv
表 次 ………………………………………………………… vi

圖 次 ………………………………………………………… vii


第壹章 緒論…………………………………………………… 1
第一節 研究動機……………………………………………… 1
第二節 研究目的與研究問題………………………………… 5
第三節 名詞釋義……………………………………………… 6

第貳章 文獻探討……………………………………………… 8
第一節 DIF研究的起源與統計方法之發展…………………… 8
第二節 傳統檢驗DIF之方法與比較…………………………… 12
第三節 HGLM分析DIF之發展與相關研究…………………… 24
第四節 DIF分析法之精確性…………………………………… 27
第五節 數學科性別間DIF相關研究…………………………… 34

第參章 研究設計與方法…………………………………………38
第一節 研究架構…………………………………………………38
第二節 研究對象…………………………………………………39
第三節 研究工具…………………………………………………40
第四節 研究程序…………………………………………………45
第五節 資料分析…………………………………………………45

第肆章 結果與討論………………………………………………47
第一節 實徵資料分析結果………………………………………47
第二節 模擬資料分析結果………………………………………56

第伍章 結論與建議………………………………………………68
第一節 研究結論………………………………………………… 68
第二節 研究限制…………………………………………………70
第三節 研究建議…………………………………………………71
參考文獻 ……………………………………………………………73

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