以Hot deck插補法推估成就測驗之不完整作答反應

Abstract

本研究之目的旨在探討成就測驗中，學生的不完整作答反應是否能利用插補法，對不完整作答反應資料進行彌補。研究者藉由試題參數與受試者能力參數的分析討論，期望能獲得支持插補技術應用於成就測驗的結論。研究欲探討的問題有三：（一）利用統計插補法所估算之替代值與實際作答反應之間是否有差異存在；（二）受試者之部分答題反應組型在經過插補後，與完全作答反應組型之分析結果是否有差異存在；（三）能否將統計插補技術應用於成就測驗模式中。\r\n 本研究程序包含兩部分，一為模擬資料（N=1000，3000，5000，l0000；缺失比例為5%，10%，15%，30%，50%）的分析，模擬研究主要作為實證研究結果的驗證與推論；另一個則為實證資料的分析與討論。針對不完整作答反應，基於IRT的強假設前提，以及成就測驗作答反應的資料型態，研究者選擇熱卡插補法(HOt Deck imputation method)的統計插補技術，分別對於實證資料與模擬資料中之各類樣本數，與不同缺失比率下的作答反應作插補。另又以EM插補法作對照分析。\r\n 根據研究結果與討論，提出以下幾點歸納結論：（一）當缺失比例不大時，能符合原本的資料分佈假設，但隨著缺失比例愈高，高至30%以上時，已漸不符合原本假設；（二）當缺失比例愈高時，各項參數之估計標準差值幾乎是最大的；若忽略未作答反應之受試者的表現時，其分析所得的參數估計值亦並未是最佳的，反而是將所有受試者的作答反應進行插補估計後，所得的參數估計標準差值才是最小、最佳的；（三）本研究中，主要以熱卡法為插補方法，而EM插補法並不符合本研究資料之性質，故若採用此法進行插補，則所得的估計標準差會是最大的；（四）經過模擬研究與實證資料的分析後，證明熱卡法所推估的未作答反應，與直接刪除未作答反應或不處理未作答反應的確有差異存在，且經過插補所產生的替代值，對於受試者的能力表現能提供更穩定有效的解釋力。\r\n 關鍵詞：熱卡插補法、不完整作答反應、成就測驗

This purpose of this study is to infer the feasibility if examinees` non response could be made up, by using imputation method in non response or missing value of achievement test. The research design contains two procedures: one is simulation research (setting sample sizes are 1000, 3000, 5000, and 10000; percents of non response are 5%, 10%, 15%, 30%, and 50%), and the other is pragmatic research. Hot deck imputation method is the main concern method in this research. To test if this method fits to achievement test, EM method is used for comparison with the Hot deck imputation method.\r\n The results are as follows: 1. The distribution of below 30% percent non response data after imputated is the same as the original data, but following the higher percents of non response, the distribution is not match what we expected. 2. Applying Hot Deck imputation method to the achievement test with different sample size and different percents of non response, the researcher found that following the higher percents of non response in any sample size, the higher standard deviation happened. Besides, ignoring or deleting these non responses is not a good way to deal with this test response pattern. Imputating an appropriate answer for the non response by Hot Deck imputation method, we could get the least standard deviation of the test and ability parameters estimation, and get largest test information for examinees. 3. We found the Hot Deck imputation method is suitable for the data pattern of achievement test than EM method. There are different outcomes between Hot deck imputation method and EM method. Hot Deck imputation method also has accuracy parameter estimation. 4. Based on above discussions, this study suggested that Hot deck imputation method could cope with non response in achievement test pretty well.\r\n Key Words: Hot Deck imputation method, Non response, Achievement test