廣義逐次機率比檢定在等第制分數評量的應用

Application of Generalized Sequential Probability Ratio Test to Ranking Evaluation

教育部規定，國民中小學的評量需要轉換為「五等第」分數，避免學生因為些許的分數差距而進行惡性競爭與比較，以培養學生更多元的發展。等第制分數的評量，可以轉換為統計上多重逐次檢定問題。本研究使用廣義逐次機率比檢定處理多重逐次檢定問題，並進一步應用至電腦化測驗中等第制分數的評量。研究結果顯示，在不限制測驗題數下，分類正確率皆達八成以上；而當等第類別數增加時，分類正確率相差不大，主要的影響反應在測驗題數的增加。而在有限制測驗題數的測驗情境下，利用概似比的檢定概念，更能有效處理在測驗終止時無法評定考生能力的問題。

To avoid destructive competition among students， Ministry of Education would like to transfer the grading system from continuity scoring system to ranking system， in which it uses only five different ratings to evaluate student’s ability. Grade ranking evaluation can be viewed as a sequential multi-hypothesis test problem. In this paper， we apply generalized sequential probability ratio test (GSPRT) to solve the problem of grade ranking evaluation. We found that the correct decision rates of GSPRT is over 80% when using GSPRT to solve grading ranking evaluation problem. Moreover， we identity that using the idea of likelihood ratio to solve the problem， it usually fail to evaluate student’s ability during the test period.