以二技聯考土木類來說，其中的工程材料算是最難的學科，多數人都是總分１００分被扣分超過６０分以上。也就是說，考試有把握的答案佔４０分，其餘６０分靠猜答案答對１５分，而答案錯誤的４５分倒扣四分之一，最終得到的分數就是４３﹒７５分。事實上，考題的４個選項會以排除法的方式，刪除１個絕對不可能的答案選項，所以靠猜答案的方式作答正確的分數應該是２０分。換言之，正確作答和猜答案的總得分是６０分，要將答案錯誤的４０分倒扣二分之一給出原始分數４０分。
在既有的考試扣分原則下，僅會倒扣１０分給出５０分的分數。我已經發表倒扣計分的合理性論文，想必以後的倒扣計分會更加符合考生的心理狀態。我的倒扣計分論文是１／Ｎ－２，其原理舉例來說就是如此。也就是說，每個人都以考試猜答案的方式，要比起已知範圍多出非常多的分數。猜答案，就是概率。誠言之，學術論文並不允許純舉例來發表論文，而我採用的是學理上的概率理論在解釋倒扣計分，此乃由於學術論文必須採用學理來做解釋，但顯然多數人並不懂概率的理論及其邏輯。
International Journal of Educational Research
February 22, 2014
Title
Examination Rule for the Reasonable Scores of Back-off
Abstract
The proposed examination rule can establish the reasonable scores of back-off for the examiners.
Keywords: Back-off, Examination Rule, Probability, Mathematical Logic
I. Introduction
In the modern examinations, some of the examinations may adopt the examination rule for the scores of back-off, and the present examination rule is the obtained score minus 1/4 score of a problem in the single-choice problem with the 4 options. In the Taiwanese examinations, most examiners may attempt guessing the unsure questions, and they can make sure the total scores should not become 0 score by the well-known common sense.
II. Examination Rule for the Reasonable Scores of Back-off
When the examiner tries to guess a single-choice problem with N options, he has 1/N and (N-1)/N probabilities to obtain the right and wrong results respectively. Hence, the reasonable scores of back-off should be the obtained scores minus the 1/(N-1) score, and the probability is 1/N - (N-1)/N × 1/(N-1) = 0 to establish a fair examination competition. However, if the examiner intends to guess a question, the thinking logic will be based on the situation that he can make sure the question has an impossible choice at least. According to the same probabilistic assumption, the examiner has 1/(N-1) and (N-2)/(N-1) probabilities to obtain the right and wrong results respectively, and the most reasonable scores of back-off should be the obtained scores minus the 1/(N-2) score to let the probability is 1/(N-1) - (N-2)/(N-1) × 1/(N-2) = 0 to establish a fairest examination competition.
III. Conclusion
The proposed examination rule can establish the reasonable scores of back-off for the examiners.
在既有的考試扣分原則下，僅會倒扣１０分給出５０分的分數。我已經發表倒扣計分的合理性論文，想必以後的倒扣計分會更加符合考生的心理狀態。我的倒扣計分論文是１／Ｎ－２，其原理舉例來說就是如此。也就是說，每個人都以考試猜答案的方式，要比起已知範圍多出非常多的分數。猜答案，就是概率。誠言之，學術論文並不允許純舉例來發表論文，而我採用的是學理上的概率理論在解釋倒扣計分，此乃由於學術論文必須採用學理來做解釋，但顯然多數人並不懂概率的理論及其邏輯。
International Journal of Educational Research
February 22, 2014
Title
Examination Rule for the Reasonable Scores of Back-off
Abstract
The proposed examination rule can establish the reasonable scores of back-off for the examiners.
Keywords: Back-off, Examination Rule, Probability, Mathematical Logic
I. Introduction
In the modern examinations, some of the examinations may adopt the examination rule for the scores of back-off, and the present examination rule is the obtained score minus 1/4 score of a problem in the single-choice problem with the 4 options. In the Taiwanese examinations, most examiners may attempt guessing the unsure questions, and they can make sure the total scores should not become 0 score by the well-known common sense.
II. Examination Rule for the Reasonable Scores of Back-off
When the examiner tries to guess a single-choice problem with N options, he has 1/N and (N-1)/N probabilities to obtain the right and wrong results respectively. Hence, the reasonable scores of back-off should be the obtained scores minus the 1/(N-1) score, and the probability is 1/N - (N-1)/N × 1/(N-1) = 0 to establish a fair examination competition. However, if the examiner intends to guess a question, the thinking logic will be based on the situation that he can make sure the question has an impossible choice at least. According to the same probabilistic assumption, the examiner has 1/(N-1) and (N-2)/(N-1) probabilities to obtain the right and wrong results respectively, and the most reasonable scores of back-off should be the obtained scores minus the 1/(N-2) score to let the probability is 1/(N-1) - (N-2)/(N-1) × 1/(N-2) = 0 to establish a fairest examination competition.
III. Conclusion
The proposed examination rule can establish the reasonable scores of back-off for the examiners.
