試題分析

這一表格是用來呈現處理過的測驗資料,以便分析和判斷每一個試題在評量功能上的表現。 這裡所用的統計參數,是要以古典測驗理論來計算和解釋的。 (ref. 1)

難易度指數(答對百分比%)

這一量數是用來說明,某一個試題對於接受測驗的學生而言,是多困難或多容易。 它的計算方式為:
FI = (Xaverage) / Xmax
這裡 Xaverage 是指所有作答者在這一試題上實際得到分數的平均數,
而 Xmax 是指在這一試題上可以達到的最高分數。
如果試題可以用答對或答錯的二分法來計分,那這數量相當於答對人數的百分比。

標準差(SD)

這一統計量可以看出所有學生在某一試題上,作答反應的分散程度。如果所有學生答案都一樣, 那 SD=0。 SD is calculated as the statistical stadard deviation for the sample of fractional scores (achieved/maximum) at each particular question.

鑑別度指數(DI)

This provides a rough indicator of the performance of each item to separate proficient vs. less-proficient users. This parameter is calculated by first dividing learners into thirds based on the overall score in the quiz. Then the average score at the analyzed item is calculated for the groups of top and bottom performers, and the average scored substracted. The matematical expression is:
DI = (Xtop - Xbottom)/ N
where Xtop is the sum of the fractional credit (achieved/maximum) obtained at this item by the 1/3 of users having tha highest grades in the whole quiz (i.e. number of correct responses in this group),
and Xbottom) is the analog sum for users with the lower 1/3 grades for the whole quiz.

This parameter can take values between +1 and -1. If the index goes below 0.0 it means that more of the weaker learners got the item right than the stronger learners. Such items should be discarded as worthless. In fact, they reduce the accuracy of the overall score for the quiz.

鑑別係數(DC)

這是試題能否區辨學生能力高低的另一種量數。
鑑別係數是指單一試題與測驗總分之間的相關係數。計算公式為:
DC = Sum(xy)/ (N * sx * sy)
這裡 Sun(xy) 是試題分數的離差和測驗總分的離差的交乘積的累加和,
N 是這一試題的作答人數
sx 是這一試題分數的標準差,
sy 是整個測驗總分的標準差。

鑑別係數和相關係數一樣,其值界於 +1.0 和 -1.0 之間。正的係數代表能力愈高的學生答對該試題的比率愈高,而能力愈低的則答對比例愈低,這種試題鑑別功能佳,應該保留。反之,負的係數代表能力愈高的反而答對比率愈低,這通常是因為正確答案在設定時出差錯,試題敘述含糊造成學生誤解,或教學上的錯誤所造成。這類題目應該刪除。
鑑別係數和鑑別指數的差別在於,前者是使用全體受測者的資料來計算,而不像後者只在兩端各取三分之一的受測者的資料來計算, 因此,這參數在檢驗試題的表現上可能更敏感。

輔助說明檔案的索引
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