????

???????????????????????????????????????? ??????????????????????????? (ref. 1)

?????(?????%)

???????????????????????????????????? ???????:
FI = (X_average) / X_max
?? X_average ????????????????????????
? X_max ??????????????????
????????????????????????????????????

???(SD)

?????????????????????????????????????????? ? SD=0? SD is calculated as the statistical stadard deviation for the sample of fractional scores (achieved/maximum) at each particular question.

?????(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 = (X_top - X_bottom)/ N
where X_top 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 X_bottom) 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.

????(DC)

?????????????????????
?????????????????????????????
DC = Sum(xy)/ (N * s_x * s_y)
?? Sun(xy) ?????????????????????????
N ??????????
s_x ????????????
s_y ????????????

???????????????? +1.0 ? -1.0 ??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
?????????????????????????????????????????????????????????? ?????????????????????