Page 306 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Educational Measurement and Evaluation

Notes other reason. The items in the test which have not been attempted because of inability
are not called unattempted items. Suppose there are 50 items in a test. A student solved
the items 1 to 20, did not solve 21 and 22, then solved the items from 23 to 45, and did not
solve any item from 46 to 50 because of lack of time or any other reason. Under this
situation, the items from 46 to 50 will only be called unattempted items, and not the
items at 21 and 22. The difficulty level of such item is known by using the following
formula :

⎛ W ⎞ 1
DL = ⎜ R – ⎟
⎝ k – 1 N – NR
⎠
Where NR = The number of students who have not reached to the item.
In the above example, if 90 students have solved the item correctly, 40 students have
solved it incorrectly and 10 students have not reached to it, the difficulty level of the item
will be found out as follows :

⎛ 40 ⎞ 1
DL = 90 – ⎟
⎜
⎝ 4– 1 150 –10
⎠
⎛ 40 ⎞ 1
= 90 – ⎟
⎜
⎝ 3 ⎠ 140
230
=
420
= .54
Difficulty level (in %) = 54%
Fourth Method : If the number of students is large, it needs more time and labour to find
out the difficulty level of each item. In such a situation, Kelley has suggested to divide
the total students, on the basis of their obtained marks, into three classes—high, medium
and low.
High class : The top 27% of the total number of students
Medium class : The middle 46% of the total number of students
Low class : The lowest 27% of the total number of students
Only the data obtained from students of high and low classes is used to know the
difficulty level of an item. Kelley has suggested that the test should be administered on
at least 370 students to use the formula propounded by him so that about 100 students
can be included in the ‘high’ and ‘low’ classes. The formula is as follows :
1 ⎡ W H ⎞ 1 ⎛ W L ⎞ 1 ⎤ ⎛
DL = ⎢ ⎜ R– ⎟ + ⎜ R – ⎟ ⎥
H
L
⎠
2 ⎝ k – 1N – NR H ⎝ k – 1N – NR L ⎦
⎠ ⎣
L
H
Where, R = The number of students in the high class answering correctly
H
W = The number of students in the high class answering incorrectly
H
N = Total number of students in the high class
H
NR = The number of students in the high class not reached
H
R = The number of students in the low class answering correctly
L
W = The number of students in the low class answering incorrectly
L
N = Total number of students in the low class
L
NR = The number of students in the low class not reached
L
300 LOVELY PROFESSIONAL UNIVERSITY