Page 305 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 26: Achievement Test: Concept, Types and Construction

R Notes
So, DL =
N

110
DL =
150
= .73
For the sake of convenience, it can be multiplied by 100 to present it in percentage.

DL = .73 100
×
= 73%

The more is the percentage of difficulty level, the easier is the item.

Second Method : There is a probability in answering multiple choice questions that
some students may give correct answers to some question by guess. In such a case, the
above formula is amended to find out the difficulty level of an item. The amended
formula is as under :

⎛ W ⎞ 1
DL = ⎜ R – ⎟
⎠
⎝ K – 1 N
Here, the value of R and N is the same as given in the above formula.
W = The number of students answering an item incorrectly
K = The number of alternatives for solving an item.
Example
In the above example No. 1, if the number of alternatives in the multiple choice questions
is four, the difficulty level of an item will be calculated as under :
Here, N = 150
R = 110
W = 150 – 110 = 40
K= 4

⎛ 40 ⎞ 1
⎜
So, DL = 110 – ⎟ ×
⎝ 4– 1 ⎠ 150
⎛ 40 ⎞ 1
= ⎜ 110 – ⎟ ×
⎝ 3 ⎠ 150

290
=
450
= .64
×
Difficulty level (in %) = .64 100 = 64%
Third Method : In the above two methods, it has been taken for granted that all the
students have solved all the items in the test. Sometimes, it may be possible that the
students are not able to write answers to the last few questions due to lack of time or any
other reason. In such a situation, the difficulty level calculated using the first two methods
cannot be considered to be correct. Such questions or items are called unattempted items
Unattempted items are those which have not been solved due to lack of time or any

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