Sunday, July 26, 2015

The difficulty index and the discrimination index of a question

Calculation of the difficulty index of a question

Difficulty index                       Index for measuring the easiness or difficulty of a test question. It is the percentage (%) of students who have correctly answered a test question j it would be more logical to call it the easiness index. It can vary from 0 to 100%.

The following formula is used:
Difficulty index = [(H +L) / N] x 100
where   H = number of correct answers in the high group
            L = number of correct answers in  the low group
N = total number of students in both groups

Calculation of the discrimination index of a question

Discrimination index
An indicator showing how significantly a question discriminates between "high" and "low" students. It varies from -1 to +1.

The following formula is used:

Discrimination index = 2 x [(H  - L) /N ]

 Critical evaluation of a question

This is based on the indexes obtained.

Difficulty index: The higher this index the easier the question j it is thus an illogical term. It is sometimes called "easiness index", but in the American literature it is always
called "difficulty index". In principle, a question with a difficulty index lying between 30% and 70%* is acceptable (in that range, the discrimination index is more likely to be high).
If for a test you use a group of questions with indexes in the range 30% - 70%, then the mean index will be around 50%. It has been shown that a test with a difficulty index in the range of 50% - 60% is very likely to be reliable as regards its internal consistency or

Discrimination index: The higher the index the more a question will distinguish (for a given group of students) between "high" and "low" students. When a test is composed of questions with high discrimination indexes, it ensures a ranking that clearly discriminates between the students according to their level of performance, i.e., it gives no advantage to the low group over the high group. In other words, it helps you to find out who are the best students.
It is most useful in preparing your question bank. Using the index", you can judge questions as follows:

0.35 and over
Excellent question
0.25 to 0.34
Good question
0.15 to 0.24
Marginal question revise
under 0.15
Poor question – most likely discard

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