๐ Item Analysis
Scenerio
 Your students have finished an MCQ test, and you want to analyse their performance
Item Difficulty & Discrimination ^{1}
Steps in Item Analysis
 Award of a
score
to each student Ranking
in order of merit Identification of
groups
: high and low  Calculation of the
difficulty index
of a question  calculation of the
discrimination index
of a question  Critical
evaluation
of each question enabling a given question to be retained, revised or rejected
Identification of High and Low Groups
 Of all the students ranked in order of merit, the first 27% would be the
high
group while the last 27% would be thelow
group
Why 27%?
Because 27% gives the best compromise between two desirable but contradictory aims: 1. Making both groups as large as possible 2. Making the two group as different as possible^{2}
Difficulty Index
 Index for measuring the easiness or difficulty of a test question.
 It is the percentage (%) of students who have answered a test question, it would be more logical to call it the easiness index.
 It can vary from 0%  100%
 The bigger the index, the easier the question
Calculation
The following formula is used:
Difficlty Index = (H + L) / N * 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
Interpretion
Difficulty Index  Interpretation 

> 70%  Easy Question 
60%  70%  Good (Slightly Easy) Question ^{3} 
50%  60%  Good [Recommended] Question ^{4} 
30%  50%  Good (Slightly Difficult) Question 
< 30%  Difficult Question 
Discrimination Index
 An indicator showing how significantly a question discriminates between "high" and "low" students.
 It varies from 1 to +1
Calculation
The following formula is used:
Discrimination Index = 2 * (H  L) / N
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
Interpretion
Discrimination Index  Interpretation 

>= 0.35  Excellent Question 
0.25  0.34  Good Question 
0.15  0.24  Marginal Question  Revise 
< 0.15  Poor Question  Most Likely Discard 
Item Distractor Analysis ^{5}
Distractor efficiency (DE) is calculated on the basis of the number of NFDs in an item and ranges from 0100%.
 Nonfunctional distractors (
NFDs
) are those options other than the key when selected infrequently by the respondents (<5%), and do not perform their function.  An item with no NFDs has a DE of 100%.
 When the item has one, two or three NFDs, the DE will be 66.66%, 33.33% and 0% respectively
NFDs  Distractor Efficiency 

0 NFDs  100% 
1 NFD  66.67% 
2 NFDs  33.33% 
3 NFDs  0% 

Guilbert JJ., Educational handbook for health personnel. Revised edition. WHO Offset Publ. 1981;(35):469. ↩

Truman Kelley showed in 1939 that when each group consists of 27% of the total, it be said with the highest degree of certainty that those in the high group are really superior (with respect to hte quality measured by the test) to those in the low group. ↩

It was interpreted as "acceptable" for 30%70% in the original literature. In that range, the discrimination index is more likely to be high. ↩

In that range, the test is very likely reliable as regards its internal consistency or homogeneity. ↩

DโSa, J. L., & VisbalDionaldo, M. L. (2017). Analysis of multiple choice questions: Item difficulty, discrimination index and distractor efficiency. International Journal of Nursing Education, 9(3), 109. https://doi.org/10.5958/09749357.2017.00079.4 ↩