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📊 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

  1. Award of a score to each student
  2. Ranking in order of merit
  3. Identification of groups: high and low
  4. Calculation of the difficulty index of a question
  5. calculation of the discrimination index of a question
  6. 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 the low 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 possible2

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 0-100%.

  • Non-functional 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%

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

  2. 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. ↩

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

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

  5. D’Sa, J. L., & Visbal-Dionaldo, 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/10.5958/0974-9357.2017.00079.4 ↩