Diffuculty index
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The document discusses calculating the difficulty index (DI) for questions in a pilot study. DI is a ratio of the number of students who correctly answered a question to the total number of students. It indicates how easy or difficult a question is. The document provides examples of calculating DI for both objective and subjective questions. Based on the DI, questions are either selected for or rejected from the final question paper. A sample data set with hypothetical student answers and calculated DIs is also included to demonstrate how questions would be evaluated.
![References
• Mathew, T.K., and Mollykutty, T.M. (2011). Science Education -Theoretical bases
of teaching and pedagogic analysis - Physical Science and Natural Science.
Kerala: Rainbow Book Publishers
• NCERT. (2013). Teaching of science. Delhi: Author
• Radha Mohan. (2007). Teaching of physical science. (3rd ed.). Delhi: PHI Learning
• Rathinasabapathy, P. (2001). கல்வியில் தேர்வு [Examination in Education].
(2nd ed.). Chennai: Shantha Publishers.
• Srinivasan, P. (2011). அறிவியல் கற்பிே்ேல் [Teaching of science].
Thanjavur: DDE, Tamil Univeristy
• Images from google](https://image.slidesharecdn.com/diffucultyindex-210509071308/85/Diffuculty-index-26-320.jpg)
Diffuculty index
- 1. Pilot Study Pilot study is a small scale advance administering of the question paper to students to stabilize the questions. Here we have to administer the questions to 100 students and collect the marks. From the obtained marks we have to go for statistical calculation. Since, it is lock down period now, I will be giving the marks for 10 students. (If number of students is more, statistical predictions will become accurate)
- 2. Difficulty Index - Concept ✓ As the name indicates, it says how easy or difficult a question is.
- 4. Difficulty Index - Formula No. of Students correctly answered a question DI = --------------------------------- Total No. of Students
- 5. Difficulty Index - Concept ✓ Difficulty Index (DI) will have to be calculated for each question ✓ For a question, It is the ratio of the students who answered correctly to the total number of students ✓ For example, let us take the 1st question. If that question is answered correctly by 4 out of 10 students then, the index of difficulty is =4/10 = 0.4
- 6. DI - Calculation ✓ Calculate DI for the 2nd question. It is correctly answered by 9 students out of 10. ✓ DI=9/10= 0.9 ✓ Compare DI of question 1 with question 2. .
- 7. DI - Calculation ✓ DI for Q1 = 0.4, Correctly answered 4/10 DI for Q2 = 0.9, Correctly answered 9/10 This means that if DI is low then, question is hard and high then, question is easy. ✓ Out of Q1 and Q2 which is easy? Q2 is easier than Q1 .
- 8. DI - Relationship ✓ What is the proportionality between DI and difficultness of a question? ✓ Inversely proportional. ✓ If DI is high then, it is easy question and low then, it is hard question .
- 9. DI - Range ✓ What is the range of DI. ✓ Think of two cases, one in which everybody answers a question and in other nobody answers a question
- 10. DI - Range ✓ It is 0 to 1. ✓ If DI=1, everybody correctly answered the question. ✓ If DI=0, Nobody correctly answered the question.
- 11. DI ✓ Likewise you can calculate DI for all questions. ✓ Calculating DI for first 20 questions is easy and further we face difficulty. What is the problem in calculating DI from Q21?
- 12. DI – Subjective and Objective Questions ✓ From Q1 to Q20, it is objective questions. After that it is subjective questions. For objective questions if the answer is correct, the mark is 1 and if it is wrong, the mark is 0. This is not the case for Q21 to Q29. How to calculate DI for that?
- 13. DI for subjective question ✓ This can be handled easily like this. If the mark is more than 70% for a question then it is considered as 1 otherwise 0. ✓ For example, let us take Q21. The maximum marks is 3 and 70% of 3 is 2.1≈2. Hence if a student gets 2 or more marks, it is taken as 1 and if he/she gets less than 2 marks it is taken and 0. Now it becomes easy to calculate DI .
- 14. DI for subjective question ✓ Let us go for calculation of DI for subjective question. For Q21, 8 students got 2 and above out of 10 students. Calculate DI. ✓ DI = 8/10 = 0.8
- 15. DI for subjective question ✓ For Q22, 2 students got 2 and above out of 10 students. Calculate DI. ✓ DI = 2/10 = 0.2 ✓ For Q23, 2 students got less than 2 out of 10 students. Calculate DI. ✓ DI = 8/10 = 0.8 (if 2 students got less than 2 means 8 students would have got 2 and above)
- 16. DI for 5 Mark Question ✓ What is 70% of 5? It is 3.5. ✓ 3.5 is borderline for 1 or 0. Hence if a student gets 3.5 or more marks, it is taken as 1 and if he/she gets less than 3.5 marks it is taken and 0 ✓ For Q26, 9 students got 3.5 and above out of 10 students. Calculate DI. ✓ DI = 9/10 = 0.9
- 17. Assessme nt ✓ Now you know, how to calculate DI for objective and subjective questions. ✓ After calculation, you will come to know that which question is easy and which is difficult. If DI is low then, it is difficult question and high then, it is question. ✓ What do you think to be done with the DI value?
- 18. Assessme nt ✓ Highly difficulty and very easy question are to be avoided. Since for highly difficult question, nobody will attend and very easy question, everybody will attend and get full marks like the question, which is the capital of India?
- 19. Judgment S.No. DI Level Result 1 0-0.3 Difficult Rejected 2 0.31-0.79 Moderate Selected 3 >0.80 Easy Rejected
- 20. Implications ✓ Based the table in previous slide, one has to select or reject the question. ✓ If all questions are selected no problem. If some questions are rejected what is to be done?
- 21. Implications ✓ Again write the question, go for pilot study, calculate new DI and based on it select or reject the question.
- 22. For Understanding ✓ Very Easy and highly difficult questions are to be avoided. Only moderate questions need to be kept in the question paper.
- 23. Model Data ✓ Model data is attached in the following slide. It gives DI for all the questions. Data is hypothetically given for learning purpose. ✓ Data Courtesy: Mr. Sridath
- 24. Q.NO. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 No. of Stu. Who Ans. Corr. Tot. No. of Stu. DI Level Decision 1 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ 2 1 1 1 1 1 1 0 1 0 1 8 10 0.8 MOD REJ 3 0 1 1 1 1 0 0 1 0 1 6 10 0.6 MOD SEL 4 1 0 1 1 0 0 1 1 1 1 7 10 0.7 MOD SEL 5 1 1 1 1 1 1 1 1 0 0 8 10 0.8 MOD SEL 6 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ 7 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ 8 0 0 1 0 0 1 0 1 1 0 4 10 0.4 MOD SEL 9 1 1 0 0 1 0 1 0 1 1 6 10 0.6 MOD SEL 10 0 1 0 1 1 1 1 0 1 1 7 10 0.7 MOD SEL 11 1 1 1 1 1 0 0 1 0 1 7 10 0.7 MOD SEL 12 1 1 1 0 0 1 1 1 1 0 7 10 0.7 MOD SEL 13 1 1 0 1 1 1 1 0 1 1 8 10 0.8 MOD SEL 14 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ 15 0 0 1 0 1 0 0 1 1 1 5 10 0.5 MOD SEL 16 1 1 1 1 1 1 1 1 0 1 9 10 0.9 EASY REJ 17 1 0 0 1 1 1 0 1 0 1 6 10 0.6 MOD SEL 18 1 1 1 1 1 1 1 1 0 0 8 10 0.8 MOD SEL 19 1 1 1 0 0 1 1 0 1 1 7 10 0.7 MOD SEL 20 0 1 1 1 1 0 1 0 1 1 7 10 0.7 MOD SEL 21 2 2 2.5 2.5 2 2 2 2.5 2 2 10 10 1 EASY REJ 22 1.5 1.5 2 1.5 1.5 2 2.5 2 1.5 2.5 5 10 0.5 MOD SEL 23 3 3 3 3 3 3 3 3 3 3 10 10 1 EASY REJ 24 2.5 2 2 2.5 2 1.5 2 1.5 2 2 8 10 0.8 MOD SEL 25 3 2 2.5 2 1.5 2 2.5 2.5 2 2 9 10 0.9 EASY REJ 26 4 3 3.5 3 2.5 2 3.5 4 4.5 4 6 10 0.6 MOD SEL 27 3 3 4 3 5 3 5 3 3 4 5 10 0.5 MOD SEL 28 4 4 4 3 4 3 4 4 4 4 8 10 0.8 MOD SEL 29 0 0 0 0 0 0 0 0 0 0 0 10 0 DIFF REJ
- 25. Assignment ✓ Based on the previous slide, have hypothetical for all questions for ten students. Calculate DI and take decision whether to accept or reject the questions.
- 26. References • Mathew, T.K., and Mollykutty, T.M. (2011). Science Education -Theoretical bases of teaching and pedagogic analysis - Physical Science and Natural Science. Kerala: Rainbow Book Publishers • NCERT. (2013). Teaching of science. Delhi: Author • Radha Mohan. (2007). Teaching of physical science. (3rd ed.). Delhi: PHI Learning • Rathinasabapathy, P. (2001). கல்வியில் தேர்வு [Examination in Education]. (2nd ed.). Chennai: Shantha Publishers. • Srinivasan, P. (2011). அறிவியல் கற்பிே்ேல் [Teaching of science]. Thanjavur: DDE, Tamil Univeristy • Images from google