Ten students have taken an objective assessment. The quiz contained 10 questions. In the table below, the students’ scores have been listed from high to low (Joe, Dave, Sujie, Darrell, and Eliza are in the upper half). There are five students in the upper half and five students in the lower half. The number “1” indicates a correct answer on the question; a “0” indicates an incorrect answer.
Student
Name |
Total Score (%) | Questions | |||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ||
| Joe | 100 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Dave | 90 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| Sujie | 80 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
| Darrell | 70 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
| Eliza | 70 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
| Zoe | 60 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| Grace | 60 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| Hannah | 50 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| Ricky | 40 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| Anita | 30 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
Calculate the Difficulty Index (p) and the Discrimination Index (D).
| Item | # Correct (Upper group) | # Correct (Lower group) | Difficulty (p) | Discrimination (D) |
| Question 1 | ||||
| Question 2 | ||||
| Question 3 | ||||
| Question 4 | ||||
| Question 5 | ||||
| Question 6 | ||||
| Question 7 | ||||
| Question 8 | ||||
| Question 9 | ||||
| Question 10 |
Answer the following questions:
1. Which question was the easiest?
2. Which question was the most difficult?
3. Which item has the poorest discrimination?
4. Which questions would you eliminate first (if any) – why?
5. Is this test overall a good test according to the discrimination index? Calculate the discrimination values both with and without the questions you may have decided to eliminate in question 4. Why or why not?
6. What is the overall difficulty level of this test? Calculate the difficulty values both with and without the questions you may have decided to eliminate in question 4. Is this test too easy, too hard, or just right?
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