Negative marking
- 1. Negative marking has two advantages: 1) it yields scores that are not inflated by guesswork, 2) it discourages random guesses, and therefore the scores are more reliable.
- 2. A good test should yield a score that is proportional to each test taker's knowledge, comprehension, or aptitude; whatever it is the test has been designed to assess.
- 3. In traditional multiple-choice tests where there is no negative marking, test takers will normally make a guess whenever they are unable to identify the correct answer to a question.
- 4. If each question has four answer options, the expected score for a test taker who has zero knowledge, comprehension, or aptitude will be 25%. This is an average score, since the test taker's actual score will be variable.
- 5. A test taker who knows the answers to 20% of the questions has an expected score of 40%, since on average they will guess the right answers to a quarter of the remaining 80% of the questions.
- 6. Let's look at it another way. Consider a collection of 50 Qs (3 marks per Q) 50 test questions. ✔ Suppose that a particular 10 Qs test taker knows the right answer to the first 10 questions, and that they make random guesses for the remaining ? 40 questions. 40 Qs
- 7. If each question is worth 3 marks, the test taker will get 30 marks for the first 10 questions. 50 Qs (3 marks per Q) (You'll soon see why we ✔ need to have 3 marks per 10 Qs 10 x 3 = 30 marks question rather than just one mark.) ? 40 Qs
- 8. If they make random guesses for the remaining 40 questions then on average they will get 10 50 Qs (3 marks per Q) of them right, which will give them another 30 ✔ marks. 10 Qs 10 x 3 = 30 marks ? 40 Qs 10 x 3 = 30 marks
- 9. This will give them 60 marks altogether, on average, out of the 150 marks that are available. 50 Qs (3 marks per Q) So their expected score ✔ is 60 out of 150, which is 10 Qs 10 x 3 = 30 marks 2/5, or 40%. Score = 60 out of 150 (expected) = 40% ? 40 Qs 10 x 3 = 30 marks
- 10. If we deduct one mark for every question answered incorrectly, this will cancel out the marks 50 Qs (3 marks or -1 mark per Q) due to lucky guesses. ✔ The idea is that for each 10 Qs 10 x 3 = 30 marks lucky guess that adds 3 marks to the score there will be (on average) 3 Score = 30 out of 150 (expected) = 20% unlucky guesses that each deducts one mark ? from the score. 40 Qs 10 x 3 = 30 marks So the expected score is 30 x -1 = -30 marks now 20%, which is in line with the profile of a "good" test (which we saw in the second slide).
- 11. To conclude, here’s the first slide again... Negative marking has two advantages: 1) it yields scores that are not inflated by guesswork, 2) it discourages random guesses, and therefore the scores are more reliable.
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