An explanation of negative marking within multiple-choice tests.

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, then 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.