Explanation regarding how wrong answers will cancel correct answers in the multiple choice
questions:
Let’s imagine that the Cope Stage 1 exam has 170 multiple choice items with five options and
that the threshold is 124. When the practice of four wrong answers cancelling out one correct
answer comes into effect, the threshold will go down to 112.5.
The formula used to calculate the threshold is as follows:
New threshold: 1.25 x (old threshold - number of items / 5)
When this comes into effect, there will be no change in the level of the questions.
In the case where wrong answers do not cancel out a correct answer, in order not to be
disadvantaged, a student needs to answer all questions to which they know and don’t know
the answers as the student has 1/5 = %20 chance of guessing the correct answer. In this
case as there is no penalty for wrong answers, answering all the questions would be an
advantage.
-Ahmet answered 115 questions to which he knew the answers and did not answer the remaining
55 questions. He scores 115 points and therefore cannot pass the threshold.
-Ayşe answered all the questions to which she knew the answers but randomly filled the
remaining questions. From the questions she has randomly filled, there is a high probability that
on average she would get 0.20 x 55 = 11 questions right. In this case, Ayşe would get 115+11=
126 points and therefore pass the threshold. On the other hand, there is also a lower probability
that out of the questions she has randomly filled, she gets 8 questions right, scores 123 points
and therefore falls below the threshold.
-Aylin answered 110 questions to which she knew the answers and randomly guessed the
remaining 60 questions. From the questions she has randomly filled, there is a high probability
that on average she would get 0.20 x 60 = 12 questions right. In this case, Aylin would be getting
110+12= 122 and therefore falling below the threshold. On the other hand, there is a low
probability that out of the questions she has randomly filled, she would get 14 questions right
and therefore pass the threshold.
-Arda has answered 125 questions to which he knew the answers. If he were to randomly fill the
remaining 45 questions, there is a high probability that on average he would get 0.20 x 45 = 9
right answers and increase his score to 134 and therefore easily pass the threshold. On the other
hand, he were not to random guess, he would still pass the threshold.
In the case where four wrong answers cancelled a correct answer and where the threshold
was 112.5/170, nothing would change if a student answered all the questions s/he knew the
answers to and either answered or did not answer the questions s/he did not know the
answers to. On the other hand, in cases where the student could eliminate some of the
options, guessing the answer would be to the advantage of the student.
Students have a 20% chance of finding the correct answer by randomly filling a question to which
they do not know the answer and an 80% chance of guessing it incorrectly. For this reason, a
student answering 20 questions through random answers with a high probability would get 0.20 x
20 = 4 right answers and 0.80 x 20 = 16 wrong answers. The student would score zero from the
20 questions.
-Ahmet answered 115 questions to which he knew the answers and did not answer the remaining
55 questions. As he scored 115 points he passed the threshold.
-Ayşe answered 115 questions to which she knew the answers and randomly filled the remaining
55 questions. For the questions she randomly filled there is a high probability that she will score
a zero, in which case she passes the threshold. On the other hand, there is a low probability that
out of the questions she randomly filled she would have 8 correct answers and the others would
be incorrect, in which case she would get 111.25 points and fall below the threshold.
-Aylin answered 110 questions to which she knew the answers and randomly filled the remaining
60 questions. There is a high probability that on average she would score zero, in which case she
would score 110 points and fall below the threshold. On the other hand, there is a lower
probability that out of the questions she randomly filled she would have 14 correct answers and
score 112.5 points and pass the threshold.
-Arda answered 125 questions to which he knew the answers. If he were to randomly fill the
remaining 45 questions, there is a high probability that he would get zero and score 125 points
and easily pass the threshold. On the other hand, he would still pass the threshold even if he did
not answer any questions randomly.
Evaluation:
In the above examples when we compare Ahmet and Ayse’s situation we can observe the
following:
-In the case where wrong answers do not cancel out correct answers, a student who has
answered 115 questions correctly, has to randomly fill the questions to which s/he does not
know the answers. It is certain that if s/he does not give randomly selected answers, s/he will
not pass the threshold. If s/he fills randomly, there is a high probability that s/he might pass;
however, there is also the possibility of the student failing to pass.
-In the case where wrong answers cancel out correct answers, a student who has answered 115
questions to which s/he knows the answers, has the freedom to decide whether or not to
randomly fill the remaining questions. It is certain that unless s/he random guesses, s/he will
pass. If s/he were to randomly fill there is a high probability that s/he might pass; however,
there is also the possibility of the student failing to pass.
The same principles apply to the multiple choice questions in the COPE Stage 2 exam.