HOW GUESSING CAN NEGATE THE PLUSES OF MCQ EXAMS

COMPETITIVE exams in India, particularly entrance tests for pursuing higher education, are mostly based on computer-based multiple-choice questions (MCQs).

- S RAJA SETHU DURAI ,P MURUGAN

These tests have some advantages in terms of transparency and quicker evaluation. However, what ability these tests are intended to assess needs an understanding.

In recent times, performance in the 10+2 schooling has been used as a mere eligibility criterion. Only these entrance exam scores hold the golden keys to the higher education citadel. As these exams gain prominence and are projected to assess merit of the younger generation, they need critical scrutiny. We are going to examine these exams only from an academic perspective.

Mathematically, a multiple-choice question with n choices will have one correct answer and n-1 wrong answers. So every choice has an equal probability of 1/n to be the correct answer. For example, in an exam consisting of 100 questions with four choices, picking any one choice (called 'guessing' in the literature) for all the questions will fetch 25 marks. This guessing can be prevented by giving negative marks for wrong answers. According to formula scoring, the negative mark should be equal to the ratio of the mark given for the correct answer and n-1. If the mark for the right answer is 1 with 4 choices, then the negative mark should equal 1/3. The logic is that even if the remaining 75 questions are marked wrongly, the 25 marks gained by guessing would be negated. Two situations can still benefit guessing: if the negative mark is less than 1/3, and when a particular choice among the 4 has more occurrences than the theoretical probability of 1/4.