Contrary to the view expressed by Hugh Fletcher, the practice of penalising wrong answers in multiple-choice tests is normatively inferior to simply counting the number of right answers (“Exams with merit”, Letters, 12 March).
For questions with k options, the punishment formula is -1/(k-1), such that random guesses on all questions lead to an expected score of zero. The purpose of such formula scoring is to deter guessing, but even with this formula there is nothing to lose overall from guessing and everything to gain (especially if your guesses are educated ones, which Fletcher alludes to). Therefore, test-takers should guess when they are uncertain, even though the whole point of the formula is to deter guessing. This means that a relative advantage is conferred upon those individuals with a greater appetite for risk. However, tests are meant to measure knowledge, not the risk attitudes of the test-takers, so formula scoring increases unwanted noise in measurement.
Another issue with multiple-choice questions is the location of the correct answer. There is a tendency to place the correct answer in the middle positions, which can be exploited by test-takers. Some setters guard against this by placing the correct answer equally often in each possible position. But people are poor intuitive randomisers and this can also be exploited. The best method is to properly randomise the answer options, which doesn’t necessarily mean the correct answer appearing equally often in each location.
David Hardman
School of Psychology
London Metropolitan University