Letter: Guessing games

May 11, 2001

Gareth Holsgrove considers the merits of multiple-choice questions ("What is the right choice?", THES , May 4) and in particular the problems of negative scoring. But there is another method for dealing with random guesses.

Imagine a student knows the correct answer to M questions and randomly guesses the remaining 100-M answers for a test of 100 multiple-choice questions. The student's score on the test, S, will on average be S = M+(100-M)/5 for the case where each question has five branches (choices). To find the true number of correct answers we simply invert the expression to get M (S-20)x5/4. The value of M is recorded as the final, adjusted mark for the test.

Randomly guessing all answers leads to an adjusted mark of M=0 (on average) and correctly answering all questions gives an adjusted mark of M=100. In the middle regime, a student who knows the answers to 50 questions and randomly guesses the remainder will score S=60 (on average) and will be given an adjusted mark of M = (60-20)x5/4=50. Note that if the student uses partial knowledge to make educated guesses then the score will be higher than S = 60 and the adjusted mark will exceed M = 50.

The advantage of this sliding-subtraction method is that it encourages students to use their partial knowledge to make educated guesses and it gives a better indication of the students' complete knowledge and reasoning skills.

John Vaccaro
University of Hertfordshire

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