Constructors of new test item formats must be wary, because test-wise examinees are looking for loopholes. Wu ("Oust the Incorrect" RMT 5,2 p.143) proposes a novel partial credit scoring method for multiple- choice questions (MCQs) based on asking each examinee to mark all options that are definitely incorrect. The score for an item is the number of incorrect options an examinee marks as incorrect, and is zero when the examinee marks the correct option as incorrect.
What happens when examinees use a guessing strategy? Then their expected score depends on how many options they decide to guess incorrect. The Table illustrates what expected scores occur when there is one correct answer. The rows are the number of options in the MCQ. The columns correspond to the number of options the examinee decides to guess incorrect in an MCQ. Then each cell gives the expected score for each row-column combination. For instance, when 2 options are guessed incorrect in a 5 option MCQ, then there will be a score of 0 if the correct option is marked incorrect, and a score of 2 otherwise. The probability of missing the correct option is 4/5 for the first mark, and 3/4 for the second mark, i.e. 4/5 * 3/4 = 3/5 for the two marks. The expected score is (the probability of missing the correct answer) * (the score for correctly selecting incorrect options) = 3/5 * 2 = 6/5 points. Only the two-option (True/False) and three-option MCQs are immune to guessing strategy abuse.
Conclusion: Use 3-option MCQs, or defeat guessing strategies by including MCQ items with none or several correct answers.
Number of MCQ Options: Number guessed incorrect: 0 1 2 3 4 5 2 0 1/2 0 - - - 3 0 2/3 2/3 0 - - 4 0 3/4 1 3/4 0 - 5 0 4/5 6/5 6/5 4/5 0 Expected Guessing Score
More "Oust The Incorrect", B Xiao Rasch Measurement Transactions, 1991, 5:3 p. 165
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