Table 2

Examples of expected gain due to knowledgeable guessing after eliminating incorrect distractors in a multiple-choice question with five possible answers

Knowledge of Correct Answer (Odds Ratioa)Question CategorybProbability Expected Confidence Score Due to Guessing
CorrectIncorrectpD=−1/4
pR=3/8
pD=−1/3
pR=1/3
pD=−1/2
pR=1/4
pD=−1
pR=0
2δ=41/3 = 0.3332/30.1670.1110.000−0.333
δ=32/5 = 0.4003/50.2500.2000.100−0.200
δ=21/2 = 0.5001/20.375c0.333c0.250c0.000c
δ=12/3 = 0.6671/30.583d0.556d0.500d0.333d
3δ=43/7 = 0.4294/70.2860.2380.143−0.143
δ=31/2 = 0.5001/20.375c0.333c0.250c0.000c
δ=23/5 = 0.6002/50.500d0.467d0.400d0.200c
δ=13/4 = 0.7501/40.688d0.667d0.625d0.500d
4δ=41/2 = 0.5001/20.375c0.333c0.250c0.000c
δ=34/7 = 0.5713/70.464d0.429d0.357d0.143d
δ=22/3 = 0.6671/30.583d0.556d0.500d0.333d
δ=14/5 = 0.8001/50.750d0.733d0.700d0.600d
  • a Odds ratio describes student knowledge relative to random guessing (Table 1); see Appendix.

  • b δ represents the number of functioning distractors; thus, the student makes final selection of response to question from among the functioning distractors and the correct answer.

  • c Equal to reward.

  • d Greater than reward.

  • Note: A student is assigned a score of +1 for a correct answer, −pD deduction for an incorrect answer, and pR if unanswered (i.e., the student recognizes and admits that he or she does not know).