Your instructor is able to use the product rule for scoring a question with binary (correct/incorrect) answer options where multiple answers can be selected.

Let’s start with the formula:

*Score = proportion correct * (1 - proportion incorrect * deduction factor)

proportion correct = number of correct options selected / number of correct options

proportion incorrect = number of incorrect options selected / number of incorrect options

deduction factor = (1/a + (((N-C)/N)*(1-1/a)))

proportion incorrect = number of incorrect options selected / number of incorrect options

deduction factor = (1/a + (((N-C)/N)*(1-1/a)))

N = total number of options

C = number of incorrect options

a = weight factor (set standard to 2.0)

C = number of incorrect options

a = weight factor (set standard to 2.0)

The product rule is a way to correct for ‘free points’ due to guessing and an alternative to using negative points for answer options. Consider for comparison a question using negative points with two correct and two incorrect options where you could get 1 point for each correct option and minus 1 point for each incorrect option. If you would select one correct option than you would score half of the maximum points. If you guess or select all options, you would score zero points on average.

The product rule will, in this scenario, result in half the points if you selected one correct option, but will still give a quarter of the points if all options are selected. This way the product rule will make the scoring for this question equivalent to guessing in the case of a single answer multiple choice question with one correct option and three incorrect options scoring zero points. For most question types the numbers of correct and incorrect options are clear. For an order question we decided that each ordered pair counts both as a correct option as well as an incorrect option. With 5 items to order, you will have 10 order pairs. This means N is 20 and C is 10 for the product rule formula.

The product rule will, in this scenario, result in half the points if you selected one correct option, but will still give a quarter of the points if all options are selected. This way the product rule will make the scoring for this question equivalent to guessing in the case of a single answer multiple choice question with one correct option and three incorrect options scoring zero points. For most question types the numbers of correct and incorrect options are clear. For an order question we decided that each ordered pair counts both as a correct option as well as an incorrect option. With 5 items to order, you will have 10 order pairs. This means N is 20 and C is 10 for the product rule formula.

*E. Terwisscha van Scheltinga (2009). Van quotiëntregel naar productregel. EXAMENS, 1, 26-27.

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