The product rule is intended to be used for questions with binary (correct/incorrect) answer options where multiple answers can be selected. Among these question types are the multiple-choice, match and order types. Instead of defining the points for each option you only need to declare if it is correct or incorrect. The score for the student is calculated based on the fraction of correct options selected and the fraction of incorrect options selected. The rule offers a standardized way for correcting the possibility that students get a good score by simply selecting all options. If a student knows one answer for sure it is more beneficial with this rule to select that single answer than to select all options. The product rule works as follows:

*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 an alternative to using negative points for answer options. Consider for comparison a question using negative points with two correct and two incorrect options. You could give each correct option 1 point and each incorrect option minus 1 point. If a student selects one correct option he/she will score half of the maximum points. If he/she guesses or selects all options the student will score zero points on average.

The product rule will, in this scenario, result in half the points if one correct option is selected, 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 one correct option is selected, 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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