Professor Nerdburger is deciding what kind of exam to give. He considers multiple choice and essay exams just as good in terms of measuring students’ performance, so he only cares about minimizing the total time-cost of creating and grading exams. The opportunity cost of his time is $60/hour (or $1/minute). It takes one hour to create an essay exam, and it takes four hours to create a multiple choice exam, regardless of the number of students. It takes 20 minutes to grade each student’s essay exam, and it takes 5 minutes to grade each student’s multiple choice exam. (a) Find the total cost function for each type of exam. (b) State the type of exam Professor Nerdberger should choose, depending on the number of students in the class.The numbers are arbitrary, of course, but the problem actually does describe – at least to a first approximation – how I think about what kind of exam to give. Essays have a low fixed (preparation) cost but a high variable (grading) cost, whereas multiple choice exams have the reverse. The variable cost is dependent on the number of students in the class. Thus, the more students there are in a class, the more sensible it is to have a multiple choice exam.
[Answer: TC(essay) = 60 + 20q; TC(mc) = 240 + 5q. Professor Nerdburger should give an essay exam for any class with fewer than 12 students, and a multiple choice exam for any class with more than 12 students. For a class of exactly 12, it doesn’t matter.]
However, this approach does leave out two main factors that I consider. First, if exam questions can be recycled from semester to semester, then the fixed preparation cost can be spread out over time. Instead of a decision-rule that depends on number of students in a class, the appropriate rule (when questions can be recycled) should depend on the number of students over time. Since that number is likely to be very large for any professor who plans to keep his job, this factor strongly shifts the balance toward multiple-choice tests.
But second, most professors (including me) disagree with Prof. Nerdburger’s judgment that essays and multiple-choice questions are “just as good in terms of measuring students’ performance.” Written answers convey some information about student learning that Scantron answers cannot. This factor points toward having more essays. As a result, professors have to make comparisons of dissimilar values. Unlike Prof. Nerdburger, who has the luxury of measuring everything in terms of time spent, we have to weigh the better information attributable to essays against the greater expenditure in time to grade them.
And then there’s the possibility of other question types. In most of my classes, I end up using a mix of multiple-choice and short-answer questions, since short answers convey most of the information I would glean from essays, but they are faster and easier to grade (though not as fast multiple choice).