Re: A misapplication of probability theory in exam grading

in article <1166203471.910768.4570@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<pauldepstein@xxxxxxx> wrote:

|In standardized multiple-choice exams, where each question has 5
|options, a common (and extremely dumb) rule used is that correct
|answers score 4 but wrong answers score -1.
|
|Presumably the inventors of this rule noticed that the ordinary
|policy of simply counting the right answers produces a randomness
|factor, and they desired to eliminate it by "penalizing random
|guessing" according to the above scheme.
|
|The irony is that this penalty clause does absolutely nothing to
|penalize random guessing because a random guess scores 0 on average,
|the same as an omitted question.

i think that you've badly misunderstood the motivation for the rule,
which is much more sensible than you seem to realize.

i wonder if robert israel (or anyone else) could give us the precise
statement and proof (or disproof if i'm wrong about this) of a nice
theorem to the effect that the rule in question is "the unique rule
that correctly measures the amount of information about which option
is the correct one that's contained in the probability distribution
representing the exam-taker's bayesian stance".


--


jdolan@xxxxxxxxxxxx

.

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