Re: A misapplication of probability theory in exam grading


pauldepstein@xxxxxxx wrote:
jankrihau@xxxxxxxxxxx wrote:
...
Hi,

I don't think it was an attempt to remove randomness, but rather to
arrange so that random guessing doesn't score better than not
answering. Hence the choice of (-1, 4): It gives the expected value 0
for random guessing. Although there is still an element of randomness,
the expected score for the whole test becomes 4 x the number of
questions the candidate actually knew the answer to, regardless of
whether he or she made random guesses or chose to leave some questions
unanswered.

---
J K Haugland
http://home.no.net/zamunda

If you want the expected score of random guessers to be 0, you don't
need to fuss with silly rule changes in this way. You can just use the
normal system and then do a final subtraction of (number of
questions)/5.

I don't know why you use the tentative formulation "still an element"
of randomness.

My whole point is that the penalty system (when used optimally by
students) has _exactly the same_ degree of randomness as the more
traditional no-penalty system.

The reason is that you are using a very strange notion of optimality.
Consider a one question test where you have no idea of the correct
answer, but where a negative score results in your immediate execution.
I strongly suspect that you would leave the question blank.

I find that usually taking risks with expected value 0 is not worth the
effort, unless you know that you will fail without said risk.

The penalty-system was introduced with a completely dishonest and
fallacious propaganda campaign that the new system is "fairer" and
removes some randomness. It does absolutely nothing of the kind.

Paul Epstein

.

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