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Tuesday, October 13, 2009

Worthless statistics of the day

Last Thursday I held my midterm exam in sports economics. Unfortunately, the exam format was multiple guess. Here is the tabulation of the answers:


. tab answer

answer | Freq. Percent Cum.
------------+-----------------------------------
A | 15 30.00 30.00
B | 10 20.00 50.00
C | 12 24.00 74.00
D | 8 16.00 90.00
E | 5 10.00 100.00
------------+-----------------------------------
Total | 50 100.00

Why is this interesting? It isn't.

However, some people might read into this and think - ah, if I don't know the answer then guess "A" because it is the most common answer. The mistake is thinking that I chose option "A" to be the most popular - I did not.

Just because a distribution of a variable exists doesn't mean that it is useful for predictive purposes.

Don't tell my undergraduate students.

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Comments:
Here's a slice of bologna: I'm guessing not all questions had an "E." what was the conditional probability (relative frequency) of the answer being "E" conditional on the fact that there was an "E" option? Just curious.
 
Good question. Eighteen of fifty questions had an "option E." Of those, five questions were answered correctly with "E". Thus, the conditional probability is 27%. If one had absolutely no clue between any of five possible answers, then choosing E would only slightly improve the odds of answering the question correctly.
 
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