## The Lake Wobegon Effect

I’m teaching introductory economics to Masters of Public Policy Students at ANU’s Crawford School this semester. As an opening exercise, I gave the students an ‘economic literacy’ test. At the end of the quiz, I asked them:

Looking around the classroom, what percentile of the relative distribution do you expect to end up? For example, 100 means you expect to top the class, 75 means you expect to outperform 75% of the class. 50 means you expect to be at the middle of the distribution, 25 means you expect to outperform 25% of the class. 1 means that you expect to be at the bottom of the distribution.

Here’s the distribution of their responses, with a horizontal red line denoting what the distribution would look like if everyone could perfectly forecast their final rank.

Out of curiosity, I randomly switched the ordering of the questions on the quiz, so half the students hit a hard question just before they had to predict their relative rank, and half the students hit an easy question just before they had to predict their relative rank. I had expected some ‘framing effect’, but found nothing significant â€“ suggesting that students’ priors about their relative rank aren’t that easy to budge.

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### 7 Responses to The Lake Wobegon Effect

1. Joshua Gans says:

So if a large proportion of the class didn’t understand the statistical concepts of “proportion” or “distribution” and were biased in a certain way (say that more was better or that is how they would like to perform), then you might also get this distribution.

They might also forecast that you are going to give everyone the same grade.

What would have happened if you gave half the class an alternatively framed quiz with expectations of what proportion they expect to outperform them?

2. Eric says:

That rank being just for the scores of the test, or over a longer time?

I must say your students collectively have a high view of themselves individually! No one put themselves below 50! A bit like the vernacular usage of “average” when one means “worse than average”.

I suspect a lot of people wrote exactly 50, so that peak could arguably be split between the 45-50 and 50-55 columns. Likewise for 75.

You could plot the actual percentile mark for each student on the test with what they expected.

3. Did they perhaps just interpret the question by saying “I’ll pass” – that is get 50%

Level of humor works exceptionally well too. Try using something of no consequence and see if it still works (e.g., amount of time spent in your garden) — it will be better, but the distribution still won’t be close to correct.

Actually, the serious problem with this level of delusional belief is that all students expect high marks and then complain when they don’t get them. Since you aren’t allowed to people they aren’t very good some things anymore (let alone stupid), that of course creates problems.

5. archer says:

This tendency of individuals to overestimate their abilities and performance is well documented in the psychological and cognitive bias literature.

A good layman’s write-up (it was the cover story at the Conference Board Review) is posted here:

http://www.nakedcapitalism.com/2008/02/dark-side-of-optimism.html

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