Tuesday, August 25, 2009

Tautological Statistics

I found this Gallup poll interesting:
Parents Rate Schools Much Higher Than Do Americans Overall

Parents Rate Schools Much Higher Than Do Americans Overall
Little change in recent years
by Frank Newport

PRINCETON, NJ -- Three in four American parents (76%) are satisfied with the education their children receive in school, compared to 45% of the general public who are satisfied with the state of schools nationwide. These findings from Gallup's annual Work and Education survey are almost identical to what Gallup found last year, and have not changed materially since 2003.

I just wanted to point out that it is mathematically guaranteed that more parents would be satisfied with their own children's education than with education as a whole, given the following fairly reasonable axiom:
Axiom. A parent who is dissatisfied with his own child's education is also dissatisfied with education as a whole.

Now it is not hard to prove the claim I just made:
Proof: Let S be the set of all parents satisfied with education as a whole, and let P be the set of all parents who are satisfied with their own children's education. By the contra positive of the above axiom, S is a subset of P. Therefore, it follows that the size of S is less than the size of P.
QED

In other words, often there's simply nothing remarkable about statistics. A little common sense (or deductive logic) will tell you what you wanted to know without doing any surveys.

On the other hand, what the survey really tells us is that nothing big government programs have done in the past several years has made any difference in results in our education system. That should have been the headline of the article.

2 comments:

  1. Ah, but there are no tautologies in survey research. That would require a kind of logical consistency that survey respondents as a group seem quite immune to. ;)

    The category of "non-parents" is wholly uninteresting. There must have been absolutely nothing in data for them to lead with this.

    It would be interesting to compare parents and employers - people who have some direct, but non-parental stake in the education system. Of course the groups overlap, but that is what statistics are for.

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  2. I agree! It would be interesting to see what employers thought of public education. I read an article today that was fairly typical of the "our educational system is going to hell in a handbasket" genre. It claimed employers were noticing a lack (decline?) in certain basic knowledge, such as civics and economics. I never know what to make of articles like that. I would think some employers might be happier with an educational system that's getting more and more specialized, even at the expense of a well-rounded education. Who knows? If education really is about preparing kids for employment, maybe we just need to go back to whole trade school idea.

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