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Saturday, November 24, 2012

The Wonderful World of Statistics

This is a table apparently making the rounds that is supposed to demonstrate that people who voted for Obama are smarter, not stupider than people who voted for Romney.
h/t Yard Sale of the Mind
There is something endearingly sad in the spectacle of people convinced of their own moral and intellectual superiority making such elementary errors of statistical inference. 

The Problem of Metrology


The first problem a statistician must come to grips with is that of metrology, a topic on which TOF has commented from time to time.  A key question is whether the measurement system actually measures what it claims to measure.  In this case, "better educated" is equated with "% of residents with college degree."  But is this true? 
  • Not all college degrees are in real subjects, after all.  
  • One may be trained to proficiency in one particular field without being educated
(Relatedly, one may ask how the "% holding college degrees" was measured.  Does it include associate degrees from community colleges (nee junior colleges)?  What about barber college?  Kay Kyser's Kollege of Musical Knowledge?  Is that % of registered voters?  % of residents of that state?  Or is it # college graduates of in-state colleges divided by total state population aged 25+.)

The Problem of Grouping

For a valid correlation, the X and the Y must be measured on the same units.  This would require determining
  • X: whether Voter A has a college degree
  • Y: who Voter A chose
But the table only tells us that some percentage of state residents have degrees and whether the majority of the voters in that state chose Obama or Romney.  It does not tell us whether actual degree-holders actually chose Obama.
TOF is reminded of a case in which the percentage of women with cancer in a census district was correlated with the percentage of households using lawn services, drawing the inference that the chemicals used for weed control led to cancer.  This was actually reported as news!  Of course, there was no effort made to determine whether those suffering cancer lived in the households using the services, or perhaps next door; nor even whether the sufferer had only recently moved into the census district.   

The Problem of Reification

When dealing with inanimate objects, correlation of % is sometimes fruitful given the prior assumption that the population drawn from is reasonably homogenous.  This means that the lot or the product stream may be treated as if it were a single "individual."  (Provided the process were in a state of statistical control.)  But it is precisely the point that voters are not precision-made piece parts from the same stamping press.  The reification of abstractions is the notion that because a bunch of people can be put in a box, they derive their opinions and preferences from the label on the box, rather than vice versa.  The bucket labeled "Women" does not consist of identically distributed pieces, but of individuals with diverse opinions.  Neither does the bucket labeled "College Degree."  These are attributes abstracted from voters, not voters themselves.  Adjectives are not nouns.

The Problem of Inference

Degree-holders comprise at best 30-40% of voters.  It is possible, given the data, for every degree-holder to have chosen Romney while Obama carried the State because the poor, working class, and minorities chose him.  In fact, exit polls have shown Obama's margin was much higher among HS-educated or less.  This would be better in line with the mythos that Democrats are the party of the poor and working class.  Higher education levels are associated with higher incomes, and higher incomes supposedly prefer Republicans. 
Other possible inferences include
  • Possessors of college degrees are snobs averse to those not well-spoken (Bush) or to Mormons (Romney).
  • College faculties brainwash their graduates.     
  • College graduates are terrified of voting for a white guy running against a black guy.

7 comments:

  1. There are two other issues that could be brought up here. First, does "better educated" mean "more intelligent"? I would love to challenge that assumption which is deeply held as a matter of faith. Second, statistics never tell us how many cemeteries voted in these states. In some states with large political machines, the cemeteries vote (and often, I might add).

    Great analysis, as usual Mr. Flynn!

    Slainte!
    D.v.

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  2. I'm reminded of a study I saw some years ago (alas, enough that I cannot remember the names of the researchers) that broke down the voting habits--or preferences, for the underaged--by level of education, for the population of the state of Michigan. The clever part was where they reported it by number of years of education, not just student/high school grad/college student/college grad. What was most interesting was that the propensity for voting red increased with education, until approximately the sophomore year in college, where things took a left turn that more than compensated for the trend in the teenage years.
    Interesting, but complicated and inconvenient for people telling a narrative of moral and intellectual superiors versus dropouts.

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  3. "For it is written: 'I will destroy the wisdom of the wise, and the learning of the learned I will set aside.' Where is the wise one? Where is the scribe? Where is the debater of this age? Has not God made the wisdom of the world foolish?. . . Consider your own calling, brothers. Not many of you were wise by human standards, not many were powerful, not many were of noble birth. Rather, God chose the foolish of the world to shame the wise, and God chose the weak of the world to shame the strong."

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  4. Thanks for the hat tip. Dug a little deeper - according to the CNN exit polls (buyer beware: self reporting caveats apply), the pattern for 2012 was that HS drop outs voted markedly blue, with a steadily increasing propensity for voting red as educational level increased, until people with college degrees voted Romney 51% to 47%.

    BUT, most interesting, people with graduate degrees - 18% of voters (doesn't that seem kind of high? Are there really that many graduate degree holders out there? How does anything get done?) tended to vote strongly for Obama.

    So increasing education seems to correspond to greater likelihood of voting red until grad school. But here's the kicker: my unscientific survey of the fields graduate degrees are awarded in show a full 60% of people getting graduate degrees are doing so to advance in public sector careers - education accounts for over 25% of graduate degrees, with Public Admin, various law enforcement and social service degrees making up the rest. (Business & engineering I assumed to be private sector leaning, while health and sociology neutral to public? - the data's probably out there, maybe I'll look it us sometime.) So, it's a little surprising that grad degree holders don't lean even farther left than they do.

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  5. It could also be headlined "Obama favored in states with more intensely indoctrinated populations".

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  6. This may be related to another phenomenon: Exit polls that Romney carried the wealthy vote but Obama carried the votes of wealthy counties. I suspect this means that Obama overwhelmingly carried the maid and butler vote.

    In the case of education, Obama clearly carried the votes of neighbors of college graduates.

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  7. 18% of voters (doesn't that seem kind of high? Are there really that many graduate degree holders out there? How does anything get done?)

    As you noted, the vast majority of graduate degrees are in education -- and not much does get done there. A Master's Degree is now a ticket that all teachers have to punch during their careers; the quality of education Master's Degrees is about what you would expect from that requirement.

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