William M. Briggs

Statistician to the Stars!

Teaching Journal: Day 7

The joke is old and hoary and so well known that I risk the reader’s ire for repeating it. But it contains a damning truth.

Most academic statistical studies are like a drunk searching for his keys under a streetlight. He looks there not because that is where he lost his keys, but because that is where the light is.

To prove this comes these four quotations from Jacqueline Stevens, professor of political science at Northwestern University (original source):

In 2011 Lars-Erik Cederman, Nils B. Weidmann and Kristian Skrede Gleditsch wrote in the American Political Science Review that “rejecting ‘messy’ factors, like grievances and inequalities,” which are hard to quantify, “may lead to more elegant models that can be more easily tested…”

Professor Tetlock’s main finding? Chimps randomly throwing darts at the possible outcomes would have done almost as well as the experts…

Research aimed at political prediction is doomed to fail. At least if the idea is to predict more accurately than a dart-throwing chimp…

I look forward to seeing what happens to my discipline and politics more generally once we stop mistaking probability studies and statistical significance for knowledge.

If our only evidence is that “Some countries which face economic injustice go to war and Country A is a country which faces economic injustice” then given this the probability that “Country A goes to war” is some number between 0 and 1. And not only is this the best we can do, but it is all we can do. It becomes worse when we realize the vagueness of the term “economic injustice.”

I mean, if we cannot even agree on the implicit (there, but hidden) premise “Economic injustice is unambiguously defined as this and such” we might not even be sure that Country A actually suffers economic injustice.

But supposing we really want to search for the answer to the probability that “Country A goes to war”, what we should not do is to substitute quantitative proxies just to get some equations to spit out numbers. This is no different than a drunk searching under the streetlight.

The mistake is in thinking that not only that all probabilities are quantifiable (which they are not), but that all probabilities should be quantified, which leads to false certainty. And bad predictions.

Incidentally, Stevens also said, “Many of today‚Äôs peer-reviewed studies offer trivial confirmations of the obvious and policy documents filled with egregious, dangerous errors.”

Modeling, which we begin today in a formal sense, is no different than what we have been doing up until now: identifying propositions which we want to quantify the uncertainty of, then identifying premises which are probative of this “conclusion.” As the cautionary tale by Stevens indicates, we must not seek quantification just for the sake of quantification. That is the fundamental error.

A secondary error we saw developed at the end of last week: substituting knowledge about parameters of probability models as knowledge of the “conclusions.” This error is doubled when we realize that the probability models should often not be quantified in the first place. We end up with twice the overconfidence.

Now, if our model and data are that “Most Martians wear hats and George is a Martian” the probability of “George wears a hat” is greater than 1/2 but less than 1. That is the best we can do. And even that relies on the implicit assumption about the meaning of the English word “Most” (of course, there are other implicit assumptions, including definitions of the other words and knowledge of the rules of logic).

This ambiguity—the answer is a very wide interval—is intolerable to many, which is why probability has come to seem subjective to some and why others will quite arbitrarily insert and quantifiable probability model in place of “Most…”

It’s true that both these groups are free to add to the premises such that probabilities of the conclusions do become hard-and-fast numbers. We are all free to add any premises we like. But this makes the models worse in the sense that they match reality at a rate far less than the more parsimonious premises. That, however, is a topic for another day.

Homework

Read about all this. More is to come. In another hurry today. Get your data in hand by end of the day. Look for typos.

4 Comments

  1. “we must not seek quantification just for the sake of quantification.”
    Epidemiologist do this all the time.

  2. My summary of the material so far:
    “The map is not the territory.”
    “All models are false, but some are useful.”

    Okay, I knew that. Where is this going?

  3. Political science is the oxymoron of our modern age.

  4. Briggs

    26 June 2012 at 6:50 am

    antares,

    It is false that “all models are false” on the premise that some models, namely mathematical theorems and the like, are true. If E = “Six-sided object, etc.” and C = “Show a 6″ then the model E is not false unless we had direct proof that it was (which we do not).

    To say something is false is an extremely strong claim. It means you have deductive proof, in the same form as a mathematical or logical theorem, the shows a proposition is false. Not just unlikely. But false.

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