“So you are saying we should…”

This post by Nathan Robinson, whose title I just shamelessly stole, underscores a fundamental problem that always seems to come up when challenging sacred cows in any setting, especially when your stock in trade in the “principle of variance.”

My view on statistics is that the “mean” is right as a statement about the whole, but almost always wrong as a statement about the particular.  In repeated coin tosses, should the coin be fair, heads probably will not outnumber tails and vice versa in the long run.  In every single coin toss, however, either head or tail will definitely outnumber the other.  The general statement about the whole, then, is of only limited utility for the single coin toss:  it provides a clue as to who is more likely to win (by giving us the odds across a large enough sample size), but even if the odds are (truly) strictly even (and the long term data says so), it never tells us that neither will win the next coin toss, so to speak.  In other words, we want to know how wrong, vis-a-vis individual observations, the general statement is and whether these “wrongness” can be generalized across multiple observations.  This, of course, is the definition of variance in non-mathematical lingo and this is the heart of statistics (and science in general)–and lack of understanding of this is how people get lied to by abuse of statistics.

The criticisms of the sort Robinson brings up are precisely what gets people lied to by statistics however:  the statement about a “mean,” so to speak, is not a moral statement of absolute truth, but a descriptive statement about the average state of affairs across a large sample, one that is almost certain to be wrong in individual cases:  I don’t know what we should do about it, but as far as I can tell from the sample that we have, Earth is round and that’s just that.  There is no “so what you are saying.”  So Trump is representing many discontented people whose existence the Democratic insiders are eager to ignore, and this is true, whether one likes them or not.  If they are, on average, rather racist, that too may be true, but it does not change the fact that they are unhappy, there are many of them, and that Trump is channeling their anger, and it may be equally true that, even if Trump is, on average, less popular and less likely to win, if Democrats screw up enough, he might actually win.  (David Byler has an instructive, if somewhat pedantic, commentary on this.)

But, if “science,” even “political science,” as a critical assessment of uncertain facts, has no “so what you are saying,” political rhetoric and advocacy, are all about “so what I am saying.”  When “science” meets “advocacy,” facts give way to “so what I am saying” and that can only be met by “so what you are saying” by those who don’t agree with the point being advocated.  This is, in a nutshell, the Dawkins disease, how, Dawkins and others of his ilk did far more damage to science than they contributed by becoming caricatures that they became.

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