12-11-07

Reading Numbers
Well, kids, the coming year will be another one for the US Presidential elections, and like the 2000 elections, with no incumbent in the mix, it will be an open field.  No doubt I'll be revisiting the area of lies and half-truths over the next ten-and-a-half months, but the most important issue of the election at this point is numbers, and how to read them.

Every time you turn around, it seems like someone is throwing another new set of numbers at you.  Or, more likely, just one number without any real reference.  It's very easy to get confused by these numbers, because they sound like they mean something, and the simple fact that someone is publicly willing to put a fixed number on something makes it sound like they've done research (or at least read a report by someone who did research). 

We, as a society, like numbers.  They're comforting and fixed in much the same way that the ground is comforting and fixed (at least for those of us that don't live on the West Coast).  Unfortunately, in debate, numbers are too often thrown at us with no reference for scale or relativity, and that's when they become meaningless, like those trig diagrams that show a right triangle with a hypotenuse of five and a leg of four.  Sure you can determine the length of the other leg (three), but so what?  It may be in proportion to itself, but it's meaningless without some sort of real scale.  Five inches?  feet?  furlongs?

Raw Numbers
Any time someone throws a raw number at you, you should always be suspicious.  More often than not, they are taking advantage of your limited human brain.  Due to the "Baby Grace" drama, a local Congressman has taken it upon himself to crusade for children killed by abuse and neglect.  Annually, he says, there are more than a thousand kids who fall victim to that.  He doesn't site a source when he does so, which we'll get to, later, but let's look at that "more than a thousand" number.

It sounds huge doesn't it?  Seriously, when you hear a number like that that's large, yet small enough to grasp, it strikes a chord.  Is Bob down the hall beating his kids?  They were wearing sweaters when he brought them to the Christmas Party to meet Santa...  Don't feel bad; when Bob hears those numbers, he's wondering the same thing about you.  It's not you, it's not him; it's the number.

The human brain isn't really equipped to conceptualize large numbers.  Especially when those numbers refer to people.  Five is easy, and so is ten.  A hundred?  Okay, maybe the crowd at Red Lobster on Mother's Day.  A thousand?  My cousin and I graduated from the same high school in the same year, and our class contained just under 900 kids, but we both ran in circles that never intersected.  Ten thousand?  Now you're talking about a stadium at a small college or minor league baseball team.  They stop being people by that point, don't they?  They all just blend into a writhing mass like a bowl of ants.

By the time you get to the numbers that politicians and special interest like to throw around the most, the hundreds of thousands, our brains collapse on themselves.  We have no useful reference for how many that is, but we know it's a lot!  But it's not, really.  That more than a thousand mentioned before hits us so hard because we think immediately.  My neighborhood contains 900 homes (more or less).  If one thousand of those kids are going to die from abuse and neglect this year, then that's an entire generation.  Two hundred thousand HIV cases extant in the US is beyond my capacity.

But those raw numbers are not in their proper context.  They're supposed to shut your brain down, because they want you to stop thinking for a moment and blindly agree to whatever they're saying.  That one thousand number is Nationwide.  Nationwide, there are more than three hundred million people.  Let me put that as a number:  300,000,000!  One thousand is three ten thousandths of a per cent of that number.  If you attend a sell-out game at Minute Maid Park, maybe one of those people will be a victim of life-threatening abuse or neglect. 

Made-up Numbers and Prestidigitation
Of course, since the Congressman doesn't cite a source, we don't have to believe that number at all.  It's easy to make up numbers.  Seven out of every ten quoted numbers have no citation or basis in reality.  See?  I pulled that number out of my ass.  I have no idea how many numbers are real or made up.  Seven out of ten struck me as a good number because it's more than half without being so alarmingly high that it makes you check my sources (or find your own, since I didn't cite any sources). 

Even if sources are cited and they match the number quoted, they ay still not be accurate because they may be out of date.  With six or seven billion people worldwide, it would be impossible to maintain a completely accurate survey of anything.  By the time you finished counting, you'd already be out of date and have to start again.  So they use statistical data.  The theory being that if you get a significant random sample of a population, you can expand that sample to represent the entire population.  That's all well and good, but it assumes a lot of things.

For one thing, it assumes that you can get a truly random sampling of the population.  The US Census Bureau tries to do that with the long-form demographic census survey every ten years, and with the intermediate surveys they conduct constantly.  They themselves admit that there is a built-in possibility of error in those samples.  A search for "collection" methods on the US Census Bureau site comes up with more than five thousand hits on various pages.  Any statistical sample will have a built-in probability of error; unfortunately, that probability is statistically derived, and doesn't include any human-error or misuse factors.  When you see "Possibility of error:  3%" posted under a newspaper or TV poll, you have to understand that that possibility is derived from the size of the sample alone.

More to the point, very few samples are even truly random.  The Census Bureau sample generator has a built-in function that excludes any home that has been surveyed in the last five years.  Most marketing surveys have demographic quotas.  Almost all national samples are limited by regional differences and the cost of long-distance communication.  World-wide sampling is even more difficult.  We live in a technologically advanced nation.  There are still places in the world where we have no idea what their population is because a full census can only be accomplished by helicopter or longboat.  And we certainly don't know what these folks are thinking.

And some numbers are designed not to be understood.  US Budget numbers, especially.  You would expect that the Federal budget worked like your own budget.  You sit down, figure out how much you spent, and how much you made, then work out how much you can expect to make next year and cut or add to the various budget lines as needed.  Wrongo!  The Federal Budget is determined first by a baseline, which (along with a few arcane twists and turns) essentially sets a spending level for each item at a certain percentage above last year's rate.  If the National Office of Paper Clip Safety had a budget of $30 million last year, then it will probably have a baseline of $40 million this year, based on inflation and the expected increase in the number of paper clip emergencies.  In this way, by removing $5 million from the baseline budget figure, your incumbent congressman can say he voted to slash that part of the budget by 12.5% and his opponent can say that he actually voted to increase the budget by 16.7% and both of them will, technically, be telling the truth.  Neither of them mentions that the congressman is using the baseline figure for his statement and that the challenger is using last year's actual budget.  (There's also off-budget spending, which allows Congress to make actual cuts to the budget without actually reducing spending, but that's a whole different discussion.)

Like doctored photographs and out-of-context video- and sound-bytes, numbers can lie.  And the worst part of it is that the lies are generally more or less effective because we've become accustomed to trusting numbers as factual references.  And there we have a problem.  How can we minimize the effect of bad numbers without all of us becoming cynical skeptics looking for redskins behind every tree?  Nine out of every fifteen economists named Steve say we can't.