Friday, April 15, 2005

Bad math, tax cuts, ANWR and a mathematical brain teaser.

(NOTE: Due to an increasing workload, blogging will be a little more sporadic than normal over the next while, but I'll always find the time to smack people who deserve smacking.)

We're all familiar with the idea that there are three kinds of lies -- lies, damned lies and statistics -- and this post is about that third kind. It's about how you can be an absolute weasel when it comes to providing mathematical or statistical "evidence" while still being technically honest. By way of explanation, consider an example.

Back in January of 2003, the Bush administration (a.k.a. "The Gang that Couldn't Think Straight") crowed about Bush's proposed tax cuts, which promised some 92 million taxpayers tax cuts with an "average" value of $1,038. Now, while this figure might have been technically correct, it was more than a little misleading since that "average" took into account the massive tax benefits to the super-rich and the almost negligible benefits to the not-so-super-rich. As the AFL-CIO pointed out here:

According to an analysis by the nonprofit group Citizens for Tax Justice (CTJ), the top 1 percent of American taxpayers—making $374,000 or more annually with an average income of $1.1 million—would save more than $30,000 a year in taxes under the Bush plan. But typical taxpayers—those with incomes of $29,000 to $46,000 a year—would save only $289. And those making between $16,000 and $29,000 would keep just $99.

The Bush administration has asserted repeatedly that "92 million taxpayers would receive, on average, a tax cut of $1,038 in 2003." But this information is misleading, according to the nonprofit Center on Budget and Policy Priorities (CBPP), because the administration has averaged the big tax cuts going to those at the top of the income spectrum with the far more modest ones going to those in the middle, plus the very smallest tax cuts going to working families with low incomes.

Yeah, it's those details that are always useful to know. But, technically speaking, what Bush said was exactly correct and that's the point here -- the best kind of statistical and mathematical deception is the kind that you can still defend with a straight face as being accurate, even when you know it's meant to bamboozle.

Here'a another example, ripped from the pages of CNN (Motto: "We don't suck as bad as Fox, but it's not for lack of trying."). Remember this little gem? Where CNN used the really tired device of messing with the values on the Y-axis of the graph to make a really stunning visual display? Once again, technically, the graph's values are correct, but it's painfully obvious what the statisticians were up to here. See the pattern? Accurate values, presented in the most misleading way imaginable.

Which brings us to my latest example, involving oil drilling in the Arctic National Wildlife Refuge (ANWR) and an absolute beaut when it comes to sleazy data presentation. As most Americans who aren't in a persistent vegetative state are probably aware, there's a roiling debate at the moment about whether or not to open up ANWR to oil exploration, with defenders of drilling talking about how this will lessen the U.S.'s dependence on foreign oil. As if.

Now, people on both sides of the debate agree that there is an estimated 10-11 billion barrels of oil that might be technologically recoverable from ANWR. This number seems to impress a disturbing number of Americans for which the suffix of "illion" generally causes their brain to shut down and their mouth to make a sound something like "Ooooooooh!" But is this amount really all that impressive?

Since, according to reliable figures, the U.S. consumes some 20 million barrels of oil per day, and if we're generous and accept a figure of 11 billion barrels in ANWR, it doesn't take a rocket surgeon to calculate that ANWR, optimistically if everything works out, represents a total supply to the U.S. of about 550 days.

That's a year and a half.

That's not that impressive. In other words, oil interests are howling and foaming at the mouth for the chance to tear up ANWR for what might represent a total of 1.5 years worth of oil, no more. One and a half years worth of oil is not going to lessen American dependency on foreign oil in any meaningful way and it's likely that, if the average American were made aware of how little effect ANWR would have on oil supply, they might not be all that excited about it. So how to bamboozle the average American? You guessed it -- hit them with a misleading table.

One of the best examples of this is over at the web site which, despite its name, isn't run by ANWR itself. Rather, it's run by reps of the oil and gas industry whose goal is to make the idea of drilling in ANWR as appealing as possible. And how do they do that? With mathematical sleight of hand, naturally.

Obviously, if you want support for drilling in ANWR, you really, really, really don't want people to know there's only a year and a half worth of oil there. Instead, you give them the table "How many years could your state run on ANWR oil?", which purports to show how many years ANWR would satisfy the petroleum needs of any individual state.

Now, while the numbers may be accurate, a more worthless example of data representation would be hard to find. What conceivable value is it to know that ANWR would keep the residents of, say, New Mexico happy for 222 years? Or North Dakota for 399? Or the District of Columbia for 1710?
Representing the potential of ANWR this way is just a tacky way of being able to toss out large numbers and hope no one notices how meaningless they are. And, you'll notice, nowhere on that page does the figure of "1.5 years" rear its ugly head, and for good reason. That's the very value you're trying to conceal, so you do it with a blizzard of larger but stupider values.

And the beauty of this table is (and you knew this was coming) that the numbers themselves are correct. Of course they are, that's the whole point of this exercise: the values are technically correct while being as dishonest as possible. Why else would anyone go to such trouble to avoid saying something as simple as "one and a half years"? But there is one way to defend oneself from mathematical dishonesty like this.

Even if all you get are the values from that table, you can make at least one obvious observation. If you wanted at least a limit on how long ANWR could supply the entire U.S. with oil, it's trivial to scan the table for the smallest value and use that as the obvious upper bound. That distinction belongs to Texas, which ANWR could supply for a whole nine years, which means (and please don't debate this upcoming point) that ANWR could supply the entire U.S. for at most nine years. Please tell me you got that -- if ANWR's only good for nine years exclusively for Texas, it's not hard to conclude that it would be good for less time than that covering the whole U.S. (And, hard to believe as it may be, I'm quite prepared for some freeper to argue that point. Just wait for it. It's coming. Yeah, I'm looking at you, Weasel Boy.)

But even being wildly generous and giving ANWR credit for nine years worth of oil for the whole country still doesn't really represent a major shift in dependency on foreign oil. That's still less than a decade, so it's not clear how that's going to solve any long-term problems. Face it -- no matter how much lipstick you put on this pig of a table, the bad news is right there if you just look for it. And here's where the mathematical puzzler comes in.

As I've pointed out, whoever came up with this table was clearly trying their damndest to hide the 1.5 year limit on ANWR oil. But even without knowing that value, just a glance at the table shows that the national limit has to be at most nine years based solely on Texas, right? That's kind of a no-brainer.

But if you were being clever, how could you use the values in that table to come up with a more accurate upper limit on the number of years ANWR could supply the entire U.S.? You don't need to know the total number of barrels in ANWR and you don't need to know the average daily U.S. consumption. Just the numbers in the table alone, and nothing more, are enough to let you at least start getting a better upper limit.

So who's the clever math weenie, and how do you do it?


Cori said...

The innumeracy of Americans (and I mean American in the sense of Unitedstatesian) is the biggest aide in letting the Republicans pull off all of their shenanigans. From electoral fraud, to Social Security, to tax cuts, to ANWR. You name it, and the main reason the people are fooled, is because they don't understand basic numerical concepts.

I'll see if I can find some time today to work on your problem, but work has been pretty heavy this week.

Cori said...

OK, got it.

If, for example, TX will use the oil in 9 years, that means that it will use 1/9 of the oil in 1 year. The same with all of the other states, plus D.C.

So, here's the method:

1)divide 1 by the number of years listed in the table for each state. This will give the fraction of oil each state will use in a year. (Putting it all in decimal form will make the next step easier.)

2)Add up all of the resulting fractions. This will generate the fraction of all of the oil that will be used in 1 year by all of the states. The answer is 0.692.

3) Divide 1 (representing 100% of the oil) by 0.692. The answer is 1.445 years, or slightly under a year-and-a half.

Not bad for an art shcool graduate, huh?

CC said...

Not bad. Now, about that spelling ...

Anonymous said...

when it comes to providing mathematical or statistical "evidence" while still being technically honest

I wouldn't call it 'honest'.

Cori said...

d'oh. that's "school".