Friday, January 30, 2009

Innumeracy

This isn't a particularly Jewish topic, but it bugs me. And I'm seeing it more and more, in connection with the economic downturn and the political blaming surrounding it. Which is, the sloppy use of numbers to make politico-economic points. It only hurts one's own argument, to be presented with innumeracy (numerical illiteracy):

First example: a conservative Facebook friend wrote:

The so-called budget surplus under Clinton... well, the national debt rose from $4 trillion to $5.6 trillion during Clinton's time in the White House. How exactly that equates to a budget surplus is the kind of sleight of hand that economists are famous for

To which I responded:

Budget deficit/surplus is figured ANNUALLY, while the National Debt is CUMULATIVE.

So the small surpluses deducted small amounts from the national debt. Nowhere near enough to wipe it out, but at least Clinton's budgets didn't add to it, the last two years.

* * *

Second example, in a published Yahoo News story:

Headline:

Q4 GDP down 3.8 percent, biggest drop since 1982

From the first paragraph:

The Commerce Department on Friday said gross domestic product, which measures total goods and services output within U.S. borders, plummeted at a 3.8 percent annual rate, the lowest pace since the first quarter of 1982, when output contracted 6.4 percent. GDP fell 0.5 percent in the third quarter.

There's a difference between CHANGE and RATE OF CHANGE. But that has eluded this writer. A 3.8% rate of change means that the GDP fell 0.95% (which is 1/4 of 3.8) during the fourth quarter. And it's not just a question of "the headlines are written by someone else," but later in the article we get this gem:

Analysts polled by Reuters had forecast GDP contracting 5.4 percent in the fourth quarter.

By 5.4%? Or at an annualized RATE of 5.4%, which would be a CHANGE of (5.4/4) or 1.35%?

If analysts were predicting a change of 5.4%, and we got a change of 0.95%, we're doing way way better than the analysts thought. If they predicted 1.35% and we dropped 0.95%, then we're still doing better, but not as dramatically.

If a car is moving 30 mph now, which is about 43 ft/sec, and 60 mph 1 minute later, it has CHANGED its speed by 30 mph, but has ACCELERATED (the word for rate of change of speed) by (43/60) ft/sec2, or 0.717 ft/sec2. Which is a very gentle acceleration.

Economics is largely a numbers game. When discussing it, it behooves one to make sure that one's assumptions are consistent, and that one's reportage of numbers is numerically consistent.

John Allen Paulos has made a name for himself writing about innumeracy. Read, and learn.

3 comments:

Micha said...

In the first case, the debt rose. Doesn't that mean that whatever surplus Clinton had in some years, the total deficit in others had to be greater by a total of $1.6bn?

-micha

Garnel Ironheart said...

There are lies, damn lies and then there are statistics.

Mark Twain

thanbo said...

Micha: No question, the debt rose. Because, as I said over and over, debt is CUMULATIVE, deficits are ANNUAL.

My correspondent wanted to deny that there were ANY budget surpluses because the total DEBT had risen in those years when there were deficits.

Garnel: To that end, I also suggest "How to Lie with Statistics", another mathematical classic that is easily accessible to most readers.