## Monday, April 16, 2007

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### Accuracy vs precision... vs truth

In science, we make a specific distinction between “precision” and “accuracy”. The former, roughly speaking, refers to the number of significant digits to which we obtain results. The latter refers to how close the results are to reality. It's easier to show it by example, somewhat oversimplified here:

Suppose I need to measure the temperature of something whose actual temperature is 84.36210349 degrees Celsius. And suppose I have a thermometer with a digital display, and the display shows four decimal places. Ideally, my thermometer would show 84.3621 degrees, and I would report it to four decimal places. I obviously can't report it to the eight decimal places that we know it to be for this example, because my thermometer isn't precise to eight places. Its precision is four decimal places.

But instead, my thermometer says 84.3607 degrees, because it's accurate to two decimal places. I have to be told what the accuracy is, lest I quote the reading with more precision than is appropriate — if my report says 84.3607, the precision exceeds the accuracy of my instrument. Instead, I just say 84.36, and everyone's happy. If my experiment needs more precision, then I have to get a more accurate instrument.

Conversely, I could have an instrument that knows the temperature accurately to four decimal places but only displays two. Accuracy and precision are different, but interrelated concepts.

Of course, in plain English we don't make much of a distinction between the two terms. We use them pretty much interchangably, with only a bit of nuance between them. I might say that “My office is on the right after a half mile or so,” and “My office is on the right after .6 miles,” are both accurate statements, but the latter is more precise.

So when Attorney General Gonzales says, as he does in his published statement that he'll give to Congress today, that he “should have been more precise” when he talked about how much he had to do with the firings of the federal prosecutors, we might not really be sure what that means. And so, in the spirit of the examples I've already given, let me give some examples to illustrate how “precision” fits in here.

Hypothetical statement: “I had something to do with the decision.”

More precise: “My input constituted 60% of the decision.”

More precise: “I decided on five of the firings, but not the others.”

Do you see how that works?

Only, the thing is, that hypothetical statement isn't what Mr Gonzales said. What he actually said was that he “was not involved in any discussions about what was going on.” In science, “0” isn't absolute, and “0.000” is a more precise way to say it. In English, though, “not involved in any” is quite specific, and precision doesn't enter into it outside of Monty Python sketches.

Well, except when Bush administration officials make statements, I suppose, because Mr Gonzales is now saying, “Of course I knew about the process because of, at a minimum, these discussions with Mr. Sampson.” Ah. Discussions with Mr Sampson, which, of course, do not qualify as “any discussions about what was going on.” Hm.

Let's try another example, then:

Actual statement: “I was not involved in any discussions about what was going on.”

More honest: “Of course I knew about the process because of, at a minimum, these discussions with Mr. Sampson.”

Fully truthful: “I knew all about it and was closely involved. I'm the boss, so what else do you expect?”

Instead we have more talk about how he “misspoke” (lied), about being unclear and confusing (lying), and about “missteps”. No, there's nothing “confusing” about what the attorney general said on 13 March. It just wasn't true. And if it were, it would be evidence that the man is unsuited to his job. Can you imagine a junior executive at a company firing 10% of his key staff without his senior-executive boss being involved in the decision? I can't; a company can't run that way, and neither can a government.

The Democratic party now has subpoena power in Congress. They need to use it liberally to open up what's really going on in the Bush administration. Make them either tell the truth or lie under oath. And then we can talk about impeachment.