Friday, January 17, 2003

Dead Horses, Alive and Kickin’

As a New Year’s resolution, D-squared has posted a list of propositions (scroll down a bit) that are so “bleedin’ obvious” that he refuses to get drawn into another pointless debate about any of them. Now, on the one hand, I’m highly sympathetic to the notion that some arguments just aren’t worth having. It irks the hell out of me when someone suggests that I’m narrow-minded because I’m no longer willing to consider the possibility that communism might really be superior to capitalism. I considered it once… and rejected it. I considered it again... and rejected it. I considered it umpteen more times… and rejected it. How many times must I perform this exercise before I can be considered open-minded? My brain-time is better spent considering the dozens of other propositions on which I’m as yet undecided.

Nonetheless, I can’t help but be shocked by some of the things D-squared considers “obvious.” Not probably true, or even very likely true, or true if you give it lots of careful thought, but “obvious.” Let me pick just three of D’s proposition and see if I can clear the very low hurdle of non-obviousness.

“That people making employment decisions are for the most part (probably unconsciously) racist in the way in which they make those decisions.” Wow. It’s one thing to say that racism still exists, that there exist some people whose decisions are motivated mostly by racism, or that most everyone harbors some amount of residual racism. But this is supposed to be a general proposition about “people making employment decisions,” and the claim is that they are *for the most part* racist. That’s an incredibly damning statement about an incredibly large and diverse group of people.

“That college admissions have never in the history of the world reflected ‘ability’ in the abstract, even if such a metaphysically dubious quality were to exist and that nor [sic] will they ever in the future, whatever happens to government policy.” Hmm. Okay, college admissions are indeed based on a variety of merit-irrelevant matters, such as race, geography, celebrity, alumni parentage, and so on. But in addition to these criteria, standardized test scores and GPAs are also used. And while these are far from perfect measures of ability, they do bear some correlation to ability, no? And if that’s the case, then college admissions almost assuredly “reflect” ability to some degree. Do a regression of college admissions for any selective university, with race, gender, parentage, etc., plus GPA and SAT scores as the explanatory variables; I’ll bet that the coefficient on GPA or SAT or both is positive and statistically significant.

“That the transatlantic slave trade was the moral responsibility of those who profited the most from it, and that it was the proximate cause of the American Civil War.” Okay, I’ll buy the first half, but as for the second… well, let me put it this way: the transatlantic slave trade ended (at least for the U.S.) in 1808. After that, most new slaves were the children of old slaves. The Civil War began in 1861. Are we using the same definition of the word “proximate”?

Enough. Suffice it to say that there’s a barrel of non-obviousness in virtually every one of D’s propositions -- even on the handful I agree with (in whole or in part).


The Anal Film Critic

I thought I had the whole Disney Dalmatian movie nomenclature straight. The original 1961 animated movie was called “One Hundred and One Dalmatians.” The 1996 live-action version with Glenn Close was called “101 Dalmatians.” And, just to confirm the alphabetic v. numeric distinction, they made a live-action sequel called “102 Dalmatians.” I figured if they ever made an animated sequel, it would be called “One Hundred and Two Dalmatians.” But now Disney’s just released a straight-to-video animated flick called “101 Dalmatians II.” And after doing a little poking around, I discovered that they’ve given the original 1961 animated version an alternative title, “101 Dalmatians,” which is indistinguishable from the 1996 live-action title. (I haven’t figured out when this renaming took place.)

Am I the only one who’s bothered by this kind of inconsistency and confusion? Is anyone else still bothered by the fact there’s a movie called “Rambo III” when there was never a movie called “Rambo” or “Rambo II”? And am I myself being inconsistent when I grouse about Stephen Spielberg’s having renamed “Raiders of the Lost Ark” as “Indiana Jones and the Raiders of the Lost Ark” to achieve retroactive consistency with the subsequent Indiana Jones movies?


Wednesday, January 15, 2003

More on Statistical Injustice

A reader responds to my post below about false positives: “That's why you test each positive at least one more time - the odds for a double-false positive are extreme. … Of course universal testing generates false positives. The idea that one test alone is sufficient for punishment is ludicrous.”

Absolutely correct, though I’m often amazed at how often ludicrous laws get passed by legislatures and school boards. (I’m thinking specifically of the southern state that passed a law setting the value of pi at 3.14.) I wouldn’t be at all surprised to hear that school districts with across-the-board drug testing suspended athletes immediately upon their getting a positive test result. Does anyone out there know the standard practice?

Also, testing a second time shrinks the problem substantially, but does not eliminate it. By my calculations (and using Brad DeLong’s hypothetical numbers again), someone who gets two positive test results in a row still has an 8% chance of not having the disease. That’s about one person in every twelve. Also, my calculations are based on the assumption that the two tests’ results are independent events, which may not be the case – it might be that the false positive is triggered by the presence of a particular protein in your blood, for instance. (I’m not a doctor or a biologist, so I don’t want to make too strong a claim here, but it seems reasonable to think that false negatives and false positives are caused by something, and that something may be related to your physiology.) Fortunately, there may exist alternative tests for the same condition, as my reader observes elsewhere in his email, and such alternatives may be both more accurate and more likely to constitute an independent event.


Uh ... Did I Just Score?

Last week I celebrated this blog's 2000th post. Earlier today, the counter was somewhere in the 2100s or 2200s, I think. But as of a few minutes ago, the counter stood at 3270! (That's an exclamation point, not a factorial sign.) What's going on? I'm thinking this must be a glitch in the counter.

UPDATE: Apparently I did score. A couple of readers let me know that my post on Raelians was linked by Instapundit. I'm thinking I probably owe thanks to Julian, who linked the same post on his much-higher-traffic blog. (Higher traffic than my blog, that is, not higher than Instapundit!)


Tuesday, January 14, 2003

Statistical Injustice

Brad DeLong has an ongoing series of One Hundred Interesting Mathematical Computations on his website. Two of the most recent jumped out at me.

First, in OHIMC #10, he describes the letter-switching paradox that I mentioned in a previous post. And unlike the website I cited that time for explanation (because I was too lazy to describe the whole problem and its solution), he gets the moral of the story right.

Second, in OHIMC #9, he describes the false-positive problem that arises in the context of tests for disease. The bottom line is that even if you test positive for a disease, there is actually a surprisingly high chance that you don't have it. The reason, in a nutshell, is that for most diseases - even ones considered epidemics - the vast majority of the population does not have it. As a result, even a small false-positive rate will result in a very large absolute number of people testing positive even though they are disease-free. Even if the test correctly identifies all people who have the disease, they are likely to be a small group compared to those who were false positives. (If this doesn't make sense, go to DeLong's site and follow the math.)

What DeLong doesn't mention is that the false-positive problem is most acute when someone takes a test for a disease without having any particular reason to think he might have it. If there is some a priori reason for thinking you have the disease (e.g., the test is for HIV, and you've been having lots of promiscuous unprotected sex and sharing needles), then the problem is not as severe, though it still exists. I think this is especially relevant in the context of proposals to, for instance, test all school athletes for steroids or drug use. Quite aside from the legal and ethical problems related to invasion of privacy, policies like these will almost assuredly punish far more innocent students than guilty ones. Taking DeLong's sample numbers, but replacing "disease" with "drug use," testing 10,000 athletes would lead to the punishment of 49 drug-users and 199 non-drug users. Of course, DeLong's numbers are only hypothetical; if a larger percentage of the whole athlete population used drugs than in the example, the disparity would not be as severe. But the qualitative result will be the same: lots of innocents getting punished.

Thus, the notion of "probable cause" has statistical as well as legal value. Restricting drug and steroid tests to those students who have evinced other signs of use would at least reduce, though not eliminate, the disparity in punishments meted out. Across-the-board testing is not just a procedural injustice; it also leads to greater substantive injustice.


Monday, January 13, 2003

Those Wacky Raelians

So the Raelians -- you know, the religious cult that claims to have created the first human clone -- believe that scientifically advanced extra-terrestrials manipulated DNA in order to create all life in Earth. Wow, that's really crazy. Don't they realize that life, along with everything else in heaven and earth, was actually created in just seven days by an omniscient, omnipotent being, who later had a mortal son, who died, was buried, rose from the dead, and ascended to heaven?