Monday, April 09, 2007

Scores on the new SAT for the 2006 cohort of college-bound seniors: Sex and ethnic breakdown Send this entry to: Spurl Ma.gnolia Digg Newsvine Reddit

You can see it here. There are no surprises.

With two exceptions, each group shows a balanced profile in that it does no better or worse on Verbal than on Math, after each test has been normed relative to the entire test-taking population. The exceptions are males overall (who do about 30 points better on Math) and the group labeled "Asian, Asian American, or Pacific Islander" (about 70 points better on Math).

The rather large standard deviation of the Asian group suggests that it is in fact composed of two or more distributions. Regardless, the mean Verbal score for Asians is about 20 points lower than that for whites; the mean Math score is about 45 points higher. In fact, Math is too easy for some subgroup of Asians; a perfect 800 places an Asian only in the 98th percentile of his or her group.

The overall sex difference on Math is about 30 points in favor of males.

The white-black difference on the overall score is exactly 200 points. The Asian-black difference on Math alone is nearly 150 points.

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posted by Darth Quixote | 12:26 PM | |  

Wednesday, April 04, 2007

New GRE cancelled - the cost of attempted gap-reduction? Send this entry to: Spurl Ma.gnolia Digg Newsvine Reddit

The NYT reports that a completely revised GRE has been deep sixed, not merely delayed (read the ETS press release here). The official story is that there is some insurmountable problem with providing access to all test-takers, an issue apparently too complicated for ETS to bother trying to explain it to us. You figure, since this was such a huge project that was suddenly halted, they'd want to clearly spell out why they dumped it -- unless that's the point. Although I'm no mind-reader, the true reason is pretty obvious: the made-over test was designed to narrow the male-female gap at the elite score level, but this diluted its g-loadedness such that it couldn't reliably distinguish between someone with, say, a 125 IQ and a 145+ IQ, which is what graduate departments who rely on super-smart students worry about. Rather than admit that this psychometric magic trick went awry and lopped off a few limbs of g-loadedness, they spun a yarn about access to the test. [1]

To put this in perspective, for those who took the SAT before spring 2005 -- which is everyone here, I assume -- the New SAT now includes a Writing test with both multiple choice grammar questions and a 25-minute persuasive essay. No admissions committee is paying serious attention to this silly addition, although high schoolers obsess over it. The real changes are that the Math test no longer includes the "quantitative comparison" questions (column A, B, equal, can't tell?), and the flavor of the questions is a bit more "book smarts"-based than before. Also, the Verbal test (now called Critical Reading) has zero analogies, fewer sentence completions, and much more passage-based reading. The gutted portions are those that are more highly g-loaded, for sure in the Verbal test, and most likely in the Math test as well. [2]

We now ask why ETS intentionally stripped the SAT of some of its g-loadedness? Certainly not because they discovered IQ had little value in predicting academic performance, or that some items tap g more directly than others -- so why re-invent the wheel? Since scores on various verbal tasks highly correlate, this change cannot have affected much the mean of any group of test-takers. But if getting a perfect score required scoring correctly on, say, 10 easy questions, 5 medium, and 5 difficult (across 3 sections), a greater number of above-average students can come within striking distance of a perfect score if the new requirement were 10 easy, 9 medium, and 1 hard. I don't know exactly how they screwed around with the numbers, but that's what they pay their psychometricians big bucks to do. Now, reducing the difficulty of attaining elite scores, without also raising mean scores (as with the 1994 recentering), can only have had the goal of reducing a gap that exists at the level of variance, not a gap between means. This, then, cannot be a racial gap but the male-female gap, since here the difference in means is probably 0-2 IQ points, although male variance is consistently greater.

Certainly this reduces the power of the SAT to detect very brainy people -- those with an IQ of 145 or 160 or whatever big number you want -- but I can easily imagine that both ETS and elite universities such as Harvard were willing to trade off a bit of g-loadedness in order to close the male-female gap at the elite level. Harvard students wouldn't look stupider, of course: their prestige is based on their mean SAT score compared to those of others. And they probably have other ways of figuring out who is very brainy vs. fairly smart. (As an aside, this also explains why lots more high-scoring applicants will be rejected by top schools, another paradox that is easily, even if only partially, resolved by clear thinking.) Moreover, attending Harvard isn't all about having a 145 IQ -- a non-trivial number of their graduates will join professions that don't require eigth-grade algebra or sophisticated analysis (say, political office). So that, too, may lessen their concern over the SAT becoming somewhat less g-loaded.

Not so with the GRE -- those who score at the elite level here are hardcore nerds who are planning to do serious intellectual work, and elite graduate departments pay attention mostly to the applicant's intellectual promise. MIT's math department probably doesn't care that an applicant scored 650 on the Math portion but showed singular potential for leadership roles. So, I imagine something similar to the SAT make-over happened, only this time the professors and/or ETS' psychometricians discovered that it would make a joke of a test used to detect the very brainy in search of elite graduate work.

To make this concrete, let's assume that, among applicants to graduate school in the arts and sciences (i.e., future scholars, not professionals), males enjoy only a 0.1 SD advantage in mean IQ (or 1.5 IQ points), as well as a 0.05 SD advantage in their standard deviation. Then a test that is reliable up to 3 SD above the female mean will have 30% of those above this threshold being female. (For comparison with the real world, grad students at CalTech are 30% female.) Almost 10 percentage points can be gained by dumbing the test down so that it's only reliable up to about 2 SD, in which case 39% at the top will be female. Dumbing it down further so that it can only detect those 1 SD above the female mean just adds about 5 further percentage points; females will make up 45%. My guess is that they weren't foolish enough to toy around with a GRE that only tested up to an IQ of 115, but that they took a risk on some version that tested up to about an IQ of 130. Though that's just about enough to get you into MENSA, the real hullabaloo over sex disparities has raged within the halls of the uber-elite: Harvard (Larry Summers), MIT (Nancy Hopkins), Stanford (Ben Barres), and so on. At such an elite level, an applicant with an IQ of 130 would be like a 6'3 guy trying out for the NBA (whose mean height is 6'7). Although the NBA doesn't automatically weed out those 6'3 and under, surely the recruiters would protest to the manufacturers if their new-fangled measuring sticks only measured up to 6'3!

Pursuing this hunch, I picked up my Kaplan GRE self-study book and found out that they knew at least roughly what the new GRE was going to look like. Here were the proposed new question types for Verbal and Math:

Reading Comprehension (4 types)
Sentence Completion (2 types)

Word Problems (4 types)
Data Interpretation (2 types)
Quantitative Comparison (1 type, as before)

Notice the huge change in the Verbal test, which parallels the change in the SAT Verbal test: analogies are gone, and most of the test is reading comprehension. As for Math, they did keep the Quant Comps, but most of the new question types thereof sound too touchy-feely to be of good use: Word Problems include old-fashioned ones, plus "Free Response," "All That Apply," and "Conditional Table" (Kaplan admits they didn't know the exact names -- maybe the last was a contingency table type?). "Free Response" sounds like it would be more g-loaded since you can't rely on answer choices, but it definitely isn't, at least not if this type was to resemble its counterpart on the SAT. Here, you grid in your own answer, but only non-negative rational numbers can be gridded, precluding the use of any questions whose answer had a root or exponent or absolute value, whose trick hinged on the properties of positives vs negatives vs 0, whose answer was an equation or inequality, and most importantly whose point was abstract symbol manipulation (such as "solve for V in terms of p, q, and r"). Since females are better than males at calculation, and worse than males on more abstract math problems, "Free Response" is an easy way to obscure the male advantage at "thinking" math.

Not knowing much about what the other two new types of Word Problems are, I think it's still safe to say they were just as vacuous. In fact, the Data Interpretation problems were to come in 2 types: the old-fashioned one, and a new one called -- don't laugh -- "Sentence Completion"! For christ's sake, why not just turn some of the harder ones into Writing problems in disguise, where the test-taker corrects the grammar of a word problem rather than actually solve it! This psychometric flimflam is ultimately what all would-be gap-reducers must reduce themselves to, at least when the concern is the sex gap at uber-elite levels where those who matter will brook no nonsense over the basic tests being dumbed down.

[1] Since I'm pretty tired by now of writing about the "women in science" topic, for background info I'll just link to a very lengthy post of mine on point, plus Steven Pinker's debate with Elizabeth Spelke.

[2] See p.2 of the full PDF linked to in this post from the GNXP archives. It contains a graphic showing the g-loadedness of various cognitive tasks. Analogies are the most highly g-loaded verbal tasks, reading comprehension one of the least so (though still enough to validate its use on tests).

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