The scores I picked were noted in the paper; I should have mentioned this but I was late for collecting kids:

Originally Posted by Bui et al.
Students can meet eligibility requirements in one of two ways. The first is having 56 total matrix points, including at least 16 points from the Stanford Achievement Test or Aprenda and 10 points from the NNAT.

Alternatively, students can qualify by having 62 total matrix points regardless of Stanford, Aprenda and NNAT scores.

So in reality, scores can be even lower than 62 for the GT program. In fact, the scores seem deliberately set up to catch kids with the 70th percentile scores on the SAT, 104-107 on the NNAT, 80-84% on their report cards, a strong teacher recommendation, and 15 bonus points. Add it up on page 32: you get 56.

By way of comparison, an IQ at the 70th percentile (15 point SD) is 108. A 35 year-old white woman who is ~5'5.5" tall is at the 70th percentile. For a white man, it's 5'11". Taller than most but not super-tall. Stuff clusters very tightly around the average when you have a normal distribution of data, and even 20 percentage points above average is still not too far away from there. (You would expect a normal distribution for scores on standardized tests; they make them that to be way).

For comparison, one standard deviation (84th percentile/IQ of 115 or height of about 5'7" or 6 feet) IS starting to move away from the average. Two standard deviations is an IQ of 130 or a male height of 6'3." Now THAT'S tall by white people standards.

IMHO, a score of 56 or 62 on this scale are very, very low for the purposes of defining someone as "gifted." This is merely kind-of-maybe-above-average.

Note also that you get three bonus points just for being in a minority group, so the qualifying score gets pushed down a bit more for some of the students.

Sure, you could play with the numbers and use high scores in one area and low scores in another. But you could also push some scores below the 70th percentile (0 points) and put some in the next score band to compensate up to 62.

The point is that the authors claim to be reporting on "high achievers," but they weren't. They were focusing on average-ish achievers.

The school district clearly set up the cutoffs to catch a lot of average-ish kids, and they're the ones most likely to score at the low end of this particular scale. Sure, there were probably a few gifties in the group the paper studied, but most of them probably weren't. Why? Well, if you define gifties as only 3% of the population, then at most a small number of the entire GT group would be gifted. Then remove anyone with a score over 72, as the authors seem to do, and you lose a lot of the gifties.

So the real question they studied was: "Did inclusion in a GT program in a large urban school district raise test scores among average students?" Their answer was "No."