an extra 10pts on your total SAT is worth an odds ratio of 1.282
We can check this interpretation by taking it to the 30th power, and seeing if we recover something sensible; unfortunately, that gives us an odds ratio of over 1700! If we had their beta coefficients, we could see how much 10 points corresponds to, but it doesn’t look like they report it.
Logistic regression is a technique that compresses the real line down to the range between 0 and 1; you can think of that model as the schools giving everyone a score, admitting people above a threshold with probably approximately 1, admitting people below a threshold with probability approximately 0, and then admitting people in between with a probability that increases based on their score (with a score of ‘0’ corresponding to a 50% chance of getting in).
We might be able to recover their beta by taking the log of the odds they report (see here). This gives us a reasonable but not too pretty result, with an estimate that 100 points of SAT is worth a score adjustment of .8. (The actual amount varies for each SAT band, which makes sense if their score for each student nonlinearly weights SAT scores. The jump from the 1400s to the 1500s is slightly bigger than the jump from the 1300s to the 1400s, suggesting that at the upper bands differences in SAT scores might matter more.)
A score increase of .08 cashes out as an odds ratio of 1.083, which when we take that to the power 30 we get 11.023, which is pretty close to what we’d expect.
I think I once calculated that a difference of one standard deviation in IQ between groups A and B leads to a difference out at 3 deviations for A vs 4 deviations for B, what is usually the cutoff for ‘genius’, of ~50x.
Two standard deviations is generally enough to get you into ‘gifted and talented’ programs, as they call them these days. Four standard deviations gets you to finishing in the top 200 of the Putnam competition, according to Griffe’s calculations, which are also great at illustrating male/female ratios at various levels given Project Talent data on math ability.
I’ll also note again that the SAT is probably not the best test to use for this; it gives a male/female math ability variance ratio estimate of 1.1, whereas Project Talent estimated it as 1.2. Which estimate you choose makes a big difference in your estimation of the strength of this effect. (Note that, typically, more females take the SAT than males, because the cutoff for interest in the SAT is below the population mean, where male variability hurts as well as other factors, and this systemic bias in subject selection will show up in the results.)
Thanks for the odds corrections. I knew I got something wrong...
Two standard deviations is generally enough to get you into ‘gifted and talented’ programs, as they call them these days.
G&T stuff, yeah, but in the materials I’ve read 2sd is not enough to move you from ‘bright’ or ‘gifted and talented’ to ‘genius’ categories, which seems to usually be defined as >2.5-3sd, and using 3sd made the calculation easier.
Eh. MENSA requires upper 2% (which is ~2 standard deviations). Whether you label that ‘genius’ or ‘bright’ or something else doesn’t seem terribly important. 3.5 standard deviations is the 2.3 out of 10,000 level, which is about a hundred times more restrictive.
I’d call MENSA merely bright… You need something in between ‘normal’ and ‘genius’ and bright seems fine. Genius carries all the wrong connotations for something as common as MENSA-level; 2.3 out of 10k seems more reasonable.
We can check this interpretation by taking it to the 30th power, and seeing if we recover something sensible; unfortunately, that gives us an odds ratio of over 1700! If we had their beta coefficients, we could see how much 10 points corresponds to, but it doesn’t look like they report it.
Logistic regression is a technique that compresses the real line down to the range between 0 and 1; you can think of that model as the schools giving everyone a score, admitting people above a threshold with probably approximately 1, admitting people below a threshold with probability approximately 0, and then admitting people in between with a probability that increases based on their score (with a score of ‘0’ corresponding to a 50% chance of getting in).
We might be able to recover their beta by taking the log of the odds they report (see here). This gives us a reasonable but not too pretty result, with an estimate that 100 points of SAT is worth a score adjustment of .8. (The actual amount varies for each SAT band, which makes sense if their score for each student nonlinearly weights SAT scores. The jump from the 1400s to the 1500s is slightly bigger than the jump from the 1300s to the 1400s, suggesting that at the upper bands differences in SAT scores might matter more.)
A score increase of .08 cashes out as an odds ratio of 1.083, which when we take that to the power 30 we get 11.023, which is pretty close to what we’d expect.
Two standard deviations is generally enough to get you into ‘gifted and talented’ programs, as they call them these days. Four standard deviations gets you to finishing in the top 200 of the Putnam competition, according to Griffe’s calculations, which are also great at illustrating male/female ratios at various levels given Project Talent data on math ability.
I’ll also note again that the SAT is probably not the best test to use for this; it gives a male/female math ability variance ratio estimate of 1.1, whereas Project Talent estimated it as 1.2. Which estimate you choose makes a big difference in your estimation of the strength of this effect. (Note that, typically, more females take the SAT than males, because the cutoff for interest in the SAT is below the population mean, where male variability hurts as well as other factors, and this systemic bias in subject selection will show up in the results.)
Thanks for the odds corrections. I knew I got something wrong...
G&T stuff, yeah, but in the materials I’ve read 2sd is not enough to move you from ‘bright’ or ‘gifted and talented’ to ‘genius’ categories, which seems to usually be defined as >2.5-3sd, and using 3sd made the calculation easier.
Eh. MENSA requires upper 2% (which is ~2 standard deviations). Whether you label that ‘genius’ or ‘bright’ or something else doesn’t seem terribly important. 3.5 standard deviations is the 2.3 out of 10,000 level, which is about a hundred times more restrictive.
I’d call MENSA merely bright… You need something in between ‘normal’ and ‘genius’ and bright seems fine. Genius carries all the wrong connotations for something as common as MENSA-level; 2.3 out of 10k seems more reasonable.