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[quote=Anonymous][quote=Anonymous][quote=Anonymous]PP here.  Thanks for the correction on my estimate of 3,000 perfect M+R SATs to the 1,922 that you report.  I believe that the right comparison is between the 1,922 and roughly 1/2 of the Presidential Scholar's nominees, because roughly half qualified based upon ACT scores.  Let's gross the "perfect board score" up to 3,000 for this analysis to account for the ACT component.  And here is why the CA cutoff must be 1600.  If you take the [b]Top 40 plus ties[/b] methodology that they use, it must mean that the 41st person must have had the same score as the 40th.  In the hypothetical case that the 40th person scored 1590 or lower, then that would mean that 39 students or less scored 1600.  This would then imply that CA had 39 of the 3,000 "perfect scores" or 1.3% versus 12% of US population.  Even if you use the 1,922 pre gross up number, it would only represent 2.0% of recipients.  1600 as a cutoff is the only way to get the math to work.[/quote]
You make a very persuasive point about how assuming a 1590 cutoff for CA would suggest that CA students account for only 1.3% of the 1600s versus 12% of the population.  But isn't the alternative just as surprising?: If we assume a 1600 cutoff for CA, then CA students account for 23.5% of the 1600s versus 12% of the population.  Even if we skim some off for the ACT (and perhaps there's good data on ACT results too), those numbers seem off-base.

But in the end, even though either CA scenario seems odd, I suppose one must be correct.  I suppose we could consider the population % part of the analysis too, to see if it makes sense.  Does CA's 12% of US population strike you as fitting a normal representation of SAT scores?  And since we know it likely cannot be that CA is supplying a truly proportional % of the 1600s -- since we know it's either roughly 1.3% or 23.5% -- which appears more likely?  I tend to think of CA's top-end students as pretty smart, which might suggest the 23.5% number makes more sense.  But on the other hand, I also suspect that a big piece of CA's population is not even taking the SAT, much less scoring 1600, which suggests the 1.3% number might make sense too.[/quote]

There are a lot of smart kids in CA:
http://www.huffingtonpost.com/2014/01/23/schools-highest-sat-scores_n_4654077.html[/quote]

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