SAT and ACT: How Hard Are They Scraping The Bottom Of The Barrel And Are They Finding Any Diamonds In The Rough?
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There was recently some publicity over the national average SAT and ACT college admission test scores dropping. The Unsilenced Science has a vast post with dozens of graphs on the latest SAT and ACT college entrance scores by demographics and state. 

However, there has always been an issue with tracking changes in average SAT/ACT scores in that not everybody takes either of the two tests, and (increasingly) some students take both tests.

However, in the comments, The U.S. and I go back and forth on how to deal with this perpetual stumbling block in SAT/ACT analyses and he points out that a number of states have recently made the SAT or ACT mandatory. 

Here are the significant, single-year participation changes: Colorado’s ACT participation went from 62% to 99% in 2002, and its ACT score fell from 21.5 to 20.1. (SAT-ACT composite fell from 501 to 472.) Illinois went from 71% to 99% in 2002 with a drop from 21.6 to 20.1 (498 to 464). Kentucky went from 72% to 100% in 2009 with a drop from 20.9 to 19.4 (478 to 444). Michigan went from 70% to 100% in 2008 with a drop from 21.5 to 19.6 (492 to 448). Utah went from 73% to 97% in 2012 with a drop from 21.8 to 20.7 (493 to 469). Maine SAT participation went from 73% to 100% in 2007, and its SAT-ACT composite fell from 501 to 469. Delaware went from 74% to 100% in 2012, and its SAT-ACT composite fell from 492 to 465. In fact, Arizona’s ACT participation more than doubled between 2009 and 2011 from 15% to 34% with a similar drop from 21.9 to 19.7. (The SAT-ACT composite went from 508 to 474 as SAT participation went from 26% to 28%.)
I'd never seen that data before and it's pretty interesting. I responded, doing some top of the head calculations:
So from this we can calculate the average score of the incremental test takers. For example, in Illinois, when 71% took the SAT, the average was 21.6, but when 99% took it, the average fell to 20.1. So, all else being equal, that means the incremental 28% averaged a 17, which is 4.6 points lower than what the 71% averaged, and 4.6 is pretty close to one standard deviation.  
If the additional 28% came from the bottom of the distribution, the 2nd to 28th percentiles, then the median of the incremental test takers would be about the 14th or 15th percentiles overall, while the median of the previous 71% would be about the 64th percentile. That would imply a drop of around 6 to 6.5 points, maybe, but instead the drop was about 3/4ths of that. So, some of the incremental scorers came from above the bottom 28% — although not too many.  
It would be interesting to see if this law made any measurable increase in high scorers (above 30 or above 25) and which race they most came from. I'm betting offhand that the new law rousted more semi-smart white kids into taking the ACT than other races. Probably kids who were set on going into the Army and had done well on the AFQT, that kind of thing.

Keep in mind that 100% participation doesn't mean 100% of all 17 year olds in the state take the SAT or ACT, just, I'm presuming, 100% of the non-dropouts.

So, I think the data is there to answer some questions about the remaining untested students, both including what are the likelihood of them succeeding in college and how many who have the right stuff to make it in college are being overlooked.

Secondly, this information on the scores of the bottom untested ranks should allow somebody to adjust the national figures for participation and track changes over time at the national level, which would be of obvious import.

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