<p>
2.3% falls above 2 standard deviations in a normal distribution. You are probably thinking of the combined amount that falls out of the +/- 2SD range – the sum of the amount below -2SDs and the amount above +2SDs.</p>
<p>
If low achieving students are dropping out of HS and/or not taking the ACT/SAT, then most of this group is not going to attend college, so they do not appear in the study’s +/ # SD range, comparing how far an individual’s score differs from mean at that college. For example, suppose a kid with a 1550 SAT chooses to go to a local state school, such as SUNYSB, instead of a more selective college. SUNYSB has a mean combined score of ~1250 and 75th percentile combined score of ~1350, so using the methodology described in the study (they mention basing SD estimates off 25th and 75th percentile reported in IPEDS), the student’s 1550 SAT would be estimated as ~+2.0 SDs above the mean of this school. 1550 is among the top ~0.3% of test takers (not including super scoring) in the United States and probably better than top 0.2% of the full US HS population in SAT dominant states, but the score barely makes it in to +2SDs at SUNYSB.</p>
<p>
The study found only a 0.5% difference in graduation rate between students who chose a college with low scores over a college with a mid or high scores, when controls were added for similar student characteristics and similar institutional characteristics (besides test scores). However, in reality the institutional characteristics will tend to vary between more and less selective colleges. Without institutional controls, the difference in grad rate for a particular student increased to 3% – not exactly a huge difference. I’m sure there are still graduation rate issues in low income students, but the study suggests those issues generally do not relate to choosing colleges whose SAT score ranges do not match well with their own score. </p>