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This relates to tk21769 dividing the rate of S&E PhDs by the rate of 700-800 math SAT scorers. So if a college had no students who scored 700+ on math, then that college would rank above all ivies/Stanford/MIT/top 50 USNWR/… under this system (assuming at least 1 student received a PhD). The top ranked college (Allegheny ) only had 8% above 700 math. HYPSMC… type colleges tend to have about 10x more 700+ scores, so Allegheny only needs ~1/10th the rate of PhDs as HYPSMC… to rank above HYPSMC… under this system. </p>
<p>If you want to control for SAT score, a more meaningful system might be identifying the typical rate of PhDs for colleges with similar SAT scores, and measuring how the PhD rate for a particular college differs from this typical rate. That said, I’d expect a variety of other criteria to correlate with the rate of S&E PhDs besides test scores, such as the proportion of students in S&E majors, and possibly the proportion of international students (one study found ~2/3 of engineering PhDs students in the US do not have a visa for remaining in the US after college).</p>