The following colleges all had higher average SAT scores than Stanford (based on the midpoints of 25th-75th percentile SAT-M + SAT-CR ranges reported in their current US News “ranking indicator” entries), notwithstanding higher admission rates than Stanford’s:
1545 (1490-1600) Caltech (99% of Freshmen were in top 10 percent of high school class)
1515 (1440-1590) Chicago (98% of Freshmen were in top 10 percent of high school class)
1505 (1410-1600) Harvard (95% of Freshmen were in top 10 percent of high school class)
1505 (1420-1590) Yale (95% of Freshmen were in top 10 percent of high school class)
1505 (1410-1600) Princeton (95% of Freshmen were in top 10 percent of high school class)
1500 (1430-1570) MIT (99% of Freshmen were in top 10 percent of high school class)
1485 (1400-1570) Columbia (93% of Freshmen were in top 10 percent of high school class)
1480 (1400-1560) Harvey Mudd (97% of Freshmen were in top 10 percent of high school class)
1475 (1380-1570) Stanford ( (96% of Freshmen were in top 10 percent of high school class)
WUSTL and Vanderbilt also appear to have higher average SAT scores than Stanford (although SAT ranges are not reported in their USNWR “ranking indicator” entries.) **The above numbers are based on 2013 data/b. Some of these positions may change slightly from year to year.
US News tracks “selectivity” by a weighted combination of SAT M+CR, class standing, and admit rates.
Their formula ignores the effects of ECs and other “holistic” inputs altogether.
I would not conclude, based only on that formula, that Caltech, Chicago or Columbia truly is “more selective” than Stanford.