Pushing the limits of the SATs at the elite schools

collegehelp · June 12, 2008, 10:41pm

Many students at Ivy League, Little Ivies, MIT, Caltech, Stanford, Duke, Chicago have pushed the limits of the SAT test. Substantial proportions score over 1560 on CR+M. This would place them roughly in the 99.5th percentile. I think there are only about 5000 students in the country out of 1.5 million who take the SATs who score 1560 or higher. (mental calculation from info on the Collegeboard website)

In a sense the SATs are too easy for these students. The SATs are not hard enough to measure their genius. Admissions officers have to be adept at identifying their special talent. The students at these schools are probably better than their high SATs indicate. They are off the charts.

Forty years ago, there were 8 million college students, now there are 18 million. Some of the increase is due to greater participation in and access to higher education. But, the increase also means there are many more of these elite students.

The following list shows the increase in undergrad enrollment 1968-2008, median SATs in 1968 and 2008, the increase in SATs adjusted for re-centering, an estimate of the proportion and number of students with SATs above 1560.

The safeties for the elite schools (the overflow schools) have probably improved their selectivity because enrollments at the elite schools increased only 55% at LACs and 75% at universities 1968-2008 while the college-going population increased 125% in the same time period.

The SATs are subject to a ceiling effect. There is an inverse relationship between how high the SAT scores were in 1968 and how much the SATs increased by 2008. The top schools had less room for growth. The correlation between 1968 median SAT and SAT increase was -.74 for both LACs and universities.

I am not trying to make any particular point, just sharing some observations to see what you think.

1968 data is from Cass and Birnbaum college guide.
Estimate of percent of students over 1560 SAT is based on assumptions for areas under the normal curve.
SATs were adjusted for re-centering by 60 from median.

Name, 1968 enrollment, 2008 enrollment, % growth, 1968 midpoint, 2008 midpoint, SAT change, adjusted SAT change, % over 1560, number over 1560, proportion over 1560

Harvey Swarthmore College 1000 Amherst College 1200 Pomona College 1253 Williams College Claremont McKenna 675 1135 Haverford College 550 1169 Middlebury College 1400 Carleton College Cooper Union 827 906 9.6% Wesleyan University 1300 Wellesley College 1753 Oberlin College 2522 Grinnell College Bowdoin College 900 1716 Reed College 962 1464 Macalester College 1858 St. Olaf College Washington and Lee 1200 Barnard College 1800 Whitman College 998 1489 Colgate University 1739 Vassar College 1602 Connecticut College 1527 Davidson College Colby College 1409 Scripps College 440 899 104.3% Wheaton College 1737 Mudd College 283 735 159.7% 1375 1495 120 60 25.0% 45 0.250
1491 49.1% 1350 1450 100 40 20.5% 76 0.205
1690 40.8% 1325 1430 105 45 19.0% 82 0.190
1547 23.5% 1320 1455 135 75 17.3% 65 0.173
1224 1993 62.8% 1315 1420 105 45 17.3% 92 0.173
68.1% 1250 1400 150 90 14.0% 41 0.140
112.5% 1340 1390 50 -10 12.6% 39 0.126
2475 76.8% 1305 1375 70 10 11.7% 66 0.117
1364 1986 45.6% 1330 1400 70 10 11.5% 58 0.115
1340 1360 20 -40 11.0% 22 0.110
2815 116.5% 1356 1385 29 -31 10.7% 77 0.107
2247 28.2% 1361 1390 29 -31 10.1% 59 0.101
2762 9.5% 1308 1355 47 -13 9.4% 66 0.094
1191 1654 38.9% 1265 1355 90 30 9.4% 38 0.094
90.7% 1260 1385 125 65 8.2% 39 0.082
52.2% 1325 1390 65 5 7.6% 29 0.076
1900 2.3% 1211 1345 134 74 6.3% 32 0.063
2448 3040 24.2% 1166 1310 144 84 6.3% 50 0.063
1784 48.7% 1226 1385 159 99 5.8% 26 0.058
2341 30.1% 1305 1350 45 -15 5.8% 32 0.058
49.2% 1166 1335 169 109 5.5% 20 0.055
2831 62.8% 1234 1340 106 46 5.0% 37 0.050
2440 52.3% 1276 1375 99 39 4.8% 32 0.048
1870 22.5% 1245 1325 80 20 4.8% 23 0.048
1000 1685 68.5% 1260 1353 93 33 4.6% 21 0.046
1867 32.5% 1236 1360 124 64 4.6% 22 0.046
1179 1360 181 121 4.6% 10 0.046
2381 37.1% 1176 1330 154 94 4.2% 24 0.042

Name, 1968 enrollment, 2008 enrollment, % growth, 1968 midpoint, 2008 midpoint, SAT change, adjusted SAT change, % over 1560, number over 1560, proportion over 1560

California Inst of Tech 717 907 26.5% 1429 1525 96 36 33.4% 71 0.334
Harvard University 6078 10000 64.5% 1417 1495 78 18 32.2% 543 0.322
Yale University 4094 5330 30.2% 1408 1485 77 17 29.7% 391 0.297
Princeton University 3240 4845 49.5% 1345 1485 140 80 29.7% 365 0.297
Massachusetts Inst of Tech 3698 4172 12.8% 1428 1470 42 -18 25.0% 250 0.250
Stanford University 5790 6422 10.9% 1300 1445 145 85 23.0% 379 0.230
Dartmouth College 3110 4164 33.9% 1323 1450 127 67 22.9% 249 0.229
Columbia University 7032 7306 3.9% 1340 1435 95 35 21.1% 287 0.211
Duke University 3939 6394 62.3% 1257 1435 178 118 21.1% 355 0.211
University of Chicago 2509 4950 97.3% 1329 1425 96 36 19.3% 243 0.193
Brown University 2450 6038 146.4% 1330 1430 100 40 19.0% 279 0.190
Washington University St L. 3499 7320 109.2% 1222 1450 228 168 17.7% 258 0.177
University of Pennsylvania 6500 11906 83.2% 1310 1425 115 55 16.9% 395 0.169
University of Notre Dame 6038 8373 38.7% 1190 1405 215 155 16.0% 325 0.160
Rice University 2077 3001 44.5% 1368 1410 42 -18 15.6% 111 0.156
Cornell University 9781 13510 38.1% 1313 1395 82 22 14.5% 461 0.145
Johns Hopkins University 1765 5650 220.1% 1333 1385 52 -8 13.0% 170 0.130
Northwestern University 6102 9312 52.6% 1220 1410 190 130 13.0% 269 0.130
Carnegie Mellon University 3579 5677 58.6% 1218 1390 172 112 12.6% 179 0.126
Georgetown University 3990 6728 68.6% 1255 1395 140 80 12.1% 192 0.121
UC Berkeley 15762 24462 55.2% 1210 1325 115 55 10.2% 424 0.102
Vanderbilt University 3400 6532 92.1% 1252 1390 138 78 10.1% 161 0.101
Tufts University 1921 5026 161.6% 1274 1415 141 81 9.6% 123 0.096
Brandeis University 2476 3211 29.7% 1337 1360 23 -37 8.9% 68 0.089
Univ of Southern Cal 8339 16384 96.5% 1142 1365 223 163 8.3% 229 0.083
Emory University 3006 6719 123.5% 1223 1385 162 102 8.2% 137 0.082
William and Mary 2934 5792 97.4% 1211 1350 139 79 7.8% 105 0.078
University of Virginia 4634 14860 220.7% 1239 1310 71 11 6.3% 193 0.063
Boston College 5765 9753 69.2% 1254 1335 81 21 5.5% 121 0.055
New York University 11595 21377 84.4% 1175 1335 160 100 5.5% 259 0.055
University of Rochester 4901 5100 4.1% 1289 1325 36 -24 4.8% 58 0.048
Wake Forest University 2363 4412 86.7% 1145 1325 180 120 3.1% 35 0.031

tokenadult · June 12, 2008, 10:57pm

There were 5252 students in class of 2007 who scored 1560 or higher for the sum of the math and critical reading scores.

<a href=“College Board - SAT, AP, College Search and Admission Tools”>College Board - SAT, AP, College Search and Admission Tools;

Down to 1550 was listed as “99+” percentile.

tokenadult · June 12, 2008, 11:00pm

How are you determining what percentage of students at each college are over 1560? That’s not a published figure, and the distribution of scores at each college may not be strictly comparable.

collegehelp · June 12, 2008, 11:30pm

I am using the 25th and 75th percentile SAT, using them to calculate the midpoint and estimate standard deviation, then finding the standard deviation of 1560 under the distribution for that school, and then the proportion under the normal curve above that standard deviation…all done with Excel.

There are about 8900 estimated 1560+ students at the schools in my tables, so evidently I am overestimating percentages. It’s approximate. The distributions at the elite schools are skewed left, truncated on the right.

stevedad · June 13, 2008, 12:25am

Ceiling effect is definitely real.

We found that the selective STEM oriented schools all requested AMC/AIME/USAMO scores, which would partially take care of the issue on the math side. Even the group of kids who had 800 math scores on their record from 9th grade or thereabouts would sort out with the competition scores.

Descartesz · June 13, 2008, 11:02am

I suspect much of the difference is due to the use of superscoring. The College Board reports only single-sitting results, but the schools cherry pick the best section scores per student when reporting the “strength” of their admitted or enrolled classes.

interelations09 · June 13, 2008, 11:08am

Maybe we need a harder SAT to better seperate the uber-intelligent people…

chuy · June 13, 2008, 11:14am

By the time you get smart enough to get 1550+ on the SAT other things matter way more than whether you could have been in the top .001% or top .00001%.

broetchen · June 13, 2008, 11:23am

Don’t forget the effect of the recalibration of the SAT.

VeryHappy · June 13, 2008, 11:27am

Agree. Otherwise, we’d do like in Asia, where one test determines your entire future. We are allegedly more holistic, and I happpen to think we are in fact more holistic. We really do care about ECs, recs, GPAs, URM status, and whether you play the violin (ho hum) or the didgerdoo (wow!!).

Not_quite_old · June 13, 2008, 11:30am

There is no doubt that the SAT is insufficiently discriminating at the high end – especially after the “re-centering” in the early 90s which made the test even easier. Hence, many schools do look at other indicators of very high achievement. To take only one example: I’m sure that all the top schools take tests like the USAMO or the International Olympiads very seriously when considering those students who are especially gifted in Math since it is much harder to do well in those contests than to score 800s on the SAT or SAT2 Math.

While doing well does not guarantee proficiency however, it is likely that doing poorly on the SAT is probably a good (though imperfect) filter for those who can’t make the cut in certain areas. Off the top of my head I would guess that most who couldn’t score at least 700 on the SAT Math would have a hard time making it through Caltech’s required math classes or Harvard’s infamous Math 55.

So the SAT has now become better for eliminating the middle than identifying the real top.

rogracer · June 13, 2008, 1:39pm

I don’t believe you can make reliable extrapolations like this based on only two data points: 25th and 75th percentiles. For one thing, the result is way to sensitive to standard deviation and assumed distribution, something which is not known with any kind of confidence.

collegehelp · June 13, 2008, 4:50pm

This table is a little easier to read. You can see the inverse relationship between 1968 SAT scores and the increase in SATs 1968-2008. You can compare with the estimated proportion of students over 1560 (~ceiling effect).

school, 1968 SAT midpoint, 2008 SAT midpoint, SAT change, adj SAT change, percent over 1560

Harvey Mudd College 1375 1495 120 60 25.0%
Wellesley College 1361 1390 29 -31 10.1%
Wesleyan University 1356 1385 29 -31 10.7%
Swarthmore College 1350 1450 100 40 20.5%
Haverford College 1340 1390 50 -10 12.6%
Cooper Union 1340 1360 20 -40 11.0%
Carleton College 1330 1400 70 10 11.5%
Amherst College 1325 1430 105 45 19.0%
Reed College 1325 1390 65 5 7.6%
Pomona College 1320 1455 135 75 17.3%
Williams College 1315 1420 105 45 17.3%
Oberlin College 1308 1355 47 -13 9.4%
Middlebury College 1305 1375 70 10 11.7%
Barnard College 1305 1350 45 -15 5.8%
Vassar College 1276 1375 99 39 4.8%
Grinnell College 1265 1355 90 30 9.4%
Bowdoin College 1260 1385 125 65 8.2%
Davidson College 1260 1353 93 33 4.6%
Claremont McKenna 1250 1400 150 90 14.0%
Connecticut College 1245 1325 80 20 4.8%
Colby College 1236 1360 124 64 4.6%
Colgate University 1234 1340 106 46 5.0%
Washington and Lee 1226 1385 159 99 5.8%
Macalester College 1211 1345 134 74 6.3%
Scripps College 1179 1360 181 121 4.6%
Wheaton College 1176 1330 154 94 4.2%
Whitman College 1166 1335 169 109 5.5%
St. Olaf College 1166 1310 144 84 6.3%

California Inst of Tech 1429 1525 96 36 33.4%
Massachusetts Inst of Tech 1428 1470 42 -18 25.0%
Harvard University 1417 1495 78 18 32.2%
Yale University 1408 1485 77 17 29.7%
Rice University 1368 1410 42 -18 15.6%
Princeton University 1345 1485 140 80 29.7%
Columbia University 1340 1435 95 35 21.1%
Brandeis University 1337 1360 23 -37 8.9%
Johns Hopkins University 1333 1385 52 -8 13.0%
Brown University 1330 1430 100 40 19.0%
University of Chicago 1329 1425 96 36 19.3%
Dartmouth College 1323 1450 127 67 22.9%
Cornell University 1313 1395 82 22 14.5%
University of Pennsylvania 1310 1425 115 55 16.9%
Stanford University 1300 1445 145 85 23.0%
University of Rochester 1289 1325 36 -24 4.8%
Tufts University 1274 1415 141 81 9.6%
Duke University 1257 1435 178 118 21.1%
Georgetown University 1255 1395 140 80 12.1%
Boston College 1254 1335 81 21 5.5%
Vanderbilt University 1252 1390 138 78 10.1%
University of Virginia 1239 1310 71 11 6.3%
Emory University 1223 1385 162 102 8.2%
Washington University St L 1222 1450 228 168 17.7%
Northwestern University 1220 1410 190 130 13.0%
Carnegie Mellon University 1218 1390 172 112 12.6%
College of William and Mary 1211 1350 139 79 7.8%
University of Cal-Berkeley 1210 1325 115 55 10.2%
University of Notre Dame 1190 1405 215 155 16.0%
New York University 1175 1335 160 100 5.5%
Wake Forest University 1145 1325 180 120 3.1%
University of Southern Cal 1142 1365 223 163 8.3%

collegehelp · June 13, 2008, 4:55pm

rogracer-
The method is imprecise but sufficient for making my point that elite schools are enrolling significant numbers near the upper limit of the SAT. I think the relative rank order is probably very accurate.

Example:
Caltech had a 1429 midpoint in 1968, increased by 36 adj. points as of 2008, with 33% over 1560.
USC had a 1142 midpoint in 1968, increased by 163 adj. points as of 2008, with 8.3% over 1560

jsmall · June 13, 2008, 5:40pm

I don’t understand why people want to make a harder test. WHY??? So that top schools become more homogenous? Are some of you 2400 scorers ****ed that you have to share your Harvard residence hall with a few 1900 scorers? Or do some of you 2400 scorers think that you’re smarter than other 2400 scorers and what to be in a different group than those inferior perfect scorers? I just don’t get it. WHY?!?!?

xiggi · June 13, 2008, 5:46pm

While the data of CH is interesting, I really don’t understand where the calls for a “tougher” standard come from. The most selective schools routinely reject a SUBSTANTIAL number of perfect SAT or ACT scorers. Getting more of those students, or more acers of a “tougher test” must be the last on the college priority lists.

Admissions’ officers have a MUCH tougher challenge in meeting their diversity numbers and uncovering more diamonds in the rough, especially (relatively) high scorers in disadvantaged circles.

Reading the Senate minutes that quote Stanford’s Dean Shaw is very telling. It would take a miracle to see Stanford’s SAT inch up in the next years. Their reputation for understanding admission is, however, bound to increase.

collegehelp · June 13, 2008, 7:30pm

jsmall-
The problem has nothing to do with human relations. The problem is that it is almost impossible for admissions officers to distinguish objectively among students near the SAT ceiling and it is getting more difficult to distinguish among schools that enroll large numbers near the SAT ceiling.

Here is a wikipedia article:
[Ceiling</a> effect - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Ceiling_effect]Ceiling”>Ceiling effect - Wikipedia)

anonymous550 · June 13, 2008, 8:26pm

what the hell? the SATs do NOT sound easy…don’t make a harder test, thats ridiculous! as if college admission isn’t so freakin hard already…jeez

tokenadult · June 14, 2008, 12:41am

Colleges can very easily distinguish between students who post high SAT scores and do little else and students who post high SAT scores and also have outstanding accomplishments in extracurricular activities. See

<a href=“http://www.college.harvard.edu/deans_office/NCAASelfStudy.pdf[/url]”>http://www.college.harvard.edu/deans_office/NCAASelfStudy.pdf</a>

for one example of a college that makes such distinctions.

jsmall · June 14, 2008, 3:34am

collegehelp:
Are you kidding me? If that is the case, then why are many perfect scorers denied from some of the most selective school when others with lower scores are accepted? The SATs are only one aspect of admissions. I really doubt that admissions officers sit there with only one spot left and two perfect scorers left in the applicant pool and cant make a decision. And then think, “Oh no!!! which one is smarter? I wish the SAT was harder so we could figure out who is smarter.” That’s just RIDICULOUS!!!

Pushing the limits of the SATs at the elite schools

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