Monday, January 16, 2012

Stanford or Harvard/Yale/Princeton/MIT, or Others?

When this article was first published on CC, a lot of details were left out. The reason was that I wanted to see any critique or additions to my original post. Obviously the math part of the article may be very complicated to most people and most comments were not critical. Some of the details cannot be obtained as the information for this PIE problem is not complete. After so long it may be the time for me to give more details and let people  reproduce the results.
Harvard, Yale, Princeton, Stanford and MIT, or HYPSM, are the main five schools that steal  prefrosh among each other. As many evidences from the school newspaper or admission official’s comments show that they don’t really concern to lose profrosh to schools other than the other HYPSM. This analysis was based on the data of Class of 2014 when Harvard and Princeton did not have SCEA. Therefore, the results could be different for the Class of 2016 as all HYPS have SCEA now.
For Class of 2014, Stanford accepted 2340 students totally, 40 students were accepted from the waitlist[1]. Its total freshman enrollment was 1672[2]. The yield was 71.5%, which means that 668 students were accepted but did not matriculate.
For those 2340 students accepted [3]:
398 students were also accepted by Harvard;
359 accepted by Yale;
 430 accepted by Princeton;
304 accepted by MIT;
630 accepted by UC Berkeley
For those 668 non-matriculates [4]:
32% went to Harvard, or 214 Stanford/Harvard cross-admits went to Harvard;
16% or 107 Stanford/Yale cross-admits went to Yale;
14% or 94 Stanford/Princeton cross-admits went to Princeton;
13%, or 87 Stanford/MIT cross-admits went to MIT.
For cross-admit yields [4]:
Stanford: Harvard=38%:62%;
Stanford: Yale=50%:50%;
Stanford: Princeton=63%:37%;
Stanford: MIT=60%:40%.

Finally, for the detailed distribution of the HYPSM cross-admits:
For those 398 Stanford/Harvard cross-admits, 214 enrolled at Harvard. This means that there were total of 214/62% = 345, or 87% of Harvard/Stanford cross-admits,  went to either Harvard or Stanford.  And hence there should be 345*38% = 131 enrolled at Stanford. The rest of cross-admits, total of 56, enrolled at somewhere else. Direct head-to-head competition: Harvard/Stanford=214:131, or 38% went to Stanford and 62% went to Harvard.
Similarly for those 359 Stanford/Yale cross-admits, 107 enrolled at Stanford,   107 enrolled at Yale, 145 enrolled at somewhere else. Direct head-to-head competition: Stanford/Yale=107:107, or 50% went to Stanford and 50% went or Yale.
For those 430 Stanford/Princeton cross-admits, 160 enrolled at Stanford,   94 enrolled at Princeton, 176 enrolled at somewhere else. Direct head-to-head competition: Stanford/Princeton=160:94, or 63% went to Stanford and 37% went or Princeton.
For those 304 Stanford/MIT cross-admits, 131 enrolled at Stanford,   87 enrolled at MIT, 86 enrolled at somewhere else. Direct head-to-head competition: Stanford/MIT=131:87, or 60% went to Stanford and 40% went or MIT.
In summary, for those 2340 admits, Stanford admitted 214/0.62+107/0.5+94/0.37+87/.4 = 1016 HYPSM cross-admits, or 1016/2340 = 43.4% of total admits were HYPSM cross-admits. Of those cross-admits, Stanford enrolled 131+107+160+131 = 529  and lost 487 students to HYPM, its HYPSM cross-admits yield was 529/1016 = 52%. Moreover, 529/1672 = 31.6% of Stanford students of Class of 2014, or about a third of the entire class, were HYPSM cross-admits.
There were 668-487 = 181 admits went to schools other than HYPSM.  None of schools other than HYPM did Stanford lose more than 2% of non-matriculates or  13 students per school[4] – those schools including ALL other Ivies, Chicago, Caltech, Duke, Rice and UCB, etc, for all the reasons that could be.



Stbentia said...

I think you meant:

Stanford: MIT=60%:40%.

instead of

Stanford: Harvard=60%:40%

Mathacle said...

Yes. And it is corrected. Thanks.

Vivian Morarty said...

Check out the latest data from Stanford's senate minutes on cross-admits (page 20) at the following website:

Mathacle said...

Thank you!

There are a lot to digest. Those cross-admits were mainly the ones from the regular decisions. The numbers of cross-admits are more interesting since every one of HYPSM has SCEA now, and the total cross-admits should be reduced significantly, compared with Class of 2014.

My initial guess of the numbers of cross-admits, if I read the labels of the chart correctly, is:

with Harvard:
Year 2014: 214
Year 2010: 345 (from my original post for class of 2014)

with Yale:
Year 2014: 184
Year 2010: 214

with Princeton:
Year 2014: 155
Year: 2010: 254

with MIT:
Year 2014: 177
Year 2010: 218

Also, I am not sure how Stanford got those data. I thought the only way to obtain the data was to get the roster of enrolled students at each HYPSM and compared the list of its own admitted students. There could be students crossed by more than three schools such as Harvard and Yale and Stanford, and they should not be double countered as S/H and S/Y cross-admits, but only countered as the school the students went.

The report dated on June, 2014, which was kind of early for the final data.

Vivian Morarty said...

My guess is that the data are from a survey filled out by admitted or denied students (everyone of HYPSM and others do these surveys). The number of respondents is at the bottom of the graph.

Richard Campo said...

This is highly skewed data, as geography has a huge influence, if not the largest influence. Students in California will overwhelmingly choose Stanford, while students in the northeast will most likely chose an ivy, most times any ivy, over Stanford. Also the top four or five ivies are pretty much competing against each other for the same students. A minority of students in the Boston-NY corridor will attend Stanford over an ivy. There is a huge regional preference. More interesting would be where Midwest or central US students attend.

Mathacle said...

The data was not a set of skewed sample data but population data. The analysis was not based on stats but on counting. We can give many imaginary reasons to argue why, especially try to abuse the stats to support the arguments, the truth was telling from the population data, if the data was reliable.