Do enrollment data really show a cap quota against Asians at Harvard? Maybe not. | #IAmNotYourWedge

January 5, 2015

Photo credit: NY Times
Photo credit: NY Times
There is an extremely popular New York Times infographic that Asian American opponents of affirmative action often share to suggest that elite Ivy League universities have implemented a cap quota on Asian American enrollees. In a nutshell, the infographic (shown above) illustrates that the enrollment of Asian American students at Harvard and other Ivies has fluctuated at around 16-20% for the last twenty years, while enrollment at Caltech has increased since 2000. An overlay of the growth in Asian Americans aged 18-21 suggests that Caltech’s admissions is keeping pace with the growth in the Asian American population, whereas Asian American enrollment at East Coast Ivies are being unnaturally depressed. This is the work of affirmative action, suggests the infographic.

The associated New York Times opinion piece (“Statistics Indicate an Ivy League Asian Quota“, penned by uber-conservative anti-affirmative action lobbyist Ron Unz) makes the same argument more explicitly.

To Unz’s credit, this infographic is superficially compelling. I’ve been writing in detail about affirmative action for the last year or more, and even I never really questioned these data. I just sort of accepted this graph, if not its larger conclusions.

That is, until today, when I sat down and asked myself whether or not Unz’s assertions really made sense mathematically? And y’know what, guys — turns out that everything we thought we knew about this infographic is wrong!

truthiness

It turns out that this infographic is classic “truthiness“.

Our first sign that there’s something suspicious about Unz’s infographic is its use of dual y-axes to superimpose two completely different sets of datapoints: Asian enrollment at several schools vs. college-aged Asian American population numbers. While there’s nothing innately wrong with doing this, it’s certainly a way of massaging data to make it appear to support your conclusion. It’s all in the scaling: Unz has chosen to scale both x-axes in such a way as to make the two datasets appear to mirror one another; yet, one could change the scaling to make it appear differently. Again, this doesn’t necessarily invalidate the infographic, but it’s a tip-off that Unz is savvy of how to make presentation choices for the data to add subconscious support to his tale.

The better question, however, is whether or not we believe Unz’s underlying message: that Ivy League schools aren’t keeping pace in their Asian American enrollment with increases in Asian American population growth. Unz seems like he might be correct: after all, Asian Americans are the fastest growing racial or ethnic group in America. It seems only intuitive that we should see massive increases in Harvard’s Asian American student population size too, right?

Actually, not necessarily.

Setting aside Unz’s infographic for a second, we can actually figure this out for a school like Harvard (a good model school since it is the target of the latest anti-affirmative action lawsuit citing an anti-Asian American cap quota). While detailed application demographics are not available for private institutions like Harvard (as they are available for UC school systems), enough information is available to make a rough calculation regarding this question.

And that’s exactly what I did.

harvard

I chose to start with the year 2000 and compare it to 2014’s enrollment data for Harvard, and to ask if the changes in Asian American enrollment paced with overall changes in Harvard’s estimated Asian American applicant pool. There are a few reasons to choose these two years: 1) US Census data for the year 2000 are readily available, 2) Harvard’s data for this year are also readily available, 3) Caltech’s rising Asian American enrollment only occurs after the year 2000, and 4) going much further back into the past beyond 2003 extends us into affirmative action policies that have not been influenced by Supreme Court rulings of the landmark Gratz and Bollinger cases, and so is no longer as applicable to contemporary interpretations of affirmative action law and policy.

In 2000, Harvard received 18,190 applications. In 2000, Asian Americans made up 3.6% of the country’s population. If we use this percentage to estimate the number of Asian American applicants to Harvard, we arrive at 655 Asian American applicants.

Last year, Harvard received 34,295 applications. Currently, Asian Americans make up 5.3% of the country’s population. Using the same process of estimation, we arrive at 1,817 Asian American applicants.

Sure, the distribution of college-aged Asian Americans might be different than our national distribution, but what’s important here is the relative increase in Asian American applications to Harvard in the last fourteen years. Our calculations estimate that Harvard is now receiving an additional ~1,162 Asian American applications every year compared to 2000, representing a ~50% increase in the Asian American population in that time.

Okay, so now we have to ask ourselves whether or not Asian American enrollment to Harvard has actually remained flat between 2000 and 2014. In 2000, 16.4% of Harvard’s incoming freshmen were Asian American (which, by the way, doesn’t reflect the apparent datapoint for the year 2000 included in Unz’s graph). Last year, 20% of Harvard’s incoming class was Asian American. When we translate this into absolute numbers based on class size for 2000 (1,985 students) vs. 2014 (2,048), we arrive at 325 Asian American students admitted in 2000 compared to 409 Asian American students admitted in 2014. That’s an increase of 84 Asian American students.

That doesn’t seem like much, except that we have to remember that Harvard is a highly selective college with a relatively tiny incoming freshman class admitted from a large (and expanding) applicant pool. So, each student in a freshman class of about 2000 students represents approximately 14 applicants (2000 admitted x 14 = 28,000 applicants, which represents a ballparked average of the number of applicants to Harvard spanning the years from 2000 vs 2014).

As calculated, 84 new Asian American students were admitted to Harvard between 2000 and 2014. So, this increase in admitted Asian American students represents an approximate (84×14) 1,176 additional Asian American applicants to Harvard. Remember how we calculated that Harvard received an approximate 1,162 new Asian American applications in that time?

Yeah, it turns out that increases in Harvard’s enrollment of Asian American students between 2000 – 2014 appears to have largely kept pace with the overall growth in the Asian American population in that time.

Put another way, our population growth results in 1,162 new Asian American applications to Harvard. That translates to a predicted (1162/14) increase to 83 new Asian American students per year in order to keep pace. Between 2000-2014, the actual reported increase of Asian American freshmen to Harvard was an additional 84 students per year.

asian-american-student-predicted-enrollees

Now, you might argue that national population distribution is not a meaningful proxy for changes in the Asian American college-aged population, and I would agree with you. Except, that Unz’s own infographic suggests that between 2000-2014, the Asian American college-aged population increased by about 50%, which is similar to the percent change used in my calculations. Second, and more importantly in my mind, I am using the same national population distribution numbers that opponents of affirmative action typically use to estimate changes in Asian American application to elite universities. In short, this approach of using national numbers as a proxy for applicant rates is rhetorically identical to what opponents of affirmative action, like Ron Unz, use in making their argument.

Let me be clear: I did not expect to arrive at this conclusion. But, thinking back on it, this actually makes sense. First of all, even though Asian Americans are the fastest growing population in this country, this statistic makes it seem as if we are now a large share of the American population. Yet, we are still a relatively small community in absolute numbers: an increase from 1% to 3% is a 300-fold increase, yet still describes a net increase of only two students in a pool of 100. Non-Asian American applicants to Harvard and other schools still vastly out-number Asian American applicants when it comes to absolute values.

A second confounding factor is that Harvard is a highly selective school that now admits less than 7% of applicants (ironically, the linked article from 2000 is headlined with the record-breaking low admission rate at 10.9% for that year). Class size at Harvard has been basically unchanged in the last two decades despite a swollen applicant pool. Because of this, extremely large changes in applicant pool are necessary to significantly impact demographics, and subsequently the racial makeup of incoming freshman classes. Finally, Harvard tends to report its racial admission rate by rounding to the nearest 10th of a decimal point, which can erase small steady increases in the Asian American population at this school. Unz exacerbates this problem because his infographic appears to further round to the closest whole number. Thus, the ~2-3% increase in Asian American students enrolling in Harvard in the last 14 years is almost entirely lost in rounding error when you look year-to-year; only by comparing across a full decade’s time can you see the difference.

The next question you might ask me is, okay: if this is true, what the heck is going on with Caltech? The short answer right now is, “I don’t know”. Unlike Harvard, Caltech is situated in a state where Asian Americans make up more than 14% of residents, and where in absolute numbers, California’s Asian Americans are more than double those living in New Jersey, New York and Massachusetts combined. How this and other factors might impact expected and actual Asian American enrollment is an unanswered question for me at the moment.

Either way, the basic calculations outlined in this post complicate our interpretation of what’s going on in Harvard. While they don’t totally exclude the possibility of anti-Asian bias (or, “negative action”, not to be confused with affirmative action) that might be disadvantaging Asian Americans in the college admissions process, they certainly raise questions about how we’re interpreting Harvard’s enrollment data. Rather than be swayed by the “truthiness” of Unz’s argument, which appears to draw on legitimate datapoints involving the rapid growth rate of the Asian American community to make an error-laden argument, we should step back and really think about the math.

And the math here says that things are a lot more complicated at Harvard than Unz suggests. If there really is an anti-Asian cap quota at Harvard, it’s not borne out by looking at enrollment data alone.

  • yoeddy

    By using the 1 in 14 acceptance rate in your calculation to estimate the number of AA applicants in 2014, you are fixing the very variable that is in question. Isn’t the whole point of this to question whether or not AA’s are being admitted at the same acceptance rate as the rest of the application pool?

  • Not really. The use of the 14 “scale up” multiplier is derived from the overall difference between the size of the applicant pool vs the admitted class, and applies to all students regardless of race. It is not suggesting that the Asian applicants are only being compared to other Asian applicants, just that every admitted Harvard student represents 14 applications that Harvard receives. (Edit: it’s also important to realize that we’re looking at % change, so even if the multiplier is off due to an abnormally high Asian American applicant fraction in the total pool, it’s similarly off for both beginning and end years of this analysis and therefore negates itself as a source of error in the calculation. This calculation is basically valid if we predict that the Asian American applicant size increased by about 50% over ten years, regardless of starting and ending distribution.)

    The question you are asking is a slightly different one than what this post aims to address. You are asking if (for example) only 3% of Asian American applicants are admitted of those applied, versus (for example) 6% of non-Asian American applicants. Turning this around would require that we demonstrate that Asian American applicants are an unusually large fraction of Harvard applicants (which we have no evidence for or against at the moment), but more importantly also misinterprets the holistic review process by assuming that Asian American applicants are only being compared against other applicants. I’ve addressed that fallacy in a previous post explaining how holistic review works.

    This post was focused on asking if enrollment data to Harvard demonstrate the existence of a cap quota, which argues that Asian American enrollment is fixed at some percentage and has not increased in the last two decades. This is the premise of Unz’s article, and is also a popular argument made in the anti-affirmative action sphere; this article demonstrates that this is not true: Asian American enrollment at Harvard has increased in the last ten years at a pace consistent with our overall population size. If there is an anti-Asian American cap quota at Harvard, available enrollment data — which is the primary evidence used by the anti-affirmative action side to argue its presence — do not actually support its existence when you go through the math.

    We can ask a different question with regard to admission rate by race, but that requires detailed application demographic criteria, which we do not have; but what you are asking basically quires the assertion that Asian Americans are far more likely to apply to Harvard than other students. The question to ask is why you think this might be a valid hypothesis?

  • Myra Esoteric

    Thank you for this. So many of us forget how controversial Ron Unz is. I saw him on CNBC once and he wanted to raise the minimum wage, but rather than out of a labor concern, his main reason for doing so was to kick undocumented people out of California.

    Of course he didn’t say the second part on national TV. But he said it on his site. Many years ago, he also tried to end bilingual education. He also has an article on his site presenting China as the ‘yellow peril’.

    http://www.unz.com/runz/the-minimum-wage-and-illegal-immigration/

  • Bob

    If the % of population increased by about 50%, then we should see the enrollment figures also increase by about 50%, which it doesn’t. (Increase from 3.6% to 5.4% of population, so the enrollment should have increased from 325 to about 488.)

    But a much bigger mistake in your calculations is that you assume that applications are at the same ratio as the general population. Asian Americans on average have higher grades in school, and there’s a lot of family pressure to apply to Ivy League schools. It could easily be a difference of a factor of 2 or even 5, and that could have increased over the years.

  • John

    “Last year, Harvard received 34,295 applications. Currently, Asian Americans make up 5.3% of the country’s population. Using the same process of estimation, we arrive at 1,817 Asian American applicants.”

    The use of 5.3% is an inaccurate way to estimate the percentage of Asian American applicants is based on a faulty assumption that the applicant demographic is similar to the US population. Case in point: the state of California has 14.9% Asian American population, according to the 2010 US Census. However, the percentage of Asian applicants to the UC undergraduate system is ~30%. Better ranked campuses have applicant percentages closer to ~40%.
    http://www.ucop.edu/institutional-research-academic-planning/_files/factsheets/2014/fall-2014-applications-table3.2.pdf

    Granted, Harvard is not in California, perhaps the applicant size is does not double from the US population. However, higher competitive colleges have self-selection process in which better scoring candidates are more likely to apply than lower scoring candidates which would screw the applicant pool to create a larger Asian applicant percentage.

    Unz’s presented pattern fits applicant patterns exhibited in California. Before any accusations should or can be made, by a conservative estimate (yours), Harvard is not demonstrating capping. However, if the applicant pattern behavior likens the UC system, the argument that Harvard caps admission has traction.

  • Keep reading. It’s not really important what fraction is Asian American: the 5.3% number is giving us a proxy number by which to calculate relative increase. Unless there is some reason to believe that the AAPI applicant pool increased at a rate completely disconnected from our existing rapid increase in overall population size, the 5.3% is basically just a proxy number to start thinking about relative changes in applicant population size.

    Also, using the California system is not necessarily appropriate since we are talking about a state school situated in a high-concentration Asian American state. It’s assumptive to argue that the same application patterns will apply to a private selective institution on the opposite side of the country like Harvard.

  • John

    (1) A relative increase can still suggest capping if it under-represents the applicant population pool. Even if the the relative increase of Harvard’s admitted application pool exceeds rate of increase in Asian American population, the existence of a positive trend does not exclude the potential that all of the numbers are undervalued.

    (2) Re: Using the California system.
    (a) Applicants can apply to any number of colleges; therefore, applying to state school does not exclude one from applying to private school.

    (b) Applicants are more likely to deter applying to states schools as a result of in-state preferences. Private institutions do not have this particular deterrent. Hence, CA school are going to be over-represented by Asian-Californians; however, the second largest saturation of Asian Americans (outside of HI) are situated on the East Coast. While it can be argued that many CA residents may have preference for UC, the argument should not completely negate the impact that East Coast Asian Americans have on applicant pool size.

    (c) Competitive colleges are self-selecting as more academically competitive applicants are more likely to apply to higher ranking universities. Asians Americans are going to be over-represented in the applicant demographic.

    Therefore, I find the use of 5.3% to be an extreme under-estimate.

  • (1) A relative increase can still suggest capping if it under-represents the applicant population pool. Even if the the relative increase of Harvard’s admitted application pool exceeds rate of increase in Asian American population, the existence of a positive trend does not exclude the potential that all of the numbers are undervalued.

    It might, but for that to be the case, two things would have to be true: 1) the Asian American applicant pool is a significant portion of the total pool, and 2) the applicant pool increased above the rate of the total population. There’s little evidence to suggest both are simultaneously true, and absent that evidence, it’s not an entirely plausible assumption to make.

    The important point here is not necessarily the increase in the population size, but that increase combined with the fact that Harvard’s student population has not changed in the last two decades. So, what you are apparently forgetting is that in the same period of time, the overall admission rate for Harvard has decreased substantially. In that same period of time, Asian American enrollment at the school has increased. So, in order for there to continue to be a cap quota, you would have to believe that the relative increase in Asian American applicant number is pretty substantial — substantial to the point of incredible. So yes, it’s true that these calculations are a possible undervaluing; but that possibility isn’t really substantiated by the available data.

    (2) Re: Using the California system. (a) Applicants can apply to any number of colleges; therefore, applying to state school does not exclude one from applying to private school.

    Yes. You’ve missed my point. I’m saying you can’t extrapolate application patterns from a California school to Harvard.

    (b) Applicants are more likely to deter applying to states schools as a result of in-state preferences. Private institutions do not have this particular deterrent. Hence, CA school are going to be over-represented by Asian-Californians; however, the second largest saturation of Asian Americans (outside of HI) are situated on the East Coast. While it can be argued that many CA residents may have preference for UC, the argument should not completely negate the impact that East Coast Asian Americans have on applicant pool size.

    Yes, but nowhere near the kind of density as the West Coast. Asian Americans on the West Coast eclipse those on the East Coast by a factor of three to one. In Cali, we are 14% of all residents and we are talking about a single state; in New York and New Jersey, we are only 8% and 9%. It’s the second largest concentration, but we’re still a fairly small fraction of local residents of East Coast states; further, there are a lot more schools on the East Coast than on the West Coast, which would further dilute this applicant population. So, what’s your reasoning that somehow California’s applicant patterns mirror that of a single elite institution on the opposite side of the continent?

    (c) Competitive colleges are self-selecting as more academically competitive applicants are more likely to apply to higher ranking universities. Asians Americans are going to be over-represented in the applicant demographic.

    1) Wow – model minority myth in action, ain’t it?

    2) The vast majority of Asian Americans are enrolled in public 4-year and 2-year programs. Given that, it is an assumption to argue that our community is “more likely to apply to higher ranking universities”, unless one actually believes that all Asian Americans are high-achieving academics.

    You should really read that full linked report, by the way.

  • Finally, I suggest you re-read this paragraph in full:

    Now, you might argue that national population distribution is not a meaningful proxy for changes in the Asian American college-aged population, and I would agree with you. Except, that Unz’s own infographic suggests that between 2000-2014, the Asian Americancollege-aged population increased by about 50%, which is similar to the percent change used in my calculations. Second, and more importantly in my mind, I am using the same national population distribution numbers that opponents of affirmative action typically use to estimate changes in Asian American application to elite universities. In short, this approach of using national numbers as a proxy for applicant rates is rhetorically identical to what opponents of affirmative action, like Ron Unz, use in making their argument.

  • Finally, you should also read this post, which deals more immediately with how to estimate the Asian American applicant pool to Harvard.

    http://reappropriate.co/2015/01/do-demographic-data-support-lower-admission-rates-for-asian-applicants-to-harvard-maybe-not-iamnotyourwedge/

  • John

    “It might, but for that to be the case, two things would have to be true:
    1) the Asian American applicant pool is a significant portion of the
    total pool, and 2) the applicant pool increased above the rate of
    the total population. There’s little evidence to suggest both are
    simultaneously true, and absent that evidence, it’s not an entirely
    plausible assumption to make.

    The important point here is not necessarily the increase in the
    population size, but that increase combined with the fact that Harvard’s
    student population has not changed in the last two decades. So, what
    you are apparently forgetting is that in the same period of time, the
    overall admission rate for Harvard has decreased substantially. In that
    same period of time, Asian American enrollment at the school has
    increased. So, in order for there to continue to be a cap quota, you
    would have to believe that the relative increase in Asian American
    applicant number is pretty substantial — substantial to the point of
    incredible. So yes, it’s true that these calculations are a possible
    undervaluing; but that possibility isn’t really substantiated by the
    available data.”

    (1) has to be true, but (2) is a potential possibility but does not have to be true. Admission rate may have improved for a given demographic of applicants exceeding its respective population increase relative to a competing group.

    So no, I have not forgotten that admission rates have decreased for all applicants. It can very well be that the admission rate decrease for Asian Americans is less than that of other groups. However, that does not discredit a continued existence of a potential cap in admission.

    On: https://professionals.collegeboard.com/profdownload/08-0608-AAPI.pdf

    It states that apparent success of Asian American appear to be overly high because Asians are concentrated in fewer institutions. Harvard is one of those more popular institutions, which suggest a much greater applicant pool make-up than your indicated 5.3%.

    On the model minority myth, I never implied that we are all high achieving academics, that is something you read into yourself. However, the statement that we constitute greater percentage of elite SAT scorers than our respective population is a fact, backed by the College Board, and that certainly does not imply that there are no Asian American groups that need assistance nor does it imply that we are robots who study all day long. The statement that more competitive applicants are likely to apply to more competitive schools has nothing to do with the model minority myth but a sociological phenomenon. http://www.frbsf.org/economic-research/files/wp07-18bk.pdf

    Furthermore, I have read through the report and I have yet to find information on applicant data. In order to be counted for enrollment the individual must (1) apply to university, (2) accepted to the university, and (3) attend the university. Applicants may be enrolled in a public institution if they specifically wanted to attend that public institution, or may be attending as a result of denied admission to private institutions. The fact that vast majority of Asian Americans are attending public 4-year programs has little indication whether or not they have also applied to a private institution.

    The implication of capping is an institutional action occurring at the decision stage of an application cycle, not the submission stage or the enrollment stage. Therefore, the demographic make-up of an applicant pool is provides a greater indication for tracking potential capping behavior rather than the use of an overall population.

  • yellowprivilege

    I hate to be that dude, but that figure uses dual y-axes not x-axes. Also, “an increase from 1% to 3%” is three-fold or 200%, increase not 300%.

  • ryan

    Huh? What? The 50% increase thing is like clearly a mistake, right? I think you saw ~650 applicants and ~1100 new applicants and concluded there was a 50% increase in applicants? But you should be comparing ~650 applicants and ~1800 applicants and getting a 200% increase.

    You used data for the *class* of 2000, which is students
    admitted in 1996. The article you link was published in 1996. This is
    the actual data you want:
    http://www.thecrimson.com/article/2000/4/3/class-of-2004-admission-letters-mailed/?page=single

    The analysis using expected gain based on average admissions rate is really contrived and introduces lots of scope for error (the averaging of the admissions rate over the decade, the fact that the admissions rate isn’t independent from the actual admissions, etc.). Your calculation of the number of expected Asian-American applicants assumes that they apply at the same frequency as the average, which is obviously untrue (by your own numbers you’re claiming that Harvard had a 50% admissions rate for Asian-Americans for the class of 2000, which is obviously nonsense). In short, your methodology here is bad, sorry.

    Here is an honest look at this, based on the data. In 2000 Harvard admitted 16.1% Asian-Americans. In 2014 they admitted 20%. This is a 25% increase in the share of Asian-Americans. Over that time, the share of the population that is Asian-American has increased 50%. So all is not quite fine and dandy. This is also a much simpler analysis to understand than the one you gave.

    One point, however, is that admissions is zero-sum, and we shouldn’t expect linear increases automatically. What I mean is: imagine the Asian-American share of the population grew 5x, to about 25%. We wouldn’t expect Harvard to be 100% Asian in this case (or at least I wouldn’t).

    Actually, there’s a further point — the infographic you’re responding to uses enrollment, while you (and I) are looking at admissions numbers.

    Anyway, it’s an interesting question. I think your argument is bunk but the conclusion may have some merit anyway. Caltech is kind of a wack comparison point since California is so Asian to begin with (ditto with Berkeley, another school often brought up in this discussion). I think it’s hard to make a purely demographic argument about this anyway; comparisons of GPA and SAT are more helpful to determine if being Asian is indeed a disadvantage when applying.

  • Re 50%: no, I didn’t conclude that from the applicant number. That comes from published data.

    I agree that the absolute applicant number is likely to be very wrong; it’s just a way to get some proxy numbers to start working with. The actual segment of the applicant pool is likely to be higher, meaning selectivity would approach the actual selectivity for the school.

    This post begins however with the fact that this is a back-of-the-envelope calculation. Are there artifacts? Are there better ways to do this? Sure. But as you rightly point out at the end, the intention here was to do some rough estimates for the purposes of starting a discussion. If given more than twenty or thirty minutes, or better data (my error re: class of 2000 was an oversight) these issues might have been resolved. But this doesn’t change the larger point which was to actually take a mathematical approach to the argument of the anti-affirmative action lobby and begin to see if the claims make some sort of sense.

    If I were to do this post over, I would probably do the math differently. But the point remains that most folks are using the fact of Census data increases in asian population size to reason a linear and proportional increase in Harvard student population as expected. They forget that Harvard’s class size is largely fixed, that the selectivity for the school has fallen dramatically, and that a large percent increase in a population size may not translate into a significant increase in absolute applicant number, and that large changes in applicant number are required to impact enrollee numbers at a highly selective school.

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