It is difficult to determine the percentage of Jews among high academic achievers (particularly on the basis of names alone), as many Jews do not have obviously Jewish names, in part because many Jews Anglicized their surnames due to anti-Semitism. Nevertheless, we can use Weyl Analysis, which is an objective and reproducible methodology (once clearly defined), to compare the proportion of Jews among NMS semifinalists and Harvard undergraduates.  Weyl Analysis yields an estimate of the percentage of Jews in a data set based on the frequency with which specific distinctive Jewish surnames like Cohen and Goldberg appear.  However,  Unz’s description of Weyl Analysis is ambiguous, and when I first performed Weyl Analysis on the Harvard alumni directory, I incorrectly assumed that Unz meant Gold* when he wrote “Gold—” (as I stated on February 13th and February 19th); I also full-counted hyphenated surnames that included one of the distinctive Jewish surnames on the Weyl list (Unz did not specify how to treat hyphenated surnames).  I asked Unz to clarify these ambiguities, but he declined to do so, so I had no option but to reproduce his NMS results in order to resolve these ambiguities.  It turns out Unz had meant {Gold, Goldberg, Golden, Goldman, Goldstein} by “Gold—”, and he had not counted hyphenated names.[13]  (Please refer to the previous footnote for the details on how I determined this.)  This is why my initial Weyl Analysis results for the percentage of Jewish NMS semifinalists, as reported by Prof. Gelman here were higher than Unz’s.  In addition, as I had counted all surnames starting with Gold and all hyphenated Weyl surnames among the Harvard alumni directory names, my initial Weyl Analysis results for the percentage of Jewish students at Harvard College, as reported by Prof. Gelman, were too high.  Using the same methodology on the Harvard alumni directory that enabled me to reproduce Unz’s result that Jews represent 6-7% of NMS semifinalists in the 25-state aggregate (as Unz reported in the first table of Appendix E), I obtained the revised estimate that Jews represented 7-9% of Harvard College students in Fall 2008.[14]  I have also performed Weyl Analysis on Harvard College’s current and publicly available directory, yielding the result that 5-6% of current Harvard undergraduates are Jewish, which is slightly lower than the percentage of Jewish NMS semifinalists determined via Weyl Analysis.[15]  Thus, when one uses the same objective methodology on the names of both NMS semifinalists (Unz’s proxy for the pool of qualified Harvard applicants) and Harvard undergraduates, one finds no evidence for Harvard’s “massive apparent bias in favor of far less-qualified Jewish applicants,” as claimed by Unz.

 

 

---

[1] According to The Crimson's Class of 2017 Freshman Survey, white Harvard freshmen reported a mean SAT score of 2233. The Crimson furnished the mean SAT score of Jewish respondents via email.

[2] http://andrewgelman.com/wp-content/uploads/2013/03/Mertz-on-Unz-Meritocracy-Article.pdf
http://andrewgelman.com/wp-content/uploads/2013/03/Mertz-response-to-Unz-March-9-post-final.pdf

[3] see section 5

[4] Unz reports here that employing Weyl Analysis on the set of names of NMS semifinalists produced estimates of the percentage of Jewish NMS semifinalists within 0.1 percentage point of the estimate he obtained by his subjective direct name inspection method.  Since both methodologies produce virtually identical results by Unz’s own admission, and I cannot replicate his subjective name inspection method, I shall henceforth state that Unz’s NMS results were based on Weyl Analysis. 

Also, note that Unz reported in Appendix E that Jews represented 6-7% of NMS semifinalists in the 25-state aggregate (i.e. the 25 states for which he had rosters of NMS semifinalist names).  Unz then extrapolated that Jews represent 6% of NMS semifinalists overall, though he did not provide details on how he arrived at this result.  In fact, Unz acknowledged here that his extrapolated Jewish % for Massachusetts (he had not included the MA lists in his original analysis) was considerably below the actual proportion of Jews.

[5] I would like to emphasize that I am not claiming that Harvard College is only 5-6% Jewish.  I’m pointing out that using the same methodology on both the set of NMS semifinalists and the Harvard College directory (which listed a total of 6,734 students) gives the same result.  As the percentage of Jewish undergrads at Harvard is undoubtedly higher than 5-6%, and Unz systematically underestimated the % of Jews in recent data sets of high academic achievers (yielding results within 0.1 percentage point of Weyl Analysis on the NMS names), it is evident that Weyl Analysis produces underestimates; i.e. Jews represent more than 6-7% of NMS semifinalists.

Also, while the Harvard College directory is publicly available, it is laborious to search for the purposes of Weyl Analysis, so I will explain in footnote 15 how to do so.

[6] See p. 6/8 of the 2011-2012 Annual Report of the National Merit Scholarship Corporation

[7] http://voices.washingtonpost.com/answer-sheet/college-admissions/if-you-live-in-west.html

Please see footnote 19 for discussion of PSAT percentiles.

[8] To be clear, the correlations are not exact (i.e. magnitude 1), but I’m trying to explain the concept of correlations to a general audience.  For the numerical values of the correlations (which I calculated in several different ways), please see section 2.

[9] More precisely: if a uniform higher national qualifying score were used, the range of [P]SAT scores among white and Asian NMS semifinalists would more closely approximate that of white and Asian Harvard students, particularly those who are neither athletic recruits nor legacies.

[10] More precisely: the average white NMS semifinalist has a lower [P]SAT score than the average white Harvard undergraduate, particularly those who are not recruited athletes.

[11] Unz defended his use of Hillel’s enrollment figures by employing the “appeal to authority” logical fallacy: various media organizations and scholars like Prof. Jerome Karabel have cited Hillel’s data in the past; thus, Unz should not be criticized for doing so too.  I would like to emphasize that when Harvard Hillel’s Jewish enrollment figures were based on religious preferences cards submitted by students (which is no longer the case), Hillel’s data was indeed worthy of citation by scholars and the media.  In fact, Unz specifically noted that the decline in Princeton’s undergraduate Jewish enrollment in the 1990s received media attention. It is interesting to note that the Princeton Hillel did respond to my inquiry regarding how it calculates its Jewish enrollment figures: Rabbi Julie Roth, Executive Director of the Princeton Hillel, stated that their data is based on students who self-identify as Jewish: those who register their religious preference as Jewish with the Princeton Office of Religious Life, as well as any additional students who register for Hillel programs.  Since the Princeton Hillel’s undergraduate Jewish enrollment figures are based on students who self-identify as Jewish (in contrast to Harvard), this data is worthy of citation.

In any case, that others have cited Hillel’s data does not mean their figures should serve as the basis of a statistical analysis comparing them to Jewish NMS semifinalists identified on the basis of an entirely different methodology, especially when it is possible to employ the same methodology on both data sets.

[12] It is likely that some ethnic Jews who are atheist or agnostic did not identify their religious affiliation as Jewish. According to The Crimson's freshman survey, 29% of white Harvard students identified as atheist or agnostic, among whom we would expect to find both ethnic Jews and non-Jewish whites. Hence, it is reasonable to expect that ~29% of ethnic Jews identified as atheist or agnostic, meaning that ~13% of Harvard freshmen are ethnically Jewish. According to the Pew Research Center, "religious disaffiliation is as common among all U.S. adults ages 18-29 as among Jewish Millennials (32% of each)," which is consistent with The Crimson's survey results. Furthermore, in spring 2013, I asked several current Harvard undergraduates for their personal estimates of the percentage of Jewish Harvard College students, and the most frequently cited figure was 10-15%, which is also also consistent with The Crimson's findings.

[13] Unz’s ambiguous description of Weyl Analysis: “we can perform the same population estimate using distinctly Jewish last names, such as the small set of Cohen, Kaplan, Levy, and "Gold—" (J1) which were suggested by blogger Steve Sailer and his Jewish correspondent, or else extended to include the full set of such names (J2) utilized by Weyl by adding Berman, Bernstein, Epstein, Friedman, Greenberg, Katz, Levine, Rosenberg, and Stern. Based on the 2000 Census estimates, the first group includes approximately 1 in 20 American Jews, while the larger set raises the fraction to 1 in 12.”  I originally thought "Gold-" meant Gold*, but I was getting higher results than Unz for the percentage of Jewish National Merit semifinalists assuming Gold- meant Gold*.  I inferred that Unz may have meant a restrictive list of Gold- names from the following sentence in his article: “…California contains nearly one-fifth of all American Jews, hence almost 60,000 Cohens, Kaplans, Levys, Goldens, Goldsteins, Goldbergs, Goldmans, and Golds, and this population produced only 4 NMS semifinalists…”  I later determined that indeed {Gold-}= {“Gold, Goldberg, Golden, Goldman, and Goldstein”} by reproducing Unz’s 12 and 20 scaling factors using the 2000 Census data found here.

I also reproduced Unz’s estimate that Jews represented only 6-7% of National Merit semifinalists in the 25 state aggregate when I restricted to those 5 Gold- surnames and half-weighted or excluded hyphenated surnames with one of the Weyl surnames.  Finally, I determined that Unz had excluded hyphenated surnames both because the US Census Bureau’s technical documentation indicated that hyphenated surnames were concatenated to form unique surnames and because Unz’s misleading claim that Weyl Analysis gives 0% for 8 states is only reproducible by excluding the hyphenated Gold surname on the Missouri list and ignoring the fact that there is one J2 name on the Tennessee roster (there are no J1 names).  

I’d also like to point out other false claims in Unz’s specious reply to Prof. Gelman’s first critique.  Unz stated that “if Mertz had provided similar results for the other seventeen states I used, Gelman would have noticed that Weyl Analysis results were smaller—sometimes considerably smaller—than my direct inspection estimates, and these latter states (which Mertz omits) actually include California and Texas whose NMS totals are by far the largest.”  This is false.  In particular, the Weyl Analysis results for California are the same as Unz’s direct inspection estimate (4%), and the Weyl Analysis results were not smaller for the other seventeen states, as I demonstrated here.  However, please note that Missouri would actually give 0 because the student in question has a hyphenated surname and that the J2 result for California is 4% if you exclude the hyphenated surname.  Finally, Unz is wrong about the logical error he claims I made (which he incorrectly attributed to Prof. Mertz) regarding sampling technique inaccuracies on small data sets.  The error I made was to full-count hyphenated surnames and to assume Unz meant {Gold*} by {Gold-}, as my erroneous assumptions gave results on the Harvard directory that were closer to reality.  Using a restrictive set of Gold- surnames and excluding hyphenated surnames gives grossly underestimated results.  By the way, as Unz was forwarded my pdf files in which I documented my Weyl Analysis results, he presumably knew that I had interpreted {Gold-} as {Gold*} and had full-counted hyphenated surnames; thus, this was the source of the discrepancy, not my inability to understand introductory statistics.

[14] Unz did not explain how he extrapolated from the 25-state aggregate to obtain his estimate of the overall percentage of Jewish NMS semifinalists.  In fact, he acknowledged here that his extrapolated Jewish % for Massachusetts (Unz had not included the MA lists in his original analysis) was considerably below the actual proportion of Jews.

[15] On August 26, 2013, I searched http://facebook.college.harvard.edu, the restricted access directory for Harvard College (which listed a total of 6,734 students), for the Weyl distinctive surnames.  However, Harvard University also has a public directory:
https://www.directory.harvard.edu/phonebook/
For less common names, like Epstein, all results are listed, only one of whom is a Harvard College student (as of September 9, 2013).  For more common names like Cohen, it returns an error message saying “Too many results to display.  Please refine your search.”  However, one can then put in A* for first name, which returns several Harvard affiliates with first names beginning with an A and last name Cohen but no Harvard College students, and continue until Z* to unearth all Harvard College students with the surname Cohen.  While checking all the results in this fashion is time-consuming, surely Unz can write a script to automate the process, just as he wrote a script to compile college enrollment data from the NCES IPEDS website.  Since Unz apparently considers the Jewish enrollment at Harvard to be a matter of great concern (as he attributes our nation’s “enormous economic and social problems” to the “absurdly skewed enrollments of our elite academic institutions,” which Unz portrays as overrun with unqualified Jewish students who are “beneficiaries of underhanded manipulation and favoritism”), surely he can dedicate an hour or two to searching the public Harvard directory in the manner I’ve described.  Anyway, since the Harvard directory is publicly available, Unz can no longer describe my data as unverifiable. 

Perhaps Unz would counter that a sample size of 6,734 is not large enough for Weyl Analysis to be accurate.  After all, Unz states that the Weyl Analysis results for the NMS competition were based on over 23,000 names.  I also performed Weyl Analysis on a set of ~6,500 names in the Harvard alumni directory from the Harvard College Classes of 2009-2012, yielding the estimate that Jews represented 7-9% of Harvard College students in Fall 2008.  Furthermore, I searched facebook.college.harvard.edu in April 2013, which gave the estimate that 6-7% of Harvard College students (for the 2012-13 academic year) were Jewish. Hence, based on ~15,000 Harvard student names, Weyl Analysis gives the estimate that 6-8% of Harvard College students (from the Classes of 2009-2017) are Jewish.

I could also look at earlier Harvard College class data in the Harvard alumni directory.  Alternatively, I was able to perform Weyl Analysis on the Yale alumni directory (which listed a total of 5,238 students from the Yale College Classes of 2009-2012), which yielded the estimate that 9-11% of Yale College students were Jewish in Fall 2008.  Finally, the Princeton directory is public, and a search of the Princeton directory gives the estimate that 8-9% of Princeton undergrads (undergraduate enrollment at Princeton: 5,222) are Jewish.  Hence, we arrive at the estimate that 7-9% of HYP (Harvard, Yale, Princeton) students are Jewish on the basis of over 25,000 names, far below Hillel’s Jewish enrollment figures that Unz used for his calculations.  (This is indeed somewhat higher than the 6-7% Weyl Analysis results from the NMS semifinalist names but is easily accounted for by the overrepresentation of students from the Northeast at HYP.  In section 3, I calculate enrollment ratios for Harvard based on the geographic distribution of Harvard students in order to demonstrate the significant impact of geography.)

[16] http://voices.washingtonpost.com/answer-sheet/college-admissions/if-you-live-in-west.html

[17] While the average scorer on the PSAT is expected to raise his/her score on the SAT, this is not the case for high scorers on the PSAT.  More precisely: on average, students score 55 points higher on the SAT than the PSAT/NMSQT (equivalent to 5.5 points on the PSAT scale); however, according to the College Board (p. 13-17), students scoring 70+ on each PSAT/NMSQT section (i.e. most NMS semifinalists) obtain similar scores on the SAT (on average).  Students scoring 70+ on the PSAT writing section tend to score somewhat lower on the SAT writing section (on average), while students scoring 70+ on the PSAT math section tend to score a bit higher; students scoring 70+ on the PSAT verbal/critical reading section tend to score about the same on the SAT.

[18] Dartmouth College, which is somewhat less selective than Harvard, reports that the mean SAT score of admitted students is 2220.  Dartmouth’s yield is lower than Harvard’s, so it stands to reason that the mean SAT score of enrolled students is a bit lower.  Both Harvard and Dartmouth publish the 25^th to 75^th percentile SAT scores of enrolled students (I placed the midpoint of the score range in parentheses):

	Harvard	Dartmouth
Verbal/Critical Reading	700-800 (750)	670-780 (725)
Math	710-790 (750)	680-780 (730)
Writing	710-800 (755)	680-790 (735)

Adding up the midpoints of each score range is probably a decent estimate of the median score of enrolled students, which gives us 2255 at Harvard and 2190 at Dartmouth.  Prior to the publication of The Crimson's survey results, I had estimated the average SAT score of Harvard students at 2250; however, according to The Crimson's survey of the Class of 2017, Harvard freshmen reported a mean SAT score of 2237.

As I discuss in section 4, the mean (math + verbal) re-centered SAT score of Asian-Americans in the Harvard College Class of 1995 was 1530 vs 1470 for whites.  The Department of Education Office for Civil Rights (OCR) found that eliminating Harvard’s preference for recruited athletes and legacies virtually eliminated the disadvantage Asians suffered in gaining admission to Harvard, i.e. the average white student admitted to Harvard who was neither a legacy nor a recruited athlete presumably had qualifications similar to the average Asian admitted to Harvard, implying that the mean SAT score of white students who were neither legacies nor recruited athletes was ~1530.  Indeed, Yale’s 2001 SAT score data clearly demonstrates the impact of the admissions preference for recruited athletes: the mean SAT score for whites was 1450 vs 1482 for Asians, but 24% of white students were athletes with a mean SAT score of 1347.  White students who were not athletes had a mean SAT score of 1482, indicating that the 76% of white Yale students who were not athletes scored 135 points higher (on average) than the 24% of white students who were athletic recruits.  Furthermore, the mean SAT score of white students who were not recruited athletes was 45 points higher than the mean SAT score of Yale students overall.  Please note that the writing section was added to the SAT in 2005.  One can multiply the re-centered scores by 1.5 to roughly estimate these scores on the new 2400 scale, implying that the mean SAT score of Asian-American and white (including Jewish) students who are neither recruited athletes nor legacies is likely ~70 points higher than the mean at HYP, i.e. 2300+.  That is, at HYP, the SAT score distribution of white students is likely bimodal, with one peak for athletic recruits around ~2100 (according to The Crimson's freshman survey, the average SAT score of recruited athletes is 2082) and one peak (representing most white students) around ~2300, giving a mean of ~2230.  (The legacy preference is smaller in magnitude.) Hence, most white students and almost all Asian students at HYP (i.e. those who are neither athletic recruits nor legacies) likely average 2300+ on the SAT today. Indeed, The Crimson found that the average SAT score of Asian freshmen is 2299.  This is significantly higher than the mean SAT score of NMS semifinalists.

[19] The most reputable source that has published NMS qualifying scores by state is The Washington Post, so I used its list for the Class of 2010 NMS qualifying scores (though it was missing Alabama, which I got from here).  I also figured 2010 was the best year to use, as the 2010 NMS semifinalist lists are available for both the two largest states (CA and TX) and the two states with the highest NMS qualifying scores (MA and MD).  The Class of 2010 National Merit semifinalists took the 2008 administration of the PSAT, the percentiles for which were obtained from “Understanding 2008 PSAT/NMSQT Scores,” a College Board publication that is no longer posted on its website.  The 2012 version is available here, though the percentiles were a bit different for the 2012 administration of the PSAT.  The number of NMS semifinalists allocated per state is from the National Merit Scholarship Corporation’s 2010-11 Annual Report, which is no longer posted on NMSC’s website.  Unz cited these figures in Appendix E.

[20] I've uploaded a pdf file of my Mathematica notebook, so interested readers can see how I performed my calculations:
https://sites.google.com/site/nuritbaytch/MeritocracyMathematica.pdf
Since the Jewish population data is not normally distributed, I also calculated the Spearman rank correlation.  The results are similar to those for the Pearson correlation: The Spearman correlation between a state’s NMS qualifying score and its % of non-Jewish whites is -0.43 (p-value = 0.002), while the correlation between a state’s NMS qualifying score and its % of Jews is 0.76 (p-value < 0.001); for Asians, the correlation is 0.73 (p-value < 0.001), which is notably higher than the corresponding Pearson correlation.  The Spearman correlation between a state’s NMS qualifying score and its percentage of Jewish NMS semifinalists (as reported by Unz) is 0.43 (p-value = 0.03), while for Asians the correlation is 0.53 (p-value = 0.006); in contrast, the correlation between a state’s NMS qualifying score and its percentage of non-Jewish white NMS semifinalists is -0.55 (p-value = 0.004).

In order to filter out any possible impact of non-Asian people of color on a given state’s NMS qualifying score, I also calculated correlations after normalizing the Jewish, Asian, and non-Jewish/non-Hispanic white population data (i.e. dividing the % of each of the aforementioned 3 ethnic/racial groups by the sum of all 3).  Once again, the results were similar: The Pearson correlation between a state’s NMS qualifying score and its normalized % of non-Jewish whites is -0.45 (p-value = 0.001), while the correlation between a state’s NMS qualifying score and its normalized % of Jews is 0.61 (p-value < 0.001); for Asians, the correlation is 0.31 (p-value = 0.03).  The Spearman rank correlation between a state’s NMS qualifying score and its normalized % of non-Jewish whites is -0.74 (p-value < 0.001), while the correlation between a state’s NMS qualifying score and its normalized % of Jews is 0.75 (p-value < 0.001); for Asians, the correlation is 0.70 (p-value < 0.001). 

[21] Unz acknowledged here that he had not counted as Jewish a two-time US IMO team member with a common Israeli/Hebrew surname.  (Please note that Unz’s claim that this single surname error accounts for virtually the entire discrepancy between his results and Prof. Mertz’s confirmed data is false, as explained by Prof. Mertz here.) Furthermore, Unz has referred to me as male despite that he knew my name and even took the liberty to name me in his first reply to Prof. Gelman; my first name is a popular Israeli/Hebrew female name.  Hence, it is clear that Unz has limited familiarity with Israeli/Hebrew names, making it all the more preposterous that he considered himself qualified to draw sweeping conclusions on the basis of his questionable skills in identifying Jews.

Famous examples of Israeli/Hebrew surnames include Peres, Refaeli, and Barak.  As you can see, Israeli/Hebrew surnames are often quite different from typical Ashkenazi names like Epstein, Goldman, and Rosenberg.

[22] I’m not-quite-correctly defining Sephardic Jews as all Jews who are not Ashkenazi Jews.  Famous people with [paternal] Sephardi heritage include Dara Torres, Hank Azaria, and Emmanuelle Chriqui (also quite different from typical Ashkenazi Jewish names).

[23] Unz repeatedly highlighted the poor showing of Jews among California NMS semifinalists (Jews comprise only 4% of CA NMS semifinalists according to Unz and 2.4% of CA high school students), suggesting that Jewish students were unable to compete in CA due to its high NMS qualifying score.  In fact, CA has not had the highest NMS qualifying score in any of the past several years; the only “states” that have had the highest NMS qualifying score in each of the past several years are Washington, DC and Massachusetts, where Jews were the most overrepresented ethnic/racial group among NMS semifinalists.  This was not the case for Maryland in 2010, when it tied Massachusetts et al for highest NMS qualifying score, and where Asians were the most overrepresented ethnic/racial group among NMS semifinalists.  This may be due to the fact that Baltimore has a large ultra-Orthodox Jewish population, who are unlikely to produce [many] NMS semifinalists.

My claim regarding Israeli and/or Sephardic Jews representing a higher fraction of NY and CA Jews than in the rest of the US is based on data from the Jewish Telegraphic Agency and from Prof. Ira Sheskin, whose figures on the Jewish population per US state were cited by Unz:
http://web.archive.org/web/20120609165711/http://www.jta.org/news/article/2010/12/22/2742296/israeli-population-jumps-in-the-us-but-is-still-hard-to-count
http://www.bjpa.org/Publications/downloadPublication.cfm?PublicationID=16101

To illustrate this, I looked at the names of NMS semifinalists in Los Angeles, North Hollywood, and Beverly Hills, and indeed, there were numerous Israeli and/or Sephardic Jewish surnames, examples of which include:  Arom, Barzideh, Barzilay, Batscha, Boodaie, Haddad, Raffi, and Soroudi.

[24] Despite Unz’s misleading statements that NMS semifinalists constitute the top 0.5% of high school students, NMS semifinalists in the majority of states merely had to surpass a threshold in the 96^th-98^th percentiles (at least in 2010).  Typically, no state has a NMS qualifying score in the top 0.5%, though in 2011, NMS semifinalists in MA, DC, and NJ actually did have to score in the top 0.5% on the PSAT, assuming the NMS qualifying scores listed here are accurate:
http://www.hhsib.org/LabDocs/National_Merit_Scores_By_State.pdf

Also, to be clear, in 2010, the three largest states (CA, TX, and NY) all had qualifying scores in the 99^th percentile, so in fact, the majority of NMS semifinalists did score in the 99^th percentile on the PSAT.  However, it is certainly not the case that all or most NMS semifinalists score in the top 0.5% on the PSAT.

[25] I shall present more details on the properties of the right tail of normal distributions to support my claim that Asians and Jews are likely to constitute a higher percentage of students scoring 230[0]+ than of NMS semifinalists in general.  Unz cited Helmuth Nyborg’s analysis of the IQ data for white adolescent Americans from the 1997 National Longitudinal Survey of Youth, highlighting Nyborg’s finding “that Americans raised in the Episcopal Church actually exceeded Jews in mean IQ.”  Unz omitted Nyborg’s extensive discussion of the higher standard deviation of Jews (emphasis mine): “The denominational high-IQ fraction was defined as the summed proportion of members with IQs ≥ 120…Interestingly, Jews surpass Episcopalians in high-IQ fraction, even if Episcopalians have slightly higher average IQ, the reason being that Jewish SD is larger that the Episcopalian (SD 13.14 versus 11.68, respectively). According to normal distribution theory there will accordingly be 1.6 Jew for each Episcopalian with IQ 145, and this ratio grows exponentially with increasing IQ…The high ranking of Jews dovetails nicely with the fact that no less than 23% of all Nobel prizes awarded 1901–2007 were harvested by Jews who represent only about .25% of the world's population.”  That is, Jews constitute a higher percentage of those with IQs > 140 than of those with IQs > 130. 

One can also see that Asian-Americans are likely to constitute a higher proportion of those scoring 230[0]+ than among those scoring 210[0]+ from the data on SAT percentile ranks by ethnicity published by the College Board here.  The category for Asians conflates Asian-Americans and Asians attending high school outside the US, who obtain higher SAT scores than Asian-Americans on average and appear to comprise a nontrivial proportion of the ethnic Asians taking the SAT, since Asians constitute a higher percentage of students taking the SAT (11%) compared to the PSAT (8%); hence, these results are likely to overstate the performance of Asian-Americans, but they illustrate the general principle that a group overrepresented among the top ~1% (NMS semifinalists) is likely to be even more overrepresented among the top ~0.5% (Harvard admits).  Making the simplifying assumption that Asians and whites comprise all of those scoring 700+ on each section of the SAT, I estimate that Asians represent 21% of those scoring 700+ and 23% of those scoring 750+ on the verbal section, 43% of those scoring 700+ and 56% of those scoring 750+ on the math section, and 28% of those scoring 700+ and 33% of those scoring 750+ on the writing section.  Thus, Asians comprise a notably higher share of those scoring 750+ on each section (i.e. Harvard material) than among those scoring 700+ on each section (roughly the set of NMS semifinalists).

[26] http://www.princeton.edu/admission/pdfs/Profile_12.pdf
http://www.usnews.com/education/articles/2009/10/07/do-elite-private-colleges-discriminate-against-asian-students

[27] assuming Unz-ian logic -- I am by no means suggesting that Harvard should admit the 2000 highest SAT scorers among its applicants.  This is not how Harvard admissions works, nor is it how it should work.

[28] http://research.collegeboard.org/programs/psat/data/cb-jr/archived/2008

Please note that in Midwestern and Southern states where the ACT is more widely used than the SAT, the mean PSAT score tends to be higher than in states where the SAT is more popular.  This is because top Midwestern students applying to elite universities outside of the Midwest often take the SAT as well and thus would take the PSAT both for practice and a shot at a National Merit Scholarship, while weaker Midwestern students are less likely to take the PSAT or SAT, as the ACT is sufficient for admission to Midwestern colleges.  (See here for further discussion on how students in ACT states who take the SAT are typically the strongest students.)

In “ACT states,” the mean PSAT scores tend to be above average, but the standard deviations are typically lower than average, which explains why these states tend to have low NMS qualifying scores.

[29] While PSAT scores are normally distributed overall, it may not be true in MA and/or TX.  The graph is intended to impart to readers a general understanding of the properties of the right tails of normal distributions; it could certainly be an inaccurate rendering of the distribution of PSAT scores in TX and/or MA.  In any case, one can peruse the exact figures on the distribution of scores in each state on each section of the PSAT here:
http://research.collegeboard.org/programs/psat/data/cb-jr/archived/2008

I generated the graph assuming that the standard deviation of the total PSAT score for each state was 0.9 * the sum of the standard deviation on each section, as that was the case for the national figures.

Finally, please note that I did not scale the graphs by population size.  I compared the raw figures for the number of high scorers in TX and MA later in the following paragraph.

[30] According to the Fall 2010 NCES IPEDS data for Harvard, 219 freshmen were from Massachusetts (out of ~1,509 American students). To be clear, Unz did not include Massachusetts in his original analysis, but after I (and perhaps others) linked to the MA NMS rosters, Unz described MA’s impact as “negligible.”  As ~15% of Harvard’s American undergrads hail from Massachusetts, the ethnic/racial distribution of MA’s NMS semifinalists clearly has a significant impact (assuming the ethnic/racial distribution of NMS semifinalists is a meaningful metric, the underlying premise of Unz’s article). 

[31] Data on the intended majors of National Merit Scholars is on p. 5/7 of the 2011-2012 Annual Report of the National Merit Scholarship Corporation.  The percentages add up to 70%; in the 2011 Annual Report, the other 30% is specifically delineated as “undecided” or intending double majors.  Hence, I divided the 15% of National Merit Scholars intending to major in engineering by 70 to arrive at the result that 21% of National Merit Scholars indicating a specific major plan to major in engineering.  The NMSC link will probably reflect the data for future National Merit Scholars at a later date and, thus, may be different from what I report.  Finally, I realize that the distribution of majors among National Merit Scholars may differ from that among National Merit Scholarship semifinalists, but I doubt it’s significantly different.

The data on incoming Harvard freshmen is here:
http://news.harvard.edu/gazette/story/2012/05/yielding-to-an-invitation/
Over 99% indicate their intended major (“concentration” in Harvard-speak). 

[32] Kimberly Goyette and Ann Mullen. 2006. “Who Studies the Arts and Sciences? Social Background and the Choice and Consequences of Undergraduate Field of Study.” The Journal of Higher Education 77(3):497-538:
http://astro.temple.edu/~kgoyette/major.pdf
http://www.jstor.org/stable/2649134
http://www9.georgetown.edu/grad/gppi/hpi/cew/pdfs/whatsitworth-complete.pdf

Also, see p. 242 of No Longer Separate, Not Yet Equal (2009) Thomas J. Espenshade and Alexandria Walton Radford:
http://books.google.com/books?id=47rORpFmuBwC&pg=PA242&lpg=PA242

[33] Studies have found that students from upper income families are significantly less likely to major in engineering than lower income students.  According to No Longer Separate, Not Yet Equal, “42% of lower-class students and 20% of students from working-class backgrounds major in engineering, as compared to 12% of those from the middle-class, 10% from the upper-middle class, and just 6% of upper-class students.”
http://books.google.com/books?id=47rORpFmuBwC&pg=PA243&lpg=PA243

American Jews have the highest mean gross household income ($114,517 in 1996 US$) compared to all other white religious denominations according to the Nyborg study cited above; thus, the finding that upper income students are significantly less likely to major in engineering lends credence to my conjecture that Jewish students are less likely to study engineering than whites in general, casting doubt on Unz’s suggestion that the lower % of Jews at MIT and Caltech vs Harvard is due to the former’s more “objective/meritocratic” admissions practices.

To be clear, my personal observation applies to American Jews, not Israeli Jews (i.e. I don’t believe this is true in Israel).  In any case, I realize my personal observations have no value has far as statistical analyses go, but I thought I’d speculate on what I believe is the reason for the apparently lower % of Jews at MIT and Caltech.

[34] Only 13% of the Stanford students with Weyl distinctive Jewish surnames were majoring in engineering vs 22% of Stanford students in general: 2 of the 15 Stanford undergraduates with Weyl distinctive Jewish surnames (whose majors were listed) were majoring in engineering when I searched the Stanford directory on May 24th.  (see footnote 47 for further discussion of the Stanford directory.)  This is obviously a small sample size and may not be representative of Jewish students at Stanford in general, so I’m not pretending my results are statistically significant (though Unz reported on similarly small data sets in his article, such as recent Putnam winners and US IMO participants).  My data on the % of engineering majors at Stanford is from here:
http://news.stanford.edu/news/2012/september/new-student-orientation-091712.html

US News currently ranks Stanford’s undergraduate engineering program higher than Caltech’s:
http://colleges.usnews.rankingsandreviews.com/best-colleges/rankings/engineering-doctorate
(This ranking is subject to change in the future, of course.)

I did the same analysis on the MIT directory: 46% of the students with Weyl distinctive Jewish surnames are engineering majors vs 63% of MIT students in general.  The directory at alum.mit.edu has info on current students (see footnote 44 for discussion of the MIT directory): 6 of the 13 undergraduates with Weyl distinctive Jewish surnames (whose majors are listed) were majoring in engineering when I searched the directory on May 24th.  (see the above footnotes for caveats)  My data on the % of engineering majors at MIT is from here:
http://web.mit.edu/ir/surveys/pdf/2012MITFreshmanSurvey_Highlights.pdf

[35] It is almost certainly the case that the % of Jewish students is much lower among the international students than among the American students, though it is nonzero, as it is likely that there are Jewish undergraduates at Harvard from Canada, UK, Israel, etc. Indeed, according to The Crimson's Class of 2017 Freshman Survey, 4.5% of international students identified as Jewish.

[36] Prof. Mertz already pointed out that Unz used the wrong enrollment data for Harvard College, an error Unz failed to acknowledge in his specious reply.  Prof. Mertz was not suggesting that Unz had included part-time undergraduates in his calculations, as Unz claimed.  Unz’s calculations are from the NCES IPEDS full-time undergraduate enrollment figures for Harvard University, which lists 3,652 male and 3,555 female full-time Harvard undergraduates in Fall 2011, summing to 7,207.  This figure is higher than the enrollment at Harvard College; nevertheless, Unz incorrectly calculated Harvard’s racial enrollment figures in Appendix C using this data: he computed that Harvard was 45.0% white (in Fall 2011) by dividing 3,244 by 7,207, that Harvard was 17.2% Asian-American by dividing 1,242 by 7,207, etc.  The correct enrollment data for Harvard College can be found on the website of the Harvard Provost’s Office.  Note that the total enrollment at Harvard College was 6,657 in Fall 2011.  This gives following enrollment data for Harvard College: 17.8% Asian-American, 44.6% white, 4.7% of two or more races, 6.0% of unknown race, 9.1% Hispanic, 6.8% black, 10.8% international students.

[37] The rest identified as Native American or Pacific Islander. 

[38] In The Crimson's freshman survey, note that the enrollment percentages for each race/ethnic group add up to 114% due to some students identifying as multiple races/ethnicities. Hence, I divided by the total (114) to obtain my figures. Also, The Crimson separated the categories for "Asian" and "Indian;" this is not consistent with the practices of the US Department of Education, which classifies both East Asians and South Asians under the umbrella term "Asian." Hence, I conformed to the federal government's classification conventions. Finally, I assume The Crimson conflated international students and American students, and since it is likely that Asians are better represented among international students, the % of Asian-Americans is somewhat lower.

[39] In the Fall 2010 NCES IPEDS data for Harvard University, the number of freshmen from each state is listed.  The total adds up to 1,670, which is identical to the number of freshmen attending Harvard College in Fall 2010 (i.e. this data does not conflate Harvard College and Extension School students).

Since Unz seems quite convinced that the Jewish provosts of Harvard are favoring their brethren seeking admission, perhaps he might claim that the overrepresentation of students from MA, NY, NJ, etc. is simply more evidence of this favoritism, as those states have high Jewish populations.  However, if you look at the 2010 IPEDS data for any university, you are likely to find that the most overrepresented state is that where the university is located.  At both Harvard and MIT, Massachusetts supplies the 2^nd greatest number of students after California, meaning Massachusetts (which is allocated only 2% of NMS semifinalists) is the most overrepresented state at both institutions.  At Yale, Connecticut appears to be the most overrepresented state while nearby NY supplies the most students.  At Princeton, New Jersey is the most overrepresented state; NJ contributes the 2^nd highest number of students after CA.  Note that more students hail from MA than TX at all of the aforementioned institutions. 

The overrepresentation of each university’s home state is, in large part, due to the preference of many teens to stay near home for college, but it may also be due to favoritism for its neighbors, as the UPenn dean of admissions stated that UPenn has a “strong commitment to its backyard.”  Indeed, more students hail from PA than from any other state at UPenn:

(Note that once again, MA supplies more students than TX.)

Likewise, students from the West Coast are disproportionately represented at Stanford and Caltech, as I discuss later in this section.

[40] I’m not claiming that Harvard should be 1% underrepresented minorities; rather, I’m merely employing Unz’s methodology of comparing the ethnic distribution of NMS semifinalists to that of Harvard students.  I disagree with Unz’s premise that Harvard students “should” mirror the demographics of [P]SAT high scorers; furthermore, Unz is overestimating the importance of SAT scores in the Harvard admissions process.

[41] I would like to emphasize that, like Unz, I’ve made no attempt to quantify the statistical significance of my enrollment ratios, and I am not actually claiming that Jews are the most underrepresented group at Harvard in comparison to their academic “merit.”  I’m simply showing an alternative (and I believe more accurate) method of calculating Unz’s enrollment ratios.  Note that I also make no attempt to correct for the greatly varying NMS qualifying scores by state; thus, even if such a calculation were to find that non-Jewish whites have the lowest enrollment ratio, one cannot validly conclude that non-Jewish whites are actually underrepresented in comparison to their “merit” due to the inherent bias in the NMS data (i.e. negative correlation between a state’s NMS qualifying score and its % of non-Jewish whites).

In any case, I’m sure one can quibble with my methodology, but I’m not drawing any conclusions from these numbers other than that there is no evidence that Harvard discriminates in favor of Jewish students as Unz claims.

I've uploaded a pdf file of my Mathematica notebook, so interested readers can see how I performed my calculations:
https://sites.google.com/site/nuritbaytch/MeritocracyMathematica.pdf

[42] Unz does not explicitly define “meritocratic,” though he presumably means admissions based purely on grades and standardized test scores.  In fact, Chris Peterson, an MIT admissions counselor, has stated: “SAT scores aren't merit. they are one component of judging academic preparedness, which itself is one component of merit.”  On the MIT Admissions blog, he wrote that “the numbers are probably the least important part of an application to MIT.”  Indeed, according to MIT’s Common Data Set, the most important factor in MIT undergraduate admissions decisions is “character/personal qualities.”  According to Caltech’s Common Data Set, the most important factor in Caltech’s undergraduate admissions decision is “rigor of secondary school record” with extracurricular activities rated as “important” along with GPA and standardized test scores; Caltech also takes into consideration “alumni/ae relation” as does Harvard.  I imagine that MIT and Caltech place a greater emphasis on standardized test scores than does Harvard, as students who score below a minimum threshold on the SAT [math section] are unlikely to succeed in math and physics majors (whereas no such phenomenon was found for humanities/social sciences majors), though Harvard can hardly be faulted for admitting, say, an exceptionally talented writer with unexceptional SAT scores or math grades, as Harvard places a greater value on humanities talent than do MIT and Caltech.  While the evaluation of writing talent may not be entirely objective, surely valuing creative writing skills (which are not captured by SAT scores) is a “meritocratic” admissions criterion.  That said, an argument can certainly be made that legacy status and/or athletic ability do not qualify as [academic] meritocratic criteria, though Caltech also claims to take legacy status under consideration.

[43] At Caltech, 0.5% of undergrads did not identify their race, while at MIT, 4% of undergrads did not identify their race.  In contrast, 6% of Harvard College students did not identify their race, meaning Harvard’s enrollment data is less reliable and that the ratio between the actual white enrollment at Harvard and that at MIT and Caltech is likely even higher.

Data for Harvard College is taken from “Fall Enrollment by Ethnicity, 2011” here:
http://www.provost.harvard.edu/institutional_research/harvard_fact_book_2012_enrollment.pdf

The Caltech and MIT data are from the Fall 2011 NCES IPEDS data.

[44] MIT’s directory is public; however, some students are listed as affiliates, so the public directory cannot be used for the purposes of Weyl Analysis.  My Weyl Analysis results are based on the MIT alumni directory, which lists current students (undergrads are indicated by their class year), along with many students’ majors. My results are based on the data for the MIT Classes of 2013-2016; at some point, the directory will be udpated with the Fall 2013 enrollment data, rendering my results outdated.

[45] Performing Weyl Analysis on the MIT directory yielded the estimate that there are 160-216 Jewish undergrads at MIT.  According to the MIT IPEDS data, there are 2407+1947= 4,354 undergrads at MIT.  Subtracting 451 international students gives 3,901 American students at MIT.  We assume that none of the international students are Jewish and that Jews are proportionately represented among students of unknown race and 2+ races, who total 145+175=320.  320/3901 = 0.08, so we reduce the Weyl estimates of total number of Jewish undergrads at MIT by 8%, yielding the result that Jews represent 147 to 199 of the 1,567 white undergrads at MIT, i.e. 9-13%.  As explained previously, the Harvard directory yielded the estimate that there are 282-338 Jews at Harvard College out of 2,966 white students at Harvard College => Jews represent 10-11% of white Harvard undergrads. http://www.provost.harvard.edu/institutional_research/harvard_fact_book_2012_enrollment.pdf

[46] As I discuss in footnote 88, the provenance and accuracy of the Jewish enrollment data for Caltech are unknown.

Caltech data: http://admissions.caltech.edu/documents/142-factsheet_final.pdf
Harvard data: http://www.admissions.college.harvard.edu/apply/statistics.html

I defined the Northeast as New England and the mid-Atlantic.  MIT’s geographic distribution is closer to Harvard’s: 32% hail from the Northeast, while only 18% are from the West:
http://mitadmissions.org/apply/process/profile

I’d also like to point out that 73% of freshmen admitted to UC-Berkeley are from CA; Unz reports that 11% of college-aged Californians are Asians, while only 2.4% are Jewish, so of course Berkeley has many times more Asians than Harvard.  Undergraduate admissions at UC-Berkeley are considerably less selective than Harvard on average (though selectivity varies by major), so a comparison of their admissions practices yields little useful info.
http://www.berkeley.edu/about/fact.shtml

All of these webpages are subject to change in the future, rendering the above data obsolete. 

[47] Stanford’s public directory is here:
https://stanfordwho.stanford.edu/SWApp/

I originally searched Stanford’s public directory in February 2013, and Prof. Gelman reported my finding that Weyl Analysis yielded the result that 4-5% of Stanford undergrads are Jewish.  This was based on my original mistaken understanding of how Unz performed Weyl Analysis (see footnote 13), so I had included students with hyphenated Weyl surnames, as well as a student with the surname Golding.  Excluding those names (i.e. performing Weyl Analysis as Unz did) gives the estimate that 3-5% of Stanford undergrads are Jewish.  When I searched the Stanford directory again in late May, both seniors in the Class of 2013 and incoming freshmen from the Class of 2017 were listed (I recognized a name from a 2013 NMS roster, in fact), so I used my results from my February search instead.  I hope that someone tried to replicate my results when Prof. Gelman originally reported them!

Data on geographic distribution of Stanford students:
http://news.stanford.edu/news/2012/september/new-student-orientation-091712.html

[48] The Chosen (2005) Jerome Karabel, pp. 504-6:
http://books.google.com/books?id=zwf-Ofc--toC&pg=PA504&lpg=PA504

Note that OCR found that the UCLA math department was discriminating against Asian-Americans for graduate admission:
http://www.thecrimson.com/article/1990/10/2/ucla-program-faulted-in-admissions-probe/

[49] http://www.thecrimson.com/article/1993/5/7/report-discloses-sats-admit-rate-pa/

[50] http://research.collegeboard.org/programs/sat/data/equivalence/sat-composites

[51] http://www.yale.edu/ncaa-certification/aintegrity.pdf

A few notes: white and Asian students probably comprised a slightly higher % of the athletes than I reported, as the “Other” category’s mean SAT scores were intermediate between those of whites and Asians.  Asian athletes had significantly higher SAT scores than white athletes, which would be more suggestive that Asian-Americans were discriminated against on the basis of race, but the number of Asian athletes was too small to draw definitive conclusions.  Finally, the gap between white and Asian students at Yale was 32 points (on the re-centered scale) in 2001, while a decade before at Harvard, the gap was 50 points, which corresponds to 60 points on the re-centered scale.  The smaller gap may reflect a narrowing gap with time, disparities between the two universities’ admissions practices, and/or disparities between their applicant pools, etc.

[52] Indeed, Michele Hernandez, a former Assistant Director of Admissions at Dartmouth whom Unz cites in his article, advised a male Asian-American student whose academic interests are science and Latin to emphasize his passion for Latin:
“‘I told him Latin was way better to stress, and that helped him a ton,’ she said. (He is already in to his first choice institution.) If, as an Asian American, you apply, ‘as another biology major, as another pre-med, you are doomed,’ Hernandez said.”
http://www.insidehighered.com/news/2012/02/03/federal-probe-raises-new-questions-discrimination-against-asian-american-applicants

[53] http://research.collegeboard.org/sites/default/files/publications/2012/7/researchreport-2006-6-psat-nmsqt-scores-academic-achievement-high-school.pdf

see Table 8 and Figure 3.  I’m comparing the top math/science students to the top humanities/social sciences students (i.e. academic intensity = 3).  Not only do top math/science students have significantly higher math scores than top humanities/social sciences students, they also have higher verbal/critical reading and writing scores.

[54] Data for Harvard College is taken from “Fall Enrollment by Ethnicity, 2011” here:
http://www.provost.harvard.edu/institutional_research/harvard_fact_book_2012_enrollment.pdf

Caltech data is from the Fall 2011 NCES IPEDS data.

[55] The Harvard College Office of Admissions Asian-American enrollment data can be found on the following sites:
http://news.harvard.edu/gazette/story/2010/05/yielding-strong-results/
http://news.harvard.edu/gazette/story/2011/05/high-yield-for-class-of-’15-2/
http://news.harvard.edu/gazette/story/2012/05/yielding-to-an-invitation/
http://www.admissions.college.harvard.edu/apply/statistics.html

I suspect that the Harvard College Office of Admissions may be counting bi/multiracial students reporting Asian heritage in their Asian-American enrollment figure.

Please see footnote 36 for details on how I determined that Unz used the incorrect enrollment data for Harvard College.

[56] http://books.google.com/books?id=47rORpFmuBwC&pg=PA92&lpg=PA92

Please note that Prof. Espenshade et al did not disaggregate Asian international students and Asian-American students, so this may account for some of the disparity, as Asian international students comprise a nontrivial percentage of ethnic Asian students at selective universities.  My understanding is that admissions for international students are more competitive than for American students.

[57] https://www.princeton.edu/main/news/archive/S26/34/81K42/index.xml?section=featured

[58] In fact, despite that Prof. Espenshade et al found that Asians had the same chances of admissions as white applicants with SAT scores that were 140 points lower (after controlling for high school GPA and several other quantifiable variables), Asians underperformed white students in college, as 25.5% of white students graduated in the top quintile vs 20.2% of Asian students.  The median class rank at graduation for white students was 57^th percentile vs 52^nd percentile for Asians.
http://books.google.com/books?id=47rORpFmuBwC&pg=PA246&lpg=PA246  

Please note that the class rank data cited above does not absolve universities of the charge that they discriminate against Asian-American students. Asian students are more likely to major in the natural sciences and engineering than white students, and science and engineering students graduate with the lowest GPAs on average (controlling for HS GPA, SAT scores, etc):
http://books.google.com/books?id=47rORpFmuBwC&pg=PA250&lpg=PA250  

Hence, the college GPA of Asians may be depressed by their disproportionate enrollment in science and engineering courses that award lower grades on average than humanities courses that are more popular among white students.    It is evident that the question of whether selective universities discriminate against Asian-Americans is a complex, nuanced issue that I believe is impossible to resolve based on public data (which is far more comprehensive than the data available for Jewish students), suggesting the potential need for another OCR investigation (which would have to control for intended major). 

[59] http://www.fairtest.org/national-merit-awards-again-biased-toward-boys

[60] http://www.fairtest.org/gender-gap-narrows-revised-psat

While females are overrepresented among high scorers on the PSAT writing section, males are overrepresented among high scorers on both the verbal and math sections, suggesting that there remains a nontrivial gender gap among NMS semifinalists.  See PSAT score data by gender here.

It is important to note that it has been shown that SAT scores tend to under-predict the college GPAs of female students:
http://spp.sagepub.com/content/4/5/600

[61] http://professionals.collegeboard.com/profdownload/sat-percentile-ranks-composite-cr-m-w-2010.pdf

[62] Note that Unz claims that 56% of the junior Phi Beta Kappa inductees in the 1970s were Jewish, yet neither Unz nor anyone else, as far as I know, has argued that Harvard had a quota for Jews at that point in time, casting doubt on the significance of the demographics of junior Phi Beta Kappa inductees.  Of course, it is not unlikely that Unz overestimated the proportion of Jewish PBKs in older data (I haven’t checked), just as he did with the IMO data (as shown by Prof. Mertz), enabling him to exhibit a spurious collapse in Jewish academic achievement.

Also, neither Unz nor I attempted to disaggregate Asian international students from Asian-American students among Harvard Phi Beta Kappa inductees.  It’s possible this may overstate the performance of Asian-American students at Harvard; for example, Prof. Mertz showed that the majority of Putnam Fellows of Asian descent were actually Asian international students, not Asian-American students here (see Table 1b on p. 5).  For further info on the ethnic background of high scorers in the Putnam math competition, please see Prof. Mertz’s article published in Notices of the American Mathematical Society.

[63] My calculations are based on the commencement data published here:
http://news.harvard.edu/gazette/story/2010/05/degrees-certificates-awarded-at-359th-commencement/
http://news.harvard.edu/gazette/story/2011/05/degrees-certificates-awarded/
http://news.harvard.edu/gazette/story/2012/05/degrees-of-success/

Harvard College is 50% female: http://www.provost.harvard.edu/institutional_research/harvard_fact_book_2012_enrollment.pdf

[64] I want to clarify that I am not contradicting myself by asserting that Asians and Jews represent a higher proportion of the highest scorers on the [P]SAT than Unz claimed and then cautioning that such data should not be used to draw sweeping conclusions about the demographics of HYP.  I’m arguing that properly applying Unz-ian logic that the ethnic/racial distribution of HYP should mirror that of the top 0.5% of [P]SAT scorers does not support Unz’s conclusion that non-Jewish whites are underrepresented at Harvard, as the % of Jews and Asians among the top 0.5% of [P]SAT scorers is almost certainly higher than their representation among NMS semifinalists.  However, my broader point is that the whole notion that the demographics of Harvard should mirror that of the top 0.5% of [P]SAT scorers is flawed.

Furthermore, Unz did not account for the fact that the Harvard applicant pool may not mirror the set of NMS semifinalists in another respect: low-income students who score in the top 10% on the SAT are less likely to apply to elite universities than high-achieving middle and upper class students:
http://www.nytimes.com/2013/03/17/education/scholarly-poor-often-overlook-better-colleges.html

Finally, as I discuss in footnote 90, white students comprised only 56% of the applicants to the most competitive private institutions studied by Prof. Espenshade:
http://books.google.com/books?id=47rORpFmuBwC&pg=PA73&lpg=PA73

[65] I presume Unz counted as Jewish only the student with a possibly Jewish name whose mother has one of the Weyl distinctive Jewish surnames according to the STS Finalists’ biographies listed here:
http://www.societyforscience.org/Document.Doc?id=168
http://www.societyforscience.org/page.aspx?pid=702

Please note that I do not feel comfortable explicitly identifying individuals as Jewish unless it is already public information that the person in question is Jewish (or if I have received permission to do so).  This is why I’m not listing the student’s name but rather providing the relevant information so interested parties can determine to whom I’m referring.

[66] I confirmed that Cotler is Jewish via personal contact.  Cotler is also listed on one of Unz’s NMS rosters, so presumably Unz did not count him as Jewish among NMS semifinalists either.  I determined that the fourth student has Jewish ancestry via biographical material included in the STS announcement; since the student has not publicly identified him/herself as Jewish (members of his/her family have), I am not listing him/her.  The biographies of the 120 STS Finalists from 2010-12 can be found at the links below:
http://www.societyforscience.org/Document.Doc?id=168
http://www.societyforscience.org/document.doc?id=284
http://www.societyforscience.org/document.doc?id=341

The list of 10 winners for each year can be found here:
http://www.societyforscience.org/sts/history/

Below are the ancestry.com listings for Cotler and Hackman describing both surnames as possibly Jewish names:
http://www.ancestry.com/name-origin?surname=cotler
http://www.ancestry.com/name-origin?surname=hackman

Unz’s methodology of classifying possibly Jewish names as non-Jewish is not legitimate, especially when there is easily accessible evidence of Hackman’s Jewish heritage (not to mention the fact that her STS bio lists her location as Great Neck, NY, an area with a high Jewish population).

[67] As discussed previously, Unz also did not classify as Jewish a two-time US IMO team member with a Hebrew/Israeli name, nor did he count as Jewish any of the individuals with surnames described as possibly Jewish by ancestry.com (some of whom are indeed Jewish).  In addition, Unz did not classify as Jewish a recent STS winner with a Russian surname despite his claim that he assumed nearly all East European surnames are likely Jewish.

[68] Unz even acknowledged here that his direct inspection technique, which Prof. Mertz and I have shown to be highly inaccurate, “constituted a central pillar of [his] entire study.”

[69] I’d also like to point out that Yuval is an Israeli/Hebrew name, so Unz may not have counted the STS finalist named Yuval as Jewish either.  Furthermore, I noticed that 3 of the 120 finalists are biracial, all of whom have Asian mothers: one has a Jewish surname; one has a non-obviously Jewish surname (whose father publicly identifies as Jewish); one has a German surname.

[70] Non-Jewish whites were significantly underrepresented among recent US IMO team members and Intel STS finalists/winners according to Unz’s own data – even in spite of the fact that he substantially over-reported the % of non-Jewish whites.

[71] The latter 4 all attended Jewish schools, so hopefully Unz counted them as Jewish, but I think it’s important to illustrate that many Jews have non-obviously Jewish names.  Also, my Asian tally is higher than Unz’s because I noticed a few biracial Asians with “white” surnames (whom I counted as half-white Gentile/half-Jewish as appropriate) and because I believe Unz classified individuals with Arabic/Muslim names as Middle Eastern (i.e. non-Jewish white) even though many South Asians have such names.  I was able to confirm that a couple such individuals were South Asian, not Middle Eastern/white.  The MD NMS semifinalist roster is here:
http://www.montgomeryschoolsmd.org/info/press/MDSemifinalists-NatlMeritProgram.pdf

[72] The latter 2 attended Jewish schools.  The MA NMS semifinalist roster that Unz used is here:
http://www.boston.com/bostonglobe/regional_editions/globe_west/west/2008/09/_dozens_of_mass.html

Another MA NMS semifinalist list is here:
http://www.boston.com/yourtown/news/needham/2009/09/by_matt_rocheleau_globe_corres_4.html

[73] I’m not sure if Unz included the junior Phi Beta Kappa inductees from the Class of 2013, though the names were announced in Spring 2012, so the data was available at the time of publication of Unz’s article.

Also, like Unz, I made no attempt to disaggregate international students from Americans.

The list of Harvard Phi Beta Kappa members is here:
http://isites.harvard.edu/icb/icb.do?keyword=k19082&pageid=icb.page189954

[74] This table is not labeled quite correctly.  It is the Phi Beta Kappa inductees from the Classes of 2010-2013 whose names had been published prior to the publication of Unz’s article, meaning it includes the junior 24 and the senior 48 Phi Beta Kappa inductees from the Class of 2013, though I’m not certain if Unz included them.

Furthermore, Unz did not include a category for URMs, but I indicated 1% for Unz since his figures for whites and Asian only added up to 99%.

Finally, it is likely that I was not able to identify some of the black Phi Beta Kappa inductees, so my URM % is probably an underestimate.

[75] I confirmed other PBK inductees as Jewish from this list of Harvard Hillel donors (the parents of a few PBK members donated), lists of winners of Jewish studies prizes (assuming the surname was also possibly Jewish), Judaism-themed Facebook groups (Friday Night Lights, Harvard Hillel, etc), and Google searches.  Since not all members of the Judaism-themed Facebook groups are Jewish, I personally confirmed the full (including paternal) Jewish heritage of the relevant individuals.

[76] Recall that Unz derived his enrollment ratios for Harvard College assuming that 25% of its students are Jewish and that only 19% are non-Jewish white.

[77] At least in 2010.  Also, to be clear, in 2010, the three largest states (CA, TX, and NY) all had qualifying scores in the 99^th percentile, so in fact, the majority of NMS semifinalists did score in the 99^th percentile on the PSAT.  However, it is certainly not the case that all or most NMS semifinalists score in the top 0.5% on the PSAT.

[78] My claim is based on a cursory search of the archives at the website of The Chronicle of Higher Education and could be inaccurate.

Also, I’d like to point out that if one multiplies the re-centered mean SAT score of the Harvard Class of 1995 (1460) by 1.5 in order to roughly estimate the equivalent score on the new 2400 scale, we obtain 2190, which is clearly lower than the mean SAT score of Harvard students today.  Hence, if anything, the academic strength of Harvard students has actually increased.

[79] http://www.thecrimson.com/article/1990/11/26/the-admissions-office-strikes-back-the/

2012 National Merit Scholar enrollment figures:
http://www.nationalmerit.org/annual_report.pdf
(The NMSC Annual Report is updated every year.)

Hillel’s Jewish enrollment data is from Unz’s Appendix D.

[80] http://chronicle.com/article/Harvard-Tops-List-of-Colleges/114440/

[81] I’m excluding universities that sponsor National Merit Scholarships from consideration.  Neither Caltech, MIT, Stanford, nor any of the Ivies sponsor National Merit Scholarships.

[82] 2002 National Merit Scholar data:
http://chronicle.com/article/2002-Freshman-Merit-Scholars/36465/

In 2011, Caltech enrolled 36 National Merit Scholars in its freshman class (vs 56 in 2002), while Stanford had 139 (vs 223 in 2002).

[83] Once again, I’ve excluded universities that sponsor National Merit Scholarships.  The data on the number of National Merit Scholars attending each university is from the 2011-2012 Annual Report of the National Merit Scholarship Corporation.  The 2010-2011 Annual Report is no longer available online.

[84] Based on the SAT score ranges of Harvard undergrads published by Harvard College, as discussed in footnote 18

[85] See p. 10/12 of the 2011-2012 Annual Report of the National Merit Scholarship Corporation

[86] See p. 26/28 and p. 27/29 of the 2011-2012 Annual Report of the National Merit Scholarship Corporation

[87] Unz also states that Weyl “estimated that over 8 percent of the 1987 NMS semifinalists were Jewish, a figure 35 percent higher than found in today’s results.”  Using Unz's data for each state and incorporating his new data for MA yields the result that Jews represent 7% of NMS semifinalists in the 26-state aggregate, which is only a small drop from Weyl's 8.1% estimate.  Unz misrepresented Prof. Mertz's discussion of this point, claiming we agreed that Unz's 7% number is correct when we said nothing of the sort.  The 7% figure is based solely on Unz's own tallies for each state and likely represents a substantial underestimate, given his penchant for undercounting the % of Jews among high academic achievers in all recent data.

Weyl concluded on the basis of his Jewish surname frequency scaling method that Jews comprised 8% of NMS semifinalists in 1987, 4 years after Unz graduated from Harvard.  Yet despite that Jews constituted only 8% of NMS semifinalists in 1987, Unz states that when he attended Harvard, “Jewish students, sometimes including myself, regularly took home a quarter or more of the highest national honors on standardized tests or in prestigious academic competitions; thus, it seemed perfectly reasonable that Harvard and most of the other Ivy League schools might be 25 percent Jewish, based on meritocracy.”  Hence, in the 1980s when Jews constituted ~8% of NMS semifinalists (according to Weyl Analysis) and 21% of Harvard students, Unz apparently found Harvard’s high Jewish enrollment to be “perfectly reasonable,” when in fact, the decline in the [Weyl Analysis-derived] percentage of Jewish NMS semifinalists since then (which is consistent with the decline in the high-school age American Jewish population, particularly the non-ultra-Orthodox Jewish population) is likely similar to the decline in the % of Jewish Harvard undergrads.  The fact of the matter is that NMS semifinalist status is simply not a sufficiently selective metric by which to judge academic merit wrt one’s potential admission to Harvard. 

Unz continues: “Moreover, in that period the math and verbal scores were weighted equally for qualification purposes, but after 1997 the verbal score was double-weighted, which should have produced a large rise in the number of Jewish semifinalists, given the verbal-loading of Jewish ability. But instead, today’s Jewish numbers are far below those of the late 1980s.”  I was a National Merit Scholar in 1995, and I immediately knew Unz’s claim is incorrect, as the verbal score was double-weighted in my year.  I also confirmed with the National Merit Scholarship Corporation that the verbal score had been double-weighted since 1971.  The change that occurred in 1997 was the addition of the writing section, and instead of double-weighting the verbal score, as was the case when I took the PSAT, each section was to be weighted equally, though it is indeed the case that the PSAT contains 2 sections that test verbal skills.  Despite this, as discussed in footnote 53, top math/science students score higher on all sections of the [P]SAT than do top humanities/social sciences students.

[88] I contacted the Caltech Hillel to find out how they determined their undergraduate Jewish enrollment.  Eli Alster, the president of the Caltech Hillel, indicated that he did not know the source of the Caltech undergraduate Jewish enrollment figures reported on Hillel.org, from which Unz concluded that Caltech has “by a very wide margin the lowest Jewish enrollment for any elite university.”  Alster stated that he had had no contact with the national Hillel organization for the past two years in which he has been president of Caltech Hillel.  He then attempted to find out the source of Hillel.org’s Caltech data but was unable to obtain a response from the national Hillel organization.  Alster indicated that he was uncertain of the percentage of Jewish undergrads at Caltech.

This illustrates the absurdity of Unz’s use of Hillel’s Jewish enrollment figures to draw sweeping conclusions about the admissions practices of elite universities.  As reported by jweekly.com, “there is no standard system that Hillel: The Foundation for Jewish Campus Life uses to count Jews. Some data comes from students who self-identify, other comes from admissions offices’ extrapolation or ‘guesstimate’ of those who identify plus those who don’t. Other campuses rely on historical data, and, most importantly, there isn’t a uniform definition of ‘who is a Jew.’”  Indeed, while Princeton Hillel’s Jewish enrollment figures are based on students who self-identify as Jewish, I was unable to obtain a response from the Harvard and Yale Hillels as to how they determined their Jewish enrollment figures, which exhibit statistical anomalies, clear evidence that their data are unreliable.

[89] Unz also commits the cum hoc ergo propter hoc logical fallacy in a statistical analysis he recently posted to his blog: Unz states that there is a strong positive correlation between the size of a state's black population and the likelihood that the local white population votes GOP, claiming "Empirically, the presence of blacks causes whites to vote the “law-and-order” Republican ticket." (emphasis mine)  Unz presented no evidence to support this causal inference, and it is not clear that is true, as whites in cities like Cambridge, NYC, and Chicago are unlikely to vote GOP despite living in close proximity to black people.

[90] I do not document all of the misrepresentations in Unz’s piece in section 6, just some of the most salient examples.  Here are a few more examples of how Unz misleadingly and selectively employs anecdotes to advance his agenda:  Unz discusses Jacques Steinberg’s book The Gatekeepers, focusing on the story of a mediocre Jewish student named B. Jannol who apparently obtains admission to Cornell via personal connections (I did not read that section of the book, so I don’t know how accurate his portrayal is); yet Unz omits the story of a NMS semifinalist named Jordan Goldman who was rejected from the Ivies to which he had applied and has arguably become the most successful of the individuals profiled in the book.  Of course, Goldman’s story does not fit into Unz’s narrative.  Unz also profiles T. Wang, an Asian-American student: “Although English was not her first language, her SAT scores were over 100 points above the Wesleyan average, and she ranked as a National Merit Scholarship semifinalist, putting her in the top 0.5 percent of high school students (not the top 2 percent as Steinberg mistakenly claims). Nevertheless, the admissions officer rated her just so-so in academics…Ultimately, he stamped her with a ‘Reject’…[Wang] was also rejected by all her other prestigious college choices, including Yale, Penn, Duke, and Wellesley.” Sounds suspicious, doesn’t it? Based on the way Unz presents the anecdote, one is led to believe that T. Wang (whose first name I’ve redacted so that Google searches for her don’t pull up this negative info about her) was rejected on the basis of her race. However, I actually read her story in The Gatekeepers, and Unz left out two critical details: 1. Wang had multiple Cs on her HS transcript. 2. In one of her submitted recommendations, the teacher stated that he was surprised that she had earned NMS semifinalist status:
http://books.google.com/books?id=e3E4hxwHyDsC&pg=PA128&lpg=PA128
Such a “recommendation” would be expected to torpedo almost any application.

In one of his blog posts discussing his “Meritocracy” article, Unz highlights the case of a non-Jewish white student who scored 2370 on the SAT and was waitlisted by Harvard, suggesting he was rejected due to his ethnic/religious background.  As I discussed earlier, Princeton, whose admissions practices are similar to Harvard’s, rejects 81% of applicants with SAT scores of 2300+ and half of applicants with perfect scores.  Hence, there are hundreds of rejected HYP applicants with similarly high GPAs and SAT scores; one cannot validly conclude that HYP have discriminatory admissions practices on the basis of a single person among this group.  Indeed, I was able to find a report of a Jewish student with similar stats who was rejected (not even waitlisted) by Harvard:
http://talk.collegeconfidential.com/14120121-post50.html
The Jewish girl had a 2340 vs the above-mentioned non-Jewish white student’s 2370 on the SAT.  It’s hard to compare the GPAs (we would need more info about their high schools), but the Jewish student had 5s on several more AP exams and was a semifinalist in the USA Biology Olympiad, which is arguably more impressive than anything Unz mentioned in his anecdote.  Furthermore, I found 3 white Christian students accepted to Harvard with SAT scores of 2340 or lower:
http://talk.collegeconfidential.com/13608004-post14.html
http://talk.collegeconfidential.com/14117664-post34.html
http://talk.collegeconfidential.com/14114931-post6.html
Thus, attributing the waitlisting of the aforementioned white Gentile to his ethnic/religious background is baseless speculation.  The truth of the matter is that the essay and extracurricular activities (which were unexceptional in the anecdote Unz relayed) play a significant role in gaining admission to HYP. 

Unz goes on to state: “Some of my Meritocracy critics have suggested that the ridiculous skew of Ivy League enrollments exists because few of the capable students from most of our major ethnic groups bother applying.  Without detailed data I obviously can neither confirm nor deny this speculative excuse, but examples such as this one leave me quite skeptical of such an explanatory cause.”  In fact, Prof. Espenshade et al reported in No Longer Separate, Not Yet Equal that while white students comprised 66% of the applicants to a group of selective public and private institutions (among which the private institutions were generally described as “most competitive,” while the public institutions were “highly competitive”), white students comprised only 56% of the applicants to the most competitive private institutions (vs 86% of the applicants to public institutions):
http://books.google.com/books?id=47rORpFmuBwC&pg=PA73&lpg=PA73
Hence, there are significant racial disparities in different universities’ applicant pools; as such, one cannot validly draw conclusions about discriminatory admissions practices of a university on the basis of only its reported enrollment.  It is interesting to note that my calculations in section 3 found that white students represented 57% of Harvard students who identified themselves as a single race (Unz used the highly misleading 44% white enrollment figure without properly accounting for students of unknown race and biracial students). 

[91] Pat Buchanan, co-founder of The American Conservative, advanced a similar argument at a talk at Harvard in 2000:
http://www.nytimes.com/2000/03/17/us/2000-campaign-reform-party-buchanan-wraps-himself-mccain-s-flag-reform.html
“Mr. Buchanan gave as good as he got, at one point defending his accusation that Harvard employs elitist quotas favoring groups like Jewish- and Asian-American students at the expense of white Christians.”

[92] Perhaps Unz would cite this Harvard Crimson article from 1992 to support his contention that Harvard College was 25% Jewish, though I’m not aware of any evidence for Unz’s upper bound of 33%.  My personal estimate is that Harvard College was 15-20% Jewish at the time.

[93] It is absurd that Unz would use the term “official statistics” (emphasis mine), as there are no official statistics on the Jewish enrollment at Harvard, just Hillel’s estimates, which are accompanied by a disclaimer stating that their statistics are estimates.

I would also like to point out that while it is true that the demographics of the white students at Harvard do not mirror that of white Americans in general (in many respects, not simply the overrepresentation of Jews -- on average, white students at Harvard are wealthier than white Americans, more likely to hail from the Northeast, and more likely to be 1^st or 2^nd generation Americans than white Americans in general, if Prof. Espenshade’s findings for the most competitive private universities extend to Harvard), this is certainly the case for African-Americans and likely the case for Asian-Americans too.  The majority of African-American undergrads at Harvard are West Indian and African immigrants or their children, not the descendants of slaves, like the majority of African-Americans:
http://www.nytimes.com/2004/06/24/us/top-colleges-take-more-blacks-but-which-ones.html  
It is also likely the case that students of Chinese descent are overrepresented within the category of Asian-American.

[94] In fact, toward the end of his article, Unz seems to have forgotten about his previous allegations that Harvard has subjected Asian-Americans to a quota, as he states that admissions officers “have been tasked by their academic superiors and media monitors with the twin ideological goals of enrolling Jews and enrolling non-whites…But by inescapable logic maximizing the number of Jews and non-whites implies minimizing the number of non-Jewish whites.”

[95] The discrimination against Jewish students was explicit, whereas I am not aware of any evidence of overt discrimination against Asian-Americans today.  For example, Harvard President A. Lawrence Lowell wrote a letter to The New York Times in 1922 in which he states that implementing quotas for Jewish enrollment would help curb anti-Semitism:
http://query.nytimes.com/mem/archive-free/pdf?res=F60A12FD39551A738DDDAE0994DE405B828EF1D3

After all, according to Lowell, “the Jews” cause anti-Semitism: “The summer hotel that is ruined by admitting Jews meets its fate, not because the Jews it admits are of bad character, but because they drive away the Gentiles, and then after the Gentiles have left, they leave also.”
http://books.google.com/books?id=zwf-Ofc--toC&pg=PA88&lpg=PA88
Indeed, Lowell warned of “the peril of having too large a number of an alien race,” (emphasis mine), justifying his efforts to “limit the proportion of Jews” at Harvard. Hence, Lowell stated that it was imperative that “every member of the Faculty understand that we had before us a problem, and that that problem was a Jew problem and not something else. We had also brought the Faculty to the point of being ready to accept a limitation of the number of Jews, for their own benefit as well as that of the college…”:
http://books.google.com/books?id=zwf-Ofc--toC&pg=PA93&lpg=PA93

In his book The Chosen, Prof. Karabel extensively documents the explicit discrimination against Jews at HYP in the early to mid 20^th century.

Furthermore, Unz’s claim that the overrepresentation of Jews among leadership positions at Harvard constitutes “overwhelming domination” similar to that of WASPs at Harvard in the 1920s-1930s does not survive scrutiny.  Here is a list of Harvard’s officers and deans:
http://www.harvard.edu/officers-and-deans

Unz saw fit to mention that current Harvard President Drew Gilpin Faust, who is a descendant of Mayflower Pilgrims and was raised in the Episcopal church, has a Jewish spouse.  How is this relevant?

Unz also conveniently omitted any reference to William Fitzsimmons, the Dean of Admissions at Harvard College for the past 25+ years, who was a member of the Catholic Students Association when he attended Harvard.

[96] In fact, some Asian-American activists have expressed similar sentiments about critics of affirmative action, suggesting that many affirmative action opponents are “co-opting this issue to make their point” and “have rarely shown their concern for Asian-Americans in other contexts,” using them “as a wedge group.”