I was replying to a post that used this method, but I agree that any of the discussed scores are unlikely to form a good normal distribution due to range restriction at the upper end. This is particularly true with estimates based on groups that are more clumped towards the upper end of the distribution, in which case range restriction on upper end may reduce SD, leading to notably underestimating the portion receiving lower scores where there is less range restriction.
Agree, @gallentjill, on the overall question, but even if there were demonstrated “benefits” to recipients and society generally, would that justify race discrimination in admissions? Because that’s what it is. For instance, if it could be empirically demonstrated that segregated schooling confers benefits on the students and society generally, should we then applaud the race discrimination that would get us there? I’d argue no. The best way to counter racial discrimination at this point in our history is to stop discriminating on the basis of race, as I think Justice Roberts wrote.
You and I don’t disagree apparently about the z-score implications (assuming Gaussian distributions) but we present them differently. You concentrate on comparisons with the average unhooked admit of any race (which includes of course the weaker black group) while I think the more relevant comparison is across race groups, as we are taking about race preference here. If you look at it that way, I think you’ll agree my 87% and 97% figures are accurate (again assuming normality).
For people following this, the data are presented in Table B.3.1R of the Arcidiacono rebuttal report.
However, your 720 versus 745 SAT comparison is misleading for at least two reasons here. First, the figure is for all admits, not just unhooked (and so includes the generally weaker athlete, legacy and development groups). Second, and more importantly, these figures were derived based on incomplete data provided by Harvard. Look at footnote 34 on page 26 of the original Arcidiacono report for the explanation. As the figures include a maximum of two sections, they will tend to understate differences.
I cannot find SAT scores for the unhooked group by race in the report, but the disparity in academic index between white and black, discussed above, hint that they are quite a lot larger than a question or two on a test.
Even given the limitations of the SAT data, the graph on that page 26 is telling. In practically every year (save one) the presented average SAT score for black admits was lower than even the applicant group of whites and Asians (which includes all weak hooked and unhooked white and Asian students). This is consistent with the academic decile information we have as well as with the Harvard adcoms assigned Academic Rating. In the latter case, only approximately 9% of black applicants meet what appears to be the threshold for Harvard admissions, absent some extraordinary attribute: a rating of higher than 3. The corresponding figures for white and Asian applicants are approximately 46% and 60%, respectively.
@Data10
Can you help me understand the statistical information in the expert reports in the lawsuit for females and their declared interests for area of study? (Sorry–I never took statistics.)
As previously noted, there are range restriction issues at the upper end, which is particularly important for groups with scores near or at the maximum, like a large portion of Asian admits. Trying to estimate how many Asian admits have lower scores based on the restricted range SD is sure to underestimate. For example, if you instead calculate the percentage of Black admits with higher AI than the average Asian admit, you get 13%. How can 13% of Black admits exceed the Asian average, if your 97% figure is accurate?
The average SAT scores of the baseline and expanded sample admits are for all practical purposes identical. Specific numbers are below. One contributing factor to why the baseline and expanded sample average scores have negligible differences is that the baseline sample excludes SCEA applicants, which is large group that tends to have stronger profiles than RD applicants on average. It’s not just excluding rare, special hooks.
Baseline Sample Admits Math Score: +0.51 (SDs)
Expanded Sample Admits Math Score: +0.50 (SDs)
Baseline Sample Admits Verbal Score: +0.64 (SDs)
Expanded Sample Admits Verbal Score: +0.63 (SDs)
Baseline Sample Admits SAT II Score: +0.55 (SDs)
Expanded Sample Admits SAT II Score: +0.54 (SDs)
The same approximation method is used consistently for all races, regardless of whether they chose the maximum of SATV or SATW. The specific numbers are also quite close to other portions of the documents that do not specify using this approximation. While there is likely a small overestimation of score due to the calculation method, the actual score of entering class was as follows. From the graph, I calculate an average score among admitted students of 745, which matches these figures almost exactly. Furthermore scores increase over time, and we are using samples from several years ago, so I expect if anything we are likely to be overstating score difference by looking at old numbers from when selectivity was lower.
Average Score: 748
Math: 710/800
CR: 700/800
The apparent discrepancy between 13% of blacks meeting or exceeding the Asian average, but fully 97% of Asians meeting or exceeding the black average is no mystery at all. There is higher standard deviation for the black group as compared with Asians. Thus the dispersion of the academic index scores for blacks is large. There right tail is relatively fat but the mean is relatively low. My guess is that these outliers are concentrated fairly close above the Asian mean (otherwise the black mean would be higher and the z-score distance would be closer) but no doubt there are some exceptional black admits in the group.
Unfortunately, we don’t have all the data we would like and so have to make some reasonable assumptions to fit the data. While I understand that you want to minimize the academic differences about the groups, it’s useful to note imo that Harvard’s own OIR analysis showed that if only academics were considered, the share of black students in the admit pool would be less than 0.75%, and even adding all holistic criteria, that figure would still be less than 3%. There is simply no way to square that with the idea that academic differences are minimal. The differences are large enough to Harvard that representation of black students would fall greater than an order of magnitude if only academic criteria were considered. Again, even with full holistic criteria (other than race preference), the OIR analysis suggests approximately 4 out of 5 black admits would not have been admitted without race preference.
My strong suspicion is that range restriction is not really a very big issue with the black admit group. If you look at the applicant numbers by academic index decile, you’ll see that there are very few black students in the top deciles and that the numbers fall off strictly monotonically as one rises through the deciles. This is not suggestive of any truncation on the right side of the distribution or that the range of available scores and ratings do not adequately capture the ability of the applicants. This is not true, clearly, of Asians (and presumably unhooked whites) where there are literally thousands of students on the right side of the distribution.
If that’s the case, then the Black score distribution more closely resembles a normal distribution, making SD based estimates using the Black score SD more accurate that trying to assume a normal distribution with the severely upper range restricted Asian SD, again suggesting that the 13% figure is more accurate than the 97% one.
The graph suggested a ~25 point score difference per section between White and Black admits. The graph shows that over time the score difference between races decreases, as applications go up and selectivity increases. If the trend for the past 5 years continued, then the average score difference would be a ~15 points difference between Black and White admits in the current class, as summarized below
Class of 2012: ~705 Black, ~740 White
Class of 2017: ~720 Black, ~745 White
Class of 2022: ~735 Black, ~750 White
I don’t doubt that being an URM is a significant hook, and much fewer URMs would be in the class without that hook. However, it’s also meaningful to ask how important this degree of score (or other qualifications) difference is? Are the Black admits who scored a 720 rather than a 745 or whatever unlikely to be academically successful at Harvard or beyond? The available stats suggest they are doing fine as a whole, in spite of this degree of score difference.
Harvard clearly wants some - rather a lot IMO - of that “generally weaker athlete, legacy and development group”", and it wants some URMs too.
This works well for Harvard, obviously. Not so much for the 95% of kids who don’t get in, and for the few hundred who might have, if not for those preferences. I don’t share some of H’s goals for the class, I think we all would remove a preference or two if we were in charge. But not our call.
Again, we could get into the weeds with statistics and have fun with that. But in the end, if Harvard’s own analysis suggests that 80% of black students would not be there absent race preference, and that 95% would not be there if the sole criteria were academic ability or promise or aptitude or however one wants to define an academic focused admissions system, well that’s enough for me to say that the preference is way too large.
I’m not convinced by 97% graduation rates, or self reported GPA either. Once a large group of less qualified students are admitted (whether through race preference, development, athletic, or whatever), there will be enormous institutional pressure to ensure that they graduate. Lowered standards are inevitable.
It should be considered that if Harvard substantially changed it’s admission priorities, perhaps it would lose some of it’s appeal.
Anyway if one is so hostile to Harvard’s policies and procedures then one is free to look elsewhere for a great education.
My nephew’s quote about his time at Yale is likely to be applicable to Harvard as well:
“It can be hard to get an A, but it is harder to get a C”
Only 2 factors are considered in the referenced academic model – AI score and academic rating. The authors do not specify +/- when listing academic rating percentages. Assuming they do not consider +/- in this model, this would make the model essentially admit the very small portion of applicants who receive a 1, admit the 2s who are within ~1 SAT/ACT question from perfect stats (higher than top decile cutoff for highest AI), and reject everyone else. Both Harvard and Plantiff agree that this is a very basic model that is not adequate, and both include a huge number of more controls in their respective models. Harvard OIR also mentions their model is very basic and missing key components in their report. The Plantiff’s far more complex model with full controls (model 6), concluded the following:
Current Admission Share: 45% White, 22% Asian, 13% Hispanic, 13% Black
No Asian Penalty : 45% White, 23% Asian, 13% Hispanic, 13% Black
No Racial Preferences : 52% White, 28% Asian, 8% Hispanic, 5% Black
No Race/Legacy/Athlete : 48% White, 32% Asian, 8% Hispanic, 5% Black
If we were to assume that 50% of the URM acceptances are due to a racial preference, what if we considered it a hook for those students (and only that 50%). What if we then compared the remaining (non-hooked) 50% of the URM admitted students to the white and Asian populations? If 50% of the class is admitted based on some sort of hook, why isn’t it reasonable that 50% of the URM acceptances are based on some sort of hook as well? The issue isn’t really about race, but about giving any group a step up in the admissions process. I hate these lawsuits because inevitably some applicant complains that they were overlooked because Candidate ABC was accepted, and Candidate ABC was less qualified, but was a URM. In reality, there are probably others who are even “less qualified” who were admitted due to some other hook. Yet the focus is put on the URM, not the weak candidate whose father donated a couple of buildings.
The data alone confirms that far fewer than 50% of the URM have lower qualifications–as I recall its more like 90%. On a separate note, you cant just infer that because 50% of the entire class is admitted based on some hook that 50% of URM are there because they are URMs. A hook is a hook and there will be variables within hooked populations of course. There may be URMs that have better stats than say some athletes–both are still less qualified than all unhooked applicants. I remind everyone that only athletes are held to an AI minimum. No other population has an AI minimum requirement.
In the Harvard Crimson senior surveys, Black seniors at Harvard report an average GPA in the A- range. Suppose the actual average GPA is lower than the surveys and a B+… They still would be nowhere near not graduating for academic reasons, or nowhere near anything to suggest not capable of being academically successful. Harvard doesn’t need to lower standards to allow B+ students to graduate.
Of course Harvard does care about their high graduation rate. They are quite proud of it and mention it throughout their website. It’s also one of the most important metrics for USNWR ranking. I’d expect Harvard goes out of their way to insure as many students as possible graduate, assisting the few students who are at risk of not graduating, regardless of race. I’d expect those few at risk students are primarily at risk for non-academic reasons. To insure the high graduation rate, I’ m sure Harvard also admits students who they expect are extremely likely to graduate, regardless of race. They may allow average SAT score to dip from 745 to 720, but they aren’t going to admit URM students who they expect to fail to graduate, without assistance.
That is probably why it does what it does. It wants to market itself to potential students, potential faculty, and potential donors. All of these groups’ tendency to want Harvard can be affected by the makeup of the student population (including by race/ethnicity, but not limited to that).
Of course, there may be no way to satisfy everyone.
Also, the stuff revealed in the lawsuit may reduce Harvard’s marketability regardless of the outcome, since there will be increasing perception among most potential students that certain in-groups that they are not members of are highly favored, increasing the perception that applying is pointless for most apparently-top-end students, and it will be more obvious to potential faculty that only a small portion of the students that they will teach are “the best of the best”.
The Economist believes that Harvard’s approach is flawed because it throws the racial bias into the controls, thereby making it disappear from the result. Note that the Mr. Card mentioned below created Harvard’s model.
There seems to be some perception that graduating from Harvard is difficult. It isn’t. The kids from our high school that attend report it is far easier than high school. The difficult part about Harvard is getting in, not getting out.
Note that this isn’t true of all Ivies. Columbia, Princeton and Cornell students all report heavy workloads.
Perhaps that has to do with harder core/GE requirements (Columbia) or greater numbers of students doing majors like engineering majors (Cornell)?
"If the trend for the past 5 years continued, then the average score difference would be a ~15 points difference between Black and White admits in the current class, as summarized below
Class of 2012: ~705 Black, ~740 White
Class of 2017: ~720 Black, ~745 White
Class of 2022: ~735 Black, ~750 White"
The case regards Asians though vs URMs right, so not sure why black vs white would be relevant for the Harvard lawsuit.
Class of 2012 : 765 Asian, Hispanic: 715
1530 vs 1410 and 1430 are big, especially as you and SatchelSF notes, many Asians would score above 800 but are being capped at that score.