First, there isn't a universal cutoff.
I know. That's why I wrote it as a conditional statement.
I discussed this with you multiple times over multiple years, including in this thread. When I last brought this up because the cutoffs vary at universities where Blacks or Hispanics are more prone to apply and Asians are not (like say in Puerto Rico or HBCUs OR different tiers of schools), all you did was insult the school instead of applying that new knowledge to your hypothesizing.
But what you say just shifts the problem. Why are schools catering to blacks and Hispanics willing to take less academically qualified applicants?
As to me "insulting" the PR med school, I was just commenting that their stats are so low that they make it similar to Caribbean schools, which enjoy a poor reputation. So I genuinely wonder about their attrition rates, as well as Step passage and match rates.
Lastly, it would be interesting to see the MCAT means by race for individual schools that do not cater to any particular race. I.e. what is the average MCAT of accepted Asian, white, black, and Hispanic students at the Medical College of Georgia for example. It's a state school, so they really should not be discriminating. Alas, I do not have that data.
Second, pure normality is indeed an assumption and there may be modes and skews within the data in particular to some variables that may be somewhat independent of race.
"Pure normality" is not required from real-world data. Assumption of normality works if the data is approximately normal. Second, the distribution of the mean trends toward normal with increasing N regardless of the underlying distribution (Central Limit Theorem). The width of the distribution of the means is also gets narrower with increasing N (inversely proportional to square root on N in fact). With thousands of students, the distribution of means becomes very narrow.
So yes, we can compare MCAT and GPA means even if the distribution is not perfectly normal.
Third, normality is a spectrum and when you begin to discuss maxima and minima, a beta distribution can fit data better than a normal distribution. I took a look at this over data of __test__ __takers__ in some year of MCATs. I found that a distribution of test takers in general with mean of 500.6, stdev of 11.2, had somewhat more normal like distribution 1 stdev out of from mean but also it was different, i.e. a beta distribution began to impact the numbers. Now 2 stdev from the mean, the beta distribution was stronger than the normal. What I mean by this is that the percents of population at the tails is more reflective of a beta distribution than a normal distribution.
That is very interesting, but does not affect the discussion of the stark differences in means between different racial groups. Also note, all test takers is a bigger set than applicants, because most people don't bother applying with a really bad score.
You ought to consider how these three factors: non-universal cutoffs, different subgroups applying to different schools, and beta distributions play a role rather than just throwing your hands up in the air and saying, "that's a shitty school!"
But you are assuming all these things work out to effect blacks and Hispanics being accepted with far lesser average scores than whites and Asians in absence of discrimination. But why should we assume that? Especially when academia is strongly in favor of practicing racial preferences in order to enhance "diversity" (except in schools like Morehouse and Meharry, where diversity doesn't matter).
At least ZiprHead, for all his faults, is honest about supporting such discrimination.
Finally, so far I am discussing with you your assumptions and the math, but as bilby and others have pointed out, this all could be besides the point. Earlier, I posted a study that suggests MCATs are not predictive of how good a doctor becomes __or__ at least that once one has gotten into medical school and made it through, the level of precision used on an MCAT score is not correlated to success as a doctor.
MCAT and GPA are correlated with passing Step 1. They are correlated with likelihood of dropping out, which is very costly for the student and not great for the school either.
MCAT is a tool used for med school
admission. There are four years of med school to get through, and variable number of years in residency. They all shape the student. So it's hardly surprising that performance on an entrance exam fades in importance in the years after. But med schools cannot look forward in time and see directly who will be successful later on. They have to make predictions from what they have. If not MCAT, what do you propose that would have a greater validity? The advantage of the MCAT is that everybody takes the same test (college classes are highly variable between institutions) and the student has to actually take the exam - can't outsource that like essay writing.
