Reply to Would you take Tufts, Emory, Wash U over UVA?

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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]^^^ I don't think you will ever get it. Yes, it is basic probability and statistics. Your data points, the number of graduates enrolled in YLS, and the total number of undergraduates from each undergraduate school, are valid and important. They mean as such as what the metrics are -- the number of graduates enrolled in YLS, and the size of graduates from those colleges.

[b]What you failed to understand is that you divided those two numbers to invent a third metrics and used it to compare[/b] "the likelihood of end up at YLS" from each school. That's wrong. Washington U's graduates are NOT 2.5 X as likely to end up at Yale Law as a UVA graduate.[/quote]

Most sports metrics are derived the same way.  Points per game, batting average, 3 point shooting percentage, passing completion percentage.  They are then used to compare.  Batting average is likelihood of getting a hit per at bat, etc.[/quote]

No, they are not. 3 point shooting percentage is calculated by # of 3 point shots made divided by 3 point shots [b]attempted[/b].

Likelihood of attending Yale should be calculated by # enrolled/ # applied.[/quote]

The point was a third metric is created and it is created all the time.  I don't think anyone would disagree that it would be great to know admission rate by school, but that isn't available.  Beyond that, what would really be ideal to know is, if you could control for all other factors, what the admission rate is by school.  By that I mean if the applicants from all schools in the study had identical stats and applications, what would their admission rate be.  That would give a better indication of the impact of the school on admissions.  It is likely that only Yale Law admissions knows this.

Reports do exactly what the PP did all the time.  If you look at Poets and Quants, a site about business schools, they'll talk about "feeder schools" to top Wall Street firms by counting the number of graduates there.  Now it could be that graduates of a certain school don't want to work for Goldman Sachs or other firms and don't apply, but we don't really have any information on that.  Given that Goldman is prestigious and pays a lot, it isn't a stretch to think a lot of business oriented graduates would like to work there.  So the metric has merit in the view of many people and they use it all the time.

Lastly, there are many likelihoods.  There is the likelihood a UVA graduate enrolls at Yale Law.  There is the likelihood of an applicant from UVA (or another school) being accepted by Yale Law.  There is the likelihood of a graduate of a given school being accepted by Yale Law with a specific set of stats (that would allow more precise comparisons).  We just need to have progressively more information to know those likelihoods, and it often isn't available.

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PP made valid points and provided valuable inputs. I was simply pointing out a math error she made.

You are fine creating as many metrics as you want. But when you use it as a metric of likelihood (probability in statistics), that metric must make mathematical sense.

'Feeder schools' is another fine metric. Ivies are feeder schools to YLS. Washington U (7) and UVA (6) are not, if your cut-off is 10. However, telling people that "Washington U's graduates are 2.5 X likely to end up in Yale Law" is plain wrong.

None of the likelihoods (probability) can use PP's calculation because the formula is wrong mathematically. When you calculate batting average, you divide the number by total hits [b]attempted[/b]. When you calculate the likelihood of making a three point shot, you divide the number by the three point shots attempted. When you try to calculate any sort of likelihoods of ending up at YLS, your population must not include students who have absolutely nothing to do with YLS -- graduates never applied to Yale.

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There is nothing wrong with the calculation.  It just says something different than you are trying to attribute to it.  They were just saying Ivy graduates (regardless of what they want to do, etc.) are more likely to end up enrolled at Yale Law.  If you say this is invalid for Washington U due, you are also saying it means nothing when you look at Yale and Harvard, which have 25X as many grads enrolled at Yale Law on a per capita basis.  It seems to me there is probably something in that.[/quote]

There is nothing right with that calculation of likelihood. [b]She divided the # of enrolled by the total # of undergraduates whether they applied to Yale or not, and used it as a measure of your likelihood of ending up at Yale.[/b]

You don't need to "adjust" for the total number of undergraduate graduates to come to the conclusion that Ivies are feeder schools to Yale Law, and UVA and Washington are not, just by looking at the number of enrolled per school. How many times likely does an Ivy graduate end up at Yale as a UVA or Washington graduate? We simply don't have data to calculate that.

Poets and Quants reports top feeder schools to Wall Street. Do they have a metric that divides their numbers by the total undergraduate population? No.[/quote]

So if Amherst (with about 2,000 undergraduate students) has the same number of Rhodes Scholars, Yale Law acceptances, or Nobel Prize winners among its graduates as Michigan (30,000 undergraduate students), it wouldn't be more productive by any measure?  Really?

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PP was not talking about 'productivity'. She was asserting a comparison of likelihood of getting in Yale Law, which was straight up bad math.

And yes to Rhodes Scholars, or Nobel Prize winners. Theoretically every student has a possibility of becoming a Rhodes Scholar or Nobel Prize winner. It's appropriate to use the total population in this context. However, not every student has a possibility of going to Yale Law, only those applied. It could very well be the case that the same number of students from each school applies to Yale Law. So without knowing the interest level for Yale Law from each school, I am not sure you can say one is more productive. It also depends on your definition of 'productivity'.

[/quote]

You have to apply for a Rhodes Scholarship.  Harvard has produced 364 Rhodes Scholars.   Berry College has produced 1 Rhodes Scholar.  We should not conclude that this is any evidence that a Harvard GRADUATE is more likely to end up a Rhodes Scholar than a Berry College graduate because we do not know the level of interest of Berry College students or the number of APPLICANTS from either.[/quote]

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