Tuesday, May 24, 2005

Gory Details, by Demand

The blogosphere once more demonstrates its power to help a geek feel less lonely! A fellow devotee of school ranking issues has asked me to post some of the gory details that I deliberately omitted from my prior post on the topic. Here, then, I offer a table comparing the scores that USN&WR gave the top-tier law schools with the scores that my model gave them—the same data I offered earlier via a graph. This table not only shows the numbers behind that graph, but also the constituent z-scores that the model used in calculating its scores.

Top Z-Scores Table

What's a "z-score"? The geek in me thought you would never ask! It provides a way to standardize a group of measurements made on different scales (such as measurements of law schools' LSATs, GPAs, etc.) so that those measurements can be compared and combined into one score (such as in the overall scores reported above). You generate a z-score for one in a set of measurements by subtracting the mean of the set from the measurement in question and dividing that amount by the standard deviation of the set.

(With all due respect to those of you eager to prove your geek bona fides, allow me to note that I realize some people reserve "z-score" for a different statistical tool. I don't think, however, that I've deviated from the standard usage. Har har.)

[NB: Please note that I've edited the above chart in response to comments from Prof. Douglas Sylvester, for which I thank him.]


Marjorie said...

Woo-hoo! My school's on it and my DH's is not! I'm better than him even if he's Order of the Coif. Just a joke, really, I'm at-home now and I need something to make me feel superior.

Yeah, I didn't read the statistical stuff...to me the "z" stands for "zzzzzzz......"

Anonymous said...

Your list is much more accurate than US News and the Law School 100. Thanks. Columbia 2L

Anonymous said...

Why is Penn's Overhead/Student score the lowest on the list by about two standard deviations?

Anonymous said...

-2.24 for student/overhead costs? Are we really supposed to believe that out of the entire top 50 Penn spends the least in that area by several standard deviations? Come on.

Anonymous said...

I used your data to try to replicate your results, and I appear to be unable to do so.

Can you explain EXACTLY how it works? I calculated weighted averages of the z-scores of the schools (weighted by the percentages in the column headers), and then I divided each school's weighted average by Yale's weighted average to get a percentage. But I get the following scores:

Harvard: 93.72
Stanford: 90.15
Columbia: 82.02, etc.

which does not match your result.

Would you mind posting the spreadsheet for download? Failing that, would you correct my calculations?

Anonymous said...

Anonymous, I too would like to know the exact method. I tried your method and came up with nonsensical results for NYU.


Anonymous said...

Also, from comparing Penn vs. Duke/Northwestern on this chart, Penn is greater in every category except two:

1. The aforementioned overhead/student worth [9.75%] where Penn has the lowest score by far on the entire chart.

2. The student/faculty [3%] where the difference appears to be insignificant.

So what I'm wondering is, can Penn's overhead/student numbers be *that* bad?


Tom W. Bell said...

Those of you who wondered about Penn's low "expenditures/student" number might want to check out my response to similar questions in my prior post on this topic. Here, I will simply say that the number accurately reflects the expenditures that Penn reported to the ABA (but probably not to USN&WR), and the they were so low because of the unusual way that Penn characterized its expenditures (it characterized them so as to qualify an unusually low amount under "expenditures/student" and an unusually high amount under "financial aid/student). Overall, Penn reported expenditures roughly equal to those of comparably ranked schools. It just characterized its expenditures differently--and, notably, in a way that hurt it under USN&WR's formula.

Those of you who wanted the formula: You cannot get an accurate result without all the data. You might, however, try something like this:

model's overall score=((97.5/(2.53-1.81)*((school's raw and weighted score-1.81))+2.5

I don't feel at liberty to release the spreadsheet containing all the data, as it included propriety and confidential information.

Anonymous said...

Anybody know where I can find updated rankings?