Last month, I blogged about the importance of visually inspecting data to ensure that ordinary least squares (OLS) is an appropriate method for estimating a relationship between two variables. As I noted, one pattern that you will occasionally observe is a monotone curvalinear relationship--i.e., an increasing or decreasing function in which the best-fitting line has an observable bend. Here is the example I posted:
Over at Moneylaw, Al Brophy (Alabama Law) posted some interesting data on the strong correlation between the various U.S. News input variables and bar passage rates of the California law schools. In a nutshell, almost every U.S. News input variable correlates with bar passage between .84 and .90. To illustrate his point, Al posted this scatterplot:
A visual inspection of Al's chart (here, bar passage and the calculated LSAT mid-point) suggests a curvalinear relationship. (Note that a correlation coefficient reflects the best-fitting straight line.) Since I don't have access to Al's data, I superimposed a rough fit line, which approximates the first graph.
Fortunately, Gary Rosin (South Texas Law) recently posted a paper, "Unpacking the Bar: Academic Qualifications, Cut Scores, MBE Scaling and Law School Bar Passage Rates," provides a very nice chart that shows the interaction between MBE cut scores and a law school's mean LSAT. It provides some insight on why the best fitting line in Al's scatterplot is probably curved. [See chart after the jump.]
In the above chart, the line for each hypothetical cut score is curved because a larger proportion of graduates from schools with lower mean LSATs score at or near the cut score. Hence, a 5 point increase in California's cut score might pr0duce a 1% decline in bar passage at an elite school and a 10% decline at schools with more modest entering credentials. In addition, the higher the cut score (and California's is quite higher), the steeper the downward slope after the curve.
It is noteworthy that deans from regional law schools essentially intuit this relationship without the benefit of fancy charts. This group is always among the most vocerifious critics of higher cut scores; the impact on lower ranked schools--already strapped for resources--can be enormous.
By the way, Gary's paper also makes a terrific argument that varying MBE cut scores and scaling practices from state to state are an example of federalism run amok; there is no coherent thread of lawyer competency that ties these standards together.