Well, it's a Saturday morning and I've been spending a lot of time reading scholarship of AALS candidates -- always fun and exciting and inspiring ... but also intense and exhausting.
Now it's time for a little fun. How about a series of scatterplots that diagram the Sisk data and a bunch of other data that I've been dealing with! You may recall that I posted a matrix correlating these data: Sisk weighted score, US News peer assessment, US News lawyer/judge assessment, 25th percentile GPA, GPA midpoint, 75th percentile GPA, 25th percentile LSAT, 50th percentile LSAT, 75th percentile LSAT, percent acceptance, and the school's bar pass percentage in the jurisdiction where the most students take the bar divided by the overall bar pass percentage in that jurisdiction.
Below are a series of scatterplots that diagram those same factors. Click on the image to bring up a more readable version. (Here's a pdf version, too, which you may find easier to read.)
Focusing for a moment on the top row and the second column in from the left (which plots the Sisk/Leiter weighted scores against US News Peer assessment scores), there is a curvilinear relationship. The linear correlation is .80. When a second-degree polynomial is fit to that data, the correlation rises to .91. The square of those correlations indicates that the linear fit accounts for 65% of the common variance and the polynomial fit accounts for 84%.
The scatterplots suggest some of the other relationships are curvilinear as well. And on that I hope to talk some more soon.
Any chance you could post a translation of that last para into English? For readers who don't do statistics, it would be helpful to know: what does your data show, and how does it matter? Thanks.
Posted by: anon | September 25, 2010 at 11:23 AM
Focusing on the box on top row and the second column in from the left, that plot shows the relationship between the Sisk/Leiter scores and the US News peer scores. As you move upward the Sisk/Leiter scores increase and as you move to the right, the US News peer assessment scores increase. Schools on the upper right have higher scores on both Sisk/Leiter and US News than schools on the lower left.
The relationship between the two sets of scores does not follow a straight line. The schools cluster along the bottom left, then move upwards as you move right -- rather dramatically at the far right. Eye-balling you can see the curve in the line.
The usual measure of correlation assumes a straight-line relationship between the variables. The correlation coefficient using a straight line was .80. But then I ran another correlation, which accommodates a curved line (aka a two degree polynomial). Unsurprisingly, because that follows the data point more closely, that yielded a correlation of .91.
Turning now to the last sentence of the paragraph: the square of the correlation coefficient is a particularly useful measure because it represents the percentage of agreement between the two sets of scores. The straight line correlation accounts for 64% and the curved correlation for 84%.
I think this is important because it shows the high degree of agreement between the Sisk/Leiter citation data and the US News peer assessment scores. Thanks for asking; I'm going to post some more on this.
Posted by: Alfred Brophy | September 25, 2010 at 12:13 PM