A heatmap would be more revealing, but I'd eat my hat if it weren't a standard distribution (and I had a hat). It's nature (but hey, anything's possible). The scales are only slightly skewed, but we're not talking logarithms. The merit of the scales ("value-added") on the other hand, is very questionable.
Clearly all the overlapping points in the first graph are obscuring most of what's going on. This is a warning flag that the author may be trying color the facts to suit their argument.
Not very clear what you are try to say:
(1) What "standard deviation"? Perhaps you mean the standard error of the correlation coefficient is large relative to the its estimated value. Given the large number of data points it is likely to be quite small. Another warning flag is the failure to report either the correlation coefficient or its standard error.
(2) What does "ellipse isn't irregular" mean? Given all the overlapping data points the shape of the plot is entirely driven outliers. To my eye this looks what you would get from plotting a bivariate normal distribution.
(3) Kepler? The linked graph? How is this helpful in understanding what's going on?
The first graph has a straightforward interpretation: you are making two imperfect measurements of each teacher's performance at two different times. There is noise in both measurements and teacher performance may have actually changed between measurements.
Typo: should have been "standard distribution"... Less colloquially: "a two-variable normal distribution."
"What does "ellipse isn't irregular" mean?"
Eccentricity. Sorry `fer the double negative.
"Kepler? The linked graph? How is this helpful in understanding what's going on?"
If you take the scattered data and draw an ellipse containing a fixed probability (presumably represented with some confidence, by the data shown), the ellipse would be more eccentric for the same enclosed probability, the higher the correlation. It's a single statistic and is analogous to Kepler's 2nd law ("a line joining a planet and the Sun sweeps out equal areas during equal intervals of time."), except with probability rather than area... (To contain the same probability, you have to adjust the ellipse's size, while holding its enclosed probability constant, and accounting for the new eccentricity, which isn't under our control. If the area is fixed and the distance changes, solve for speed... I think visually. Alternatively, think V=IR.; if V is constant and R is known, solve for I.). The link was just illustrative of any such scatter plot. It was the best I could find, but I agree, it could have been better.
I agree that the article is low on quantitative statistics though.
Sorry don't mean to belabor this point but I think "standard distribution" (changed from standard deviation) is still incorrect. "Standard" referers to standardized parameters (i.e. mean, variance) as in "standard normal" which has a mean of zero and variance of one (and standard deviation of one). Certainly not the case here. Maybe you mean "bivariate normal with positive correlation"?
No worries. Statistics can be very confusing. Part of the reason it is so confusing is all the sloppy usage we come across in the media and on the internet.
Everyone wants to use statistics as a tool to bolster their point of view but don't want to bother to actually learn enough statistics to deal with the situation they are trying to analyze.
But the relation, whatever it is describing, is pretty weak since the ellipse isn't very irregular (it's only "slightly" irregular). http://www.emeraldinsight.com/content_images/fig/08702801090... Think Kepler's laws.
Edit: The first post in the series shows a scatter of the direct (non-delta) scores, and it looks like San Fransisco in the morning: http://garyrubinstein.teachforus.org/2012/02/26/analyzing-re...