Andy Baxter writes:

I wondered if you had a suggestion for a good graphical way of showing changes in the distribution of a population among quantile categories from one time period to another. I’m working on a project in which I need to show our district leadership the stability of various value-added estimates of a given teacher’s effectiveness from year to year. For example, how many teachers in the first quintile remain in the first quintile 1 year later? I know I could probably just do it with a table, but I wondered if there was a better way to do it with a graph. Any ideas or links to good examples?

My reply:

I imagine there’s been a lot of work on this general task: it’s basically the same problem as summarizing transition matrices, which is a bit issue in sociology. Anyway, here’s my quick suggestion.

Label i as the starting quintile and j as the quintile one year later. You then have 25 data points, corresponding to the percentage of teachers that start in quintile i and end up in quintile j. Call these p_ij. The sum of the 25 p_ij’s will be 100% (by definition).

The natural next step would be to make a scatterplot showing these 25 values, perhaps a circle in each grid point with the size of the circle at (i,j) being proportional to p_ij. But I have a slightly different idea which takes up a bit more space but might be more helpful in showing what you’re looking for.

I’m thinking of a display with 5 narrow plots, side by side. Plots i=1,2,3,4,5 correspond to starting quintiles 1,2,3,4,5. Plot i has 5 arrows, each starting at position (0,i) and going to positions (0,j), j=1,2,3,4,5. The width of the j-th arrow here is proportional to p_ij. The separate plots can be pretty narrow because they are only going from 0 to 1 on the x-axis.

My suggestion is to give this a try. If it works out, please let me know–I can post the graph on the blog.

I’m thinking of a graph with 25 lines, where the width of line ij is proportional to p_ij. The positions of the lines

How about a set of five graphs, one for each of the five “before” quintiles. Each graph has five lines showing the number of cases starting in