This graph from the Cato Institute is making a pretty big splash over at Big Government, among other places, and rightfully so:
I have two problems with the graphic:
First, the scale for expenditure per child is absolute, in constant dollars. It shows an almost four-fold increase. However, it commits a cardinal sin: it doesn’t start at zero. This makes the increase look worse than it is.
Second, the scale for “achievement” is not absolute, it’s relative, a percentage of the starting point. It has no units; we don’t know what’s actually being measured here, and it’s hard to understand where we could expect the achievement to be, given the increase in expenditure.
I think the easiest way to present that would be to make the expenditure scale a percentage as well.
If we do that, a four-fold increase would display as a four hundred percent improvement.
The original graph scales achievement from -10% to +100%. A 100% improvement would represent a doubling in achievement. We had a four-fold increase in expenditure; we’d like to see a four-fold increase in achievement.
The actual achievement increase wanders around less than 10%, except for science, which falls off to about MINUS 5% and then stays constant.
If we rescaled the graph so that both sides went to 400%, the achievement lines would be essentially flat; the variation would be not much more than the line thickness.
As bad as this graph is; the achievement scale has actually been magnified so you can see the variation. The actual situation is even worse.
Since we don’t know what’s actually being measured by the “achievement” scale, let me take a wild-ass guess that the original metric has itself shifted over the years. Educators are grading themselves on the curve, and that curve has been adjusted so that student achievement can at least be shown to remain constant.
The expenditure scale is in “constant 2009 dollars”.
I bet that if “achievement” were being measured in, say, “constant 2009 grade point averages”, the achievement graphs would be decline almost as precipitately as the expenditures have risen.