[Graphic problem resolved]

A few weeks ago New York City public school teachers started getting a weekly e-mail bulletin from the Chancellor. I would have shut it off, except maybe, at some point, something interesting? I don’t know.

Anyhow, today’s arrives, with a contorted lying explanation of why school budgets got cut so hard (from 1.4 to 6% he says, but the high end is actually a bit higher).

Watch this. He says that since 2002 DoE budgets have risen 79% while the rest of the City spending has increased 43% (there is lots of hemming and hawing about which funds and which agencies are included. The truth is out there. But not in the e-mail).

But here’s the good part. This is their graphic:

See those arrows? Most people will visually measure the shaft part, and ignore the “roof.” The base of the left arrow is wider than the base of the right arrow (I get 1.9cm vs 1.7cm), not wide enough for most people to consciously notice, but wide enough to make an impression. The shaft’s are 2.4cm vs 1.0cm, far more than double the length (and that’s what people will notice, or rather, that’s what people will visually measure). The base of the roof is again wider: 3.8cm vs 3.3 cm. Only the height of the roofs tilt to the smaller.

There is something dishonest about comparing percentages anyhow: most people don’t really “get” them.

But 79 is 88% more than 42. The length of the part of the arrows that people visually read? 140% more. The areas of the parts up to the numbers? 168% more.

And these numbers are one-dimensional objects. If we want a good visual comparison, a bar graph with negligible thickness is the way to go. Area confuses people, and DoE Central is staffed by people who know that.

May 30, 2008 pm31 8:25 pm 8:25 pm

I took a shot at analyzing the graph, and it isn’t hugely off if you compare areas of the entire arrows.

Method: Saved the image file to my local computer, printed it using Windows Photo Printing Wizard as a full page print, then measured the dimensions by hand.

Results:

total heights (base to tip) of each arrow: 96mm vs 60mm

rectangle base dimensions: 72mm by 58mm vs 32mm by 52mm

triangular top dimensions: 24mm by 113 mm vs 28mm by 96mm

total area: 5532 sq. mm vs 3008 sq mm

Conclusions: the total area ratio is pretty close to the target ratio of 79:42, but none of the one-dimensional comparisons are close at all.

But more importantly, comparing these two overall percentages isn’t terribly meaningful. One would want a more nuanced analysis, breaking down spending by category. What portion of the spending was for infrastructure and capitol improvements? What portion is discretionary? etc etc. And why choose the year 2002 as the baseline? Does the trend differ if we look at 2003 – present, or 2001-present, or…? We need more data, please. :-)