**One picture is worth a thousand lies**

Whenever I teach statistics, I make a point of recommending to my students that they read Darrell Huff's

*How to Lie with Statistics*, a splendid little book on the use and misuse of data. Huff warns his readers about many statistical sleights of hand, including the misleading graph.

I was reminded about Huff's cautionary tales while browsing Tim Lambert's

*Deltoid*. His recent posts include a lovely example of how a climate-change skeptic uses a doctored graph to argue that recent global warming fits beautifully into a long-term cyclic pattern. All you have to do is screw with the time scale and suddenly any suggestion of human-induced temperature seems to vanish. It's all

*natural*! (Lambert points us toward Stefan Rahmstorf's dissection of the bogus graph over at RealClimate. Stefan reads German so you don't have to.)

There's an old math joke whose punch-line relies on our fondness for different kinds of graph paper. Almost everyone is familiar with the good old Cartesian system: a rectangular grid of equally spaced horizontal and vertical lines. Cartesian graphs are relatively simple and highly functional, but get a little unwieldy when we try to graph things that change very rapidly or very slowly. In the graphs below, I have depicted two ways of illustrating the behavior of the curve

*y*= 2

^{x}. Exponential functions have extremely high growth rates, requiring us to severely compress the scale on the

*y*axis. That's what you see in the left-hand graph. If, however, we use a

*logarithmic*scale on the

*y*axis (which we call a semi-log graph), the nature of our exponential graph is transformed. We get a nice straight line, On semi-log paper, the graphs of exponential functions become much neater.

There are many other forms of graph paper, too, including log-log paper, where both axes are in logarithmic scale. A good choice of scales can make a big difference in the clarity with which your functions or data are illustrated.

And that old math joke I mentioned? It's in the form of a riddle, sort of:

Hilarious, right? I'll give you a moment to recover from your fits of helpless laughter....Q:How do you graph a linear function?A:As a straight line—on Cartesian graph paper.Q:How you you graph an exponential function?A:As a straight line—on semi-log graph paper.Q:How do you graph an arbitrary monotonic functionf(x)?A:As a straight line—onfpaper!

I imagine that most people have never seen a real-life example of

*f*paper, but today's climate-change denialists may be in the forefront of exciting new developments in lying with statistics. In their honor, I now present my own modest contribution to the practical application of

*f*paper. You will observe that the left-hand graph immediately below depicts a function that is both increasing and oscillatory. With the proper use of

*f*paper, as shown in the right-hand graph, we can damp out any vestige of the oscillation, preserving only the monotonic increase. Unless one takes a hard look at the scale on the

*y*axis (and now you know why one should always examine the axes carefully!), the embedded periodic motion of the function is completely suppressed. The right-hand graph is a breakthrough in information hiding. I fear it will not be the last example you see.

## 2 comments:

f-paper... nice.

What software are you using to make your graphs?

What grade would you give a student who turned in his homework on

f-paper?;-)

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