Thursday, July 19, 2012

(MIS)USING TWO VERTICAL AXES



If you show two variables (often time series) that are either measured on different scales (like $ and volume), using two axes is required. If the variables are on the same scale, but the magnitude is very different, you can do the same... but if the magnitudes are fairly similar, using two axes can be very misleading as you see in the graph below...
 source: http://seekingalpha.com/article/118072-u-s-and-bric-world-market-share

The careless consumer of the graph will undoubtedly at first think the BRICs have overtaken the United States temporarily. Only at second glance the true story unfolds.

Here is an example for the same unit (seconds), but vastly different magnitudes - the problem is the scaling. If you want to show and compare progression, you need to use the same zero point on both axes. Even if the point is not shown, the two scales need to increase in proportion. Otherwise you can show anything.
Funnily, The Economist (the source for the graph) wanted to show that the 100 meter free-style swimming world record improve at a faster rate than the 100 meter running WR, but the graph only gives the impression of a less than twice as fast improvement, while checking the numbers reveals that the WR for swimming improved by 22.9% and for running by 8.8%. Thus the swimming WR improved 2.6 times faster - somewhat more than the graph suggests. When 9 seconds (running axis) and 45 seconds (swimming) correspond, they should have also matched 10 seconds with 50, 11 with 55, etc... which would have (visually) suppressed the improvement of the running WR.

    Source: economist.com

Last, different scales can greatly suppress volatility. In the graph below you see the annual percentage changes of U.S. and German gross capital formation for 1971 to 2010. For the U.S. (Germany) the average annual growth was 6.56% (6.76%) with a standard deviation of 7.05% (13.60%) so the German numbers fluctuated a lot more. However, in the graph, thanks to using two axes, the fluctuations seem to be quite similar! The second graph shows the same data in a graph with only one scale, clearly a much more accurate representation of the data.






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