79  Aspect Ratio

A plot’s proportions can have a large effect on how data is perceived. Therefore, finding the optimal aspect ratio (height divided by weight) is of particular interest. ?fig-aspectRatio is a classic example from William S. Cleveland. Here we have empirical data going back to 1750 — the number of sun spots which appear on the surface of the sun. There are three clear trends in this data. In the upper plot, we can see two trends.

First, sun spots appear and disappear in a period of approximately 11-years. The beginning and end of these periods has been recorded and we’ll get to the individual trends shortly. Second, there are global rises and dips in the peaks and troughs.

The upper plot has an aspect ratio of 1:1, meaning that one unit on the y axis takes up the same physical space as one unit on the x axis. this is highlighted by the red, perfectly square, box. In this case, there’s no reason for a 1:1 aspect ratio. The axes are on completely different scales — the number of sun spots and the date.

Reducing the aspect ratio to 1:2 (0.5, ?fig-aspectRatio middle plot) or even further, to a much smaller aspect ratio of 1:20 (0.05, fig. ?fig-aspectRatio lower plot), allows us to see the relationship between sun spot peak and intensity. The higher the number of sun spots in a cycle are, the my asymmetrical it is. That is, sun spots take a longer time to disappear than they do to appear in high-peack cycles.

265 years of sun spot counts. The very low aspect ratio of the lower plot helps show the recurring trend that sun spots take longer to disappear than they do to appear.

Although the relationship between intensity and symmetry in sun spot oscillations is a well-observed phenomena, it is admittedly still somewhat difficult to see in low aspect ratio plot of fig. ?fig-aspectRatio. Now that we have a clear message we want to communicate, let’s see if we can make a plot that emphasizes that point.

Individual cyccles, loess smoothed.

We can reduce the complexity even further by plotting only wlhat we’re interested in. Here, for each cycle, we can plot the maximum number of sun spots and distance from the middle of the cycle. As we expected, the higher the maximum number is, the earlier the peak occurs.

Individual cycles, max versus symmetry.

Although Cleveland tried to implement an analytical solution to choosing the optimal aspect ratio, it was not applicable in all cases and was never widely adopted. This means you’re at your own discretion to choosing an aspect ratio.

Aspect ratios must not distort the data to the point of deception (e.g. emphasizing or eliminating trends).

Except in some rare circumstances, use an aspect ratio of 1 when the axes have equivalent units (i.e. equivalent physical distances reflect equivalent scales).