Textbook of Usability

The Cleveland-McGill hierarchy is an empirically validated ranking of how accurately people can judge quantitative values from different visual encodings. William Cleveland and Robert McGill (1984) conducted a series of psychophysical experiments measuring the accuracy of different encoding types.

From most to least accurate:

1. Position along a common scale (scatter plots, dot plots, aligned bar charts)
2. Position along non-aligned scales (multiple scatter plots side by side)
3. Length (bar charts)
4. Direction / angle (pie charts, radar charts)
5. Area (bubble charts, treemaps)
6. Volume (3D charts)
7. Colour saturation / density (heat maps)

The hierarchy provides practical design guidance: choose the encoding that maximises perceptual accuracy for the viewer's task. A bar chart (position/length) supports more accurate comparisons than a pie chart (angle) showing the same data. A scatter plot (position) is more accurate than a bubble chart (area).

The hierarchy also justifies the common critique of pie charts: angles and areas rank lower than positions and lengths. For precise comparison with more than 2–3 categories, a bar chart is almost always preferable.

There are trade-offs. Lower-ranked encodings are less precise but can scale to more data: colour heat maps display thousands of data points where position encoding would be impractical. The hierarchy is a guide to perceptual accuracy, not an absolute prescription — the right encoding depends on the data volume, the task, and the precision required.