Log scales, truncated axes and other ways a chart misleads

What it is

The Vega-Lite scale documentation describes a log scale as one that applies a logarithmic transform to the domain value before mapping it to pixels, and calls it particularly useful for data that varies over multiple orders of magnitude. Because log(0) is minus infinity, a log scale's domain must be strictly positive or strictly negative; the domain must not include or cross zero. For data with zeros or negatives it offers the symmetric log (symlog) scale, described as scaling similar to a log scale while supporting non-positive numbers. Matplotlib's built-in scales include 'linear', 'log', 'symlog', 'logit' and 'asinh'; its symlog scale is logarithmic in both directions from the origin and has a linthresh parameter that defines the range around zero within which the plot is linear. Vega-Lite's zero scale property, which ensures that a zero baseline is included in the domain, defaults to true for quantitative x and y channels unless the field is binned or a custom domain is set: the default chart keeps the baseline, and cutting it off is a deliberate act.

Why it matters

On a log axis, a doubling looks the same whether it is 2 to 4 or 2,000 to 4,000, which is exactly right for growth rates and latency distributions and exactly wrong when the reader is meant to see absolute cost. On a linear axis with a truncated baseline, a bar that is 2% taller can look twice as tall. Readers rarely inspect tick labels, so the choice of scale is the message.

How to apply

• Use a log axis when ratios are the point: latency histograms, throughput across machine sizes, growth over years. State it in the axis title and put gridlines at each decade.
• Keep bars anchored at zero; if the interesting variation is a small band near a large value, use points or lines and say that the axis is zoomed.
• Use symlog for counts that include zero or for signed quantities; document the linear threshold.
• Use the same axis ranges for panels meant to be compared; let the tool choose ranges only for standalone charts.
• Avoid dual y-axes; two series on different scales can be made to cross anywhere.
• Name the smoothing window on any averaged line, and put the denominator next to any percentage.

Pitfalls

A point at zero silently disappears from a log chart, so an outage that drops throughput to nothing vanishes. Percentage changes plotted on a log axis compound confusions. Cumulative charts always rise and hide a slowdown. Colour scales with an unlabelled midpoint suggest a threshold that does not exist.