Use a Logarithmic Axis for Multiplicative Comparisons

Match visual distance to the effect scale

A logarithmic axis represents multiplicative changes as equal distances. For a ratio effect, 0.5 and 2 are reciprocal departures from the null of one. On a log axis they lie equally far from one; on a linear axis they do not.

The Matplotlib axis-scale documentation describes setting logarithmic scales. The plotting option changes the coordinate transformation, not the scientific definition of the effect. Keep the axis title and tick labels clear about the original measure.

Check values before transformation

An ordinary logarithmic axis requires positive values. A zero or negative ratio estimate or interval endpoint should trigger investigation, not an arbitrary replacement with a tiny positive number. Such values may indicate a wrong interval method, a misidentified effect scale or a data-entry error.

Distinguish plotting original ratios on a log axis from plotting already logged values on a linear axis. Both can represent the same geometry, but applying a log axis to log ratios transforms the data twice and can fail for negative log effects.

Verify a hypothetical axis

Consider ratios 0.25, 0.5, 1, 2 and 4. Their base-two logarithms are −2, −1, 0, 1 and 2, so they should appear equally spaced on a logarithmic axis. The null ratio of one sits between reciprocal pairs.

Suppose a ratio estimate is 2 with interval [1, 4]. Its interval is symmetric in log distance around 2 even though the raw endpoint distances are 1 and 2. Do not alter the interval to make its raw distances look equal; that would change the reported uncertainty.

Make the display self-explanatory

Label ticks with interpretable ratios such as 0.5, 1 and 2, and identify the log scale in the caption when helpful. Avoid visual breaks or tick spacing that imply equal additive changes. Include a null reference line and explain whether values above one correspond to more events, higher rates or another outcome quantity.

Test the plot using known reciprocal values before applying it to the final analysis. Inspect mobile and print versions because cramped labels can obscure the scale. The resulting figure should help readers compare proportional effects without requiring them to mentally undo an undocumented transformation.

Source verification: 6 November 2026. Examples are hypothetical.