Transformations, scales and zero values

Summary

Axis transformations must respect data semantics. Logarithmic (and other) scales cannot accommodate zero or negative values: such points must be handled (e.g. offset or omitted with note). Indicate transforms clearly in axis labels (e.g. “log10(x)”). Zero values on log scales give misleading gaps; instead, either transform data (with pseudocount) or use a broken axis, explaining the gap. Uniform linear scales should start at zero for count/proportion data to avoid exaggerating differences, unless space demands (then clearly indicate break).

Core rules

• Zero handling: On log scales, remove or specially mark zero measurements (e.g. “below detection”). Don’t plot zero as log(infinite).
• Broken axes: If omitting zero (for visual focus), use a visible break or annotation. Always note it in the caption.
• Consistent baselines: Bar charts and area charts should start at zero to avoid misinterpretation of area.
• Axis labels: When transforming, include the transformation in the label (e.g. “Concentration (log10 ng/ml)”).
• Proportions/ratios: If data are fractions, an appropriate scale (e.g. 0–1) or logit transform may be needed, with explanation.

Required context

• Minimum data value and whether zeros are true values or censored (detection limit).
• Reason for any transformation applied (e.g. normality, visualization).
• If using log scale, the base of the log.

AI behaviour

• Detect invalid log: If data contain zeros, flag before choosing log scale. Suggest alternative (like log(x+1) or no log).
• Axis conversion: Automatically include “log” in axis labels when transform is applied.
• Check continuity: If data nominally include zero, prefer linear scale or clearly mark the omission.

Common failure modes

• Log on zero: Plot with scale_y_log10() without noting that some bars at zero actually had measurable value = 0 (misleads viewer).
• Unmarked break: Cutting the y-axis to ignore outlier (starting axis at >0) without indicating it, inflating apparent differences.
• Mixed units: Using linear for some plots and log for others in same figure without explanation.

Authoritative standards

• ggplot2 usage: The grammar allows axis transforms, but documentation emphasizes user must handle zeros.
• Data visualization norms: Bars/areas must start at 0 for integrity.

Examples

Example: Cell count bar chart

• Data: Counts per million. One category has 0 cells.
• Check: If log scale is needed for others, represent zero as missing or small number and note it.
• Good outcome: Y-axis label “log10(Cell count + 1)” with caption “Zero values shown as 0 on plot (log scale)”.

Example: Fold-change scatter

• Data: Gene expression fold-change (can be <1).
• Check: Use log2 fold-change to symmetrize up/down regulation. Label as “log2(fold-change)”.
• Good outcome: The axis is centered at 0 for no change, with explicit unit labeling.

Sources

• R4DS/ggplot2 guide (implied: user ensures data are within domain for chosen scale).