An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.
Truncated axes
A truncated axis starts somewhere other than zero. Whether that is a distortion or a necessity depends on how the chart encodes value. A bar chart encodes by length, measured from the baseline, so moving the baseline rescales every bar and misstates the comparison. A line chart encodes by position, and the reader judges the shape of the movement rather than the distance to the floor, so a non-zero baseline is often the only way to see anything at all. The size of the distortion is measurable. Tufte defines a lie factor comparing the change a reader sees with the change in the data.
Why it matters
Bars are objects with a size. Cut the floor away and you have changed the size of the object, which is exactly the thing the reader is comparing. Lines are a path. Cut the floor away and the path keeps its shape, it just fills more of the frame. That one difference explains most of the argument about zero baselines, and it is why the same edit is dishonest in one chart and necessary in the other.
Which of these charts most clearly requires a zero baseline?
Formulas
Worked examples
A quarterly results chart shows two bars, customer satisfaction of eighty-eight per cent last quarter and eighty-nine point five this quarter, on an axis running from eighty-seven to ninety.
The drawn heights are one and two point five, so this quarter looks two and a half times last quarter. The actual improvement is one and a half points on a base of eighty-eight, about one point seven per cent. The reader therefore sees a change roughly ninety times the real one. If the small movement genuinely matters, the honest form is a line or dot plot with the axis range clearly annotated and the change stated in percentage points on the chart, not bars standing on a cut baseline.
A treasury analyst charts a ten-year government bond yield over a year, moving between three point one and three point six per cent, and is told to start the axis at zero.
A zero baseline would compress the whole year of movement into the top seventh of the frame, and the shape that matters, when the yield turned and how quickly, becomes invisible. A line chart encodes by vertical position, and the reader is judging the path rather than the distance to the floor. Starting the axis near three and labelling the range clearly is the correct choice here. The obligation is to make the range obvious, not to force a floor that destroys the information.
Common mistakes
- ✗Every chart must start at zero. The rule applies to charts that encode value by length or area, such as bars and bubbles. Line charts and dot plots encode by position, and forcing a zero baseline on a narrow-range series hides the pattern the chart exists to show.
- ✗A truncated axis is fine as long as the axis is labelled. Readers take the impression from the geometry first and read the axis second, if at all. Experimental work on deceptive charts finds that labelled truncation still shifts what people conclude, so labelling reduces the problem without removing it.
- ✗Truncation is always deliberate deception. Charting tools routinely auto-scale to the data range, so most truncated axes come from a default rather than from intent. That is why the responsibility sits with whoever publishes the chart, not with whoever set the software default.
- ✗If the underlying numbers are printed on the chart, the scale does not matter. Printed values let a careful reader recover the truth, and the visual comparison still lands first and lasts longer. The geometry is what most of the audience will remember seven days later.
Revision bullets
- •Bars encode by length from the baseline, so bars need a zero baseline
- •Lines encode by position, so a non-zero baseline can be necessary
- •Lie factor is the effect shown divided by the effect in the data, honest near one
- •Bars of ninety-eight and one hundred and two, cut at ninety-seven, give a lie factor near ninety-eight
- •Labelling a truncated axis reduces but does not remove the misreading
- •Auto-scaling defaults produce most truncation, publishing it is still your call
Quick check
Which of these charts most clearly requires a zero baseline?
A supplier chart shows on-time delivery moving from ninety-four to ninety-five per cent, with bars drawn on an axis from ninety-three to ninety-six. Roughly what is the lie factor?
Connected topics
More in Visual Communication
Sources
- Tufte (2001)Tufte, E. R. The Visual Display of Quantitative Information. 2nd ed. Graphics Press, 2001.Defines the lie factor and the principle that the graphic surface should be proportional to the quantity.
- Pandey et al. (2015)Pandey, A. V., Rall, K., Satterthwaite, M. L., Nov, O., & Bertini, E. "How Deceptive are Deceptive Visualizations? An Empirical Analysis of Common Distortion Techniques." Proceedings of CHI 2015, 1469-1478.Experimental evidence that truncated axes and area-as-quantity measurably change reader conclusions.
- Correll, Bertini & Franconeri (2020)Correll, M., Bertini, E., & Franconeri, S. "Truncating the Y-Axis: Threat or Menace?" Proceedings of CHI 2020.Argues the zero-baseline rule is more contested than usually presented, and tests reader responses directly.
- Huff (1954)Huff, D. How to Lie with Statistics. W. W. Norton, 1954.The popular origin of the cut-baseline critique, written for a general readership.