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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.

Before you read on — recall

Which of these charts most clearly requires a zero baseline?

Formulas

Tufte lie factor
lie factor=size of effect shown in the graphicsize of effect in the data\text{lie factor} = \dfrac{\text{size of effect shown in the graphic}}{\text{size of effect in the data}}
Each effect size is a proportional change, that is the later value minus the earlier value, divided by the earlier value. A chart is honest on this measure when the ratio sits close to one, and Tufte treats a narrow band either side of one, from about zero point nine five to about one point zero five, as acceptable. Values far above one mean the geometry is overstating the movement, and values well below one mean it is burying a real change.
What truncation does to a two-bar comparison
apparent ratio=x2bx1b,true ratio=x2x1\text{apparent ratio} = \dfrac{x_{2} - b}{x_{1} - b}, \qquad \text{true ratio} = \dfrac{x_{2}}{x_{1}}
Here bb is the value where the axis is cut. Take two bars of ninety-eight and one hundred and two. With the axis at zero the true ratio is about one point zero four, a rise of four per cent, and the bars look almost identical, which is honest. Cut the axis at ninety-seven and the drawn heights become one and five, an apparent ratio of five, so the second bar looks four hundred per cent larger. Dividing the shown effect by the real effect gives a lie factor of roughly ninety-eight.

Worked examples

Scenario

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.

Solution

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.

Scenario

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.

Solution

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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
How to cite this page
Dr. Phil's Quant Lab. (2026). Truncated axes. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-truncated-axes
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