The Misleading Bar Chart
A regional health board publishes a chart of weekly clinic attendance over eight weeks. The vertical axis starts at 400 rather than zero and the bars are drawn three-dimensionally with a perspective effect. Week 1 shows 430 attendances and Week 8 shows 520. On the chart, the Week 8 bar appears roughly four times the height of the Week 1 bar. A newspaper reports the headline "Clinic use quadruples in two months". A board member defends the chart, saying the truncated axis "shows up the real variation, which a zero-based chart would flatten out". The board also wants to compare male and female attendance across the same eight weeks.
1. Explain, using the numbers given, why the truncated axis distorts the visual comparison, and calculate what the true proportional increase is.
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With the axis starting at 400, the bar heights represent attendance minus 400, not attendance itself. Week 1's bar encodes 430 − 400 = 30 units; Week 8's encodes 520 − 400 = 120 units. The ratio of bar lengths is 120/30 = 4, which is exactly the "four times" the chart appears to show.
The true change is from 430 to 520: an increase of 90, or 90/430 ≈ 20.9%, not 300%.
The general rule is that a bar chart encodes quantity by length, so the scale must start at zero for lengths to be proportional to the values. Truncating the axis breaks that proportionality and makes small absolute differences look dramatic. The board member's defence confuses showing variation with showing it honestly: if fine detail matters, a line graph with a clearly labelled non-zero axis is acceptable, because a line encodes position rather than length.
2. Explain the additional problem created by the three-dimensional perspective, and state how the chart should be redrawn.
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The 3-D effect adds depth and perspective, so the front face, the top face and the receding edges all contribute area. Bars further back or drawn at an angle appear different sizes for the same value, and the eye judges area or volume rather than length. Area grows as the square of a linear scale factor, so a doubling of height looks like a quadrupling of ink. This compounds the truncation problem.
Redraw as follows:
- Plain two-dimensional vertical bars, no shading effects.
- Vertical axis starting at 0, with a clear scale and gridlines.
- Week numbers on the horizontal axis, attendance labelled with units.
- A title and source note stating the period covered.
- If the board genuinely needs to show small week-to-week variation, use a line graph with a labelled non-zero axis and say so explicitly in the caption.
3. The board wants to compare male and female attendance over the same eight weeks. Recommend a display and justify it, noting one thing to avoid.
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Recommendation: a multiple (grouped) line graph, with weeks on the horizontal axis and attendance on the vertical axis, two clearly distinguished lines (different colour plus different marker shape, not colour alone), a legend, and a zero-based axis.
Justification: the data are a time series - attendance measured at successive points in time - so a line graph shows trend and week-to-week movement, which a bar chart obscures. Two lines on the same axes allow direct comparison of the two groups at each week and of their overall trends. Because both series share one scale, differences between them are read directly rather than inferred.
Avoid: a 3-D clustered bar chart, or two separate charts with different vertical scales. Separate scales make cross-group comparison impossible, and 3-D clustering creates the same area-distortion problem as before. Also avoid pie charts: attendance counts across weeks are not parts of a single whole.