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Truncated axes, the baseline

Every number plotted in these three panels is correct, and every chart here can still mislead. A bar encodes value by length measured from the baseline, so moving the baseline changes the size of the very thing the reader is comparing. Move the floor and watch the lie factor, the effect shown divided by the effect in the data.

Tufte lie factor, 88.0 / 1.088
87.087.888.589.390.088.0%89.5%Last quarterThis quarterCustomer satisfaction, per cent. Frame 87.0% to 90%. Bars, encoded by length.
Drawn heights 1.0 pp and 2.5 ppApparent ratio 2.50xTrue ratio 1.0170xTrue change 1.5 pp, 1.70%

Both ratios above are shown rounded. The lie factor in the headline is the exact division 88.0 over 1.0, so the rounded operands will not always reproduce it by hand.

Counter-case. A line, where a zero floor is the wrong choice
3.003.233.473.70Months 1 to 12, yield in per cent. Frame 3.0% to 3.7%.

Illustrative ten-year government bond yield, twelve monthly points built for this widget. The year moves between 3.10% and 3.60%, a spread of 0.50 percentage points, and that spread fills 71.4% of the frame height here.

Satisfaction chart, baseline
Cut position87.0%

The cut control stops at 87.5%. A floor of 88.0% leaves the first bar with no length at all, and a ratio with nothing in its denominator has no value.

Mark
Yield line, floor
With the floor at 87.0% the bars are drawn 1.0 pp and 2.5 pp tall, so this quarter looks 2.50 times last quarter. The real move is 1.5 pp on a base of 88.0%, a rise of 1.70%. Dividing the shown effect by the real one gives a lie factor of 88. The shortcut is the first value divided by the first value minus the floor, here 88.0 over 1.0, and it holds exactly because both bars lose the same amount when the floor rises. Work instead from the two rounded ratios in the readout and you will land near the lie factor rather than on it. Labelling the axis reduces the misreading and does not remove it, because the reader takes the geometry first.