Imagine a company's customer-satisfaction score rising from 52 to 54 out of 100. One slide shows two bars of almost the same height, and the audience yawns. Another slide shows the same two bars on an axis that starts at 50, so the second bar towers over the first at twice the height, and the audience applauds. Nothing in the data differs. The first slide is honest about size. The second is accurate about every number and misleading about the change.
Drawing data has been a deliberate craft for a long time. In 1786 the Scottish engineer William Playfair put the first line and bar charts of economic data in his Commercial and Political Atlas, and in 1801 what were probably the first pie charts in his Statistical Breviary. In 1869 the French engineer Charles Joseph Minard drew Napoleon's army shrinking on its march to Moscow and back as a band that thins, with the temperature underneath. Edward Tufte, whose 1983 book made the whole field respectable, says it may well be the best statistical graphic ever drawn.
This piece is about the handful of ideas that separate a chart that informs from one that merely decorates. They come from perception research and from decades of watching charts mislead, and each one can be tested with your own eyes.
To draw a number you must turn it into something visible: a position, a length, an angle, an area, a colour. The eye is not equally good at reading these. In 1984 William Cleveland and Robert McGill, statisticians at Bell Labs, ran experiments in which people judged how large one value was relative to another under different encodings. Their ranking, from most to least accurate, was roughly: position along a common scale; position along non-aligned scales; length, direction and angle; area; then volume, curvature and shading. In 2010 Jeffrey Heer and Michael Bostock repeated the study with hundreds of online volunteers and reproduced the broad pattern.
That ranking explains a good deal of advice. Bars on a shared baseline are easy to compare; pie slices are harder, except when you only want to see "about half" or "a small slice"; bubbles are hardest. Try it on yourself below: the page shows two values with the numbers hidden, you guess what per cent the second is of the first, then it reveals the truth. Do a few rounds with each encoding.
Your scores live only on this page and vanish when you leave. A few guesses by one person are a demonstration, not a study.
Without JavaScript: in Cleveland and McGill's ranking, position on a common scale is judged most accurately, then length and angle, then area. Bars on a shared baseline beat pie slices, which beat circles scaled by area.
Before choosing an encoding, choose the chart by the question you are answering. This is the short version of what most courses teach.
| The reader's question | A good starting chart | Why |
|---|---|---|
| Which is bigger? | Bars on one baseline, sorted | Length on a common scale |
| How has it changed? | Line over time | The slope carries the change |
| How is it spread out? | Histogram or box plot | Shows shape, not just the average |
| Are these two related? | Scatter plot | Each point is one case |
| What share is each part? | Stacked bar; a pie only for two or three parts | Angles are read less precisely |
A bar chart tells the eye to compare lengths. The length is only a fair stand-in for the value if the bar starts at zero, because then a bar twice as long means twice the value. Cut the axis and the lengths stop meaning that. The reader sees a ratio of heights that no longer matches the ratio of values.
A line chart is different. It marks positions, not lengths, so a line may use an axis that starts well above zero, as every temperature or share-price chart does. But even there a stretched axis exaggerates the slope, and the honest move is the same: the labels must say what range you are looking at. Designers do argue about how strict the bar rule should be. A 2020 paper by Michael Correll, Enrico Bertini and Steven Franconeri found that truncating the axis raises how large people judge an effect to be, in bar charts and other chart types alike, and that this persisted even when the chart carried explicit cues such as an axis break. They also argued that truncation is sometimes defensible when the meaningful differences in the data are small, as with body temperature, and that designers should think about the scale of the effect they want to show. The common advice, which most style guides follow, is still to start bars at zero unless you have a very good reason and say so.
Invented satisfaction scores, 52 last year and 54 this year.
Without JavaScript: with the axis starting at 0, bar B is 1.04 times as tall as bar A. Start the axis at 50 and B looks twice as tall, though both numbers are unchanged.
Time-series charts have a quieter way to mislead: the start and end dates. Real series wander. Almost any long, noisy series contains stretches that rise sharply and stretches that fall, and anyone who picks the window picks the story. This is cherry-picking, and it needs no false number at all.
The sound practice is to show the whole series, or to say why a window was chosen and what the rest of the series looks like. A reader can also ask the cheap question: why does the chart begin here? Drag the window over 48 invented months below, then let the page find the most extreme 12-month-or-longer stretches in each direction.
An invented index; a random walk with a gentle upward drift, labelled illustrative. Windows are at least 6 months wide.
Without JavaScript: over all 48 months the fitted trend is slightly up (about +0.5 per month). The steepest 12-month stretch rises about 2.1 per month; another stretch falls about 1.1 per month.
About 1 in 12 men and 1 in 200 women have some form of red–green colour vision deficiency, the most common kind. In a room of a hundred readers that is a few people for whom a red line and a green line are the same dull colour. Red-versus-green is the most common colour scheme in business charts, and it fails exactly for them.
A well-tested alternative is the eight-colour palette published by Masataka Okabe and Kei Ito (2002, revised 2008; both are themselves colour-blind), chosen so that its colours stay distinct for the common deficiencies. The simulation below converts colours to what a person with deuteranopia or protanopia would roughly see, using the model of Machado, Oliveira and Fernandes (2009) at full severity. It is an approximation: real vision varies from person to person.
Without JavaScript: a red (#d62728) and green (#2ca02c) pair have a colour distance of about 209 for typical vision but only about 30 for deuteranopia. A vermillion (#D55E00) and blue (#0072B2) pair stay at about 206.
Two further rules follow. First, never let colour alone carry the meaning: add direct labels, line styles or markers. The luminance gap in the readout above shows why, since two colours can differ in hue and still print as the same grey. Second, use colour sparingly: grey for the context, one strong colour for the thing the reader should see.
A chart that needs a paragraph of explanation beside it is only half finished. The strongest single change is the title. "Figure 3: Bike trips" names the topic. "Bike trips in City A rose by half in five years; City B's barely moved" states the finding, so the reader looks at the chart to check it instead of hunting for it. Journalists and consultants write chart titles as sentences for this reason.
The second change is to remove what does not carry data. Tufte called the share of ink that shows data the data-ink ratio and urged designers to erase the rest: heavy gridlines, boxes, shadows, three-dimensional effects. The advice is a good default, though not a law. In a 2010 experiment Scott Bateman and colleagues found that charts with pictorial embellishment were recalled better after a gap of two to three weeks than plain ones, and were read about as accurately, so decoration is not always harmful. Embellishment that distorts the data, such as a three-dimensional pie whose front slice looks bigger, remains a plain loss.
Invented data for two cities, in thousands of trips a day, labelled illustrative.
Without JavaScript: City A's daily trips go 42, 45, 38, 47, 55, 63 (thousands, 2019 to 2024), a rise of 50 per cent; City B's go 30, 31, 24, 28, 31, 33, a rise of 10 per cent.
Many misleading charts have honest bars and a missing divisor. A map or ranking of raw counts mostly shows where the people are. Cases, crimes, accidents and sales need dividing by population, exposure or time before regions or years can be compared. Per-capita rates have their own trap, since small places have noisy rates, but they answer the question the reader is usually asking.
Four invented regions and invented case counts, labelled illustrative.
Without JavaScript: by raw count the order is Norte (5,400), Sur (1,500), Valle (1,020), Costa (600). Per 100,000 people it reverses to Costa (100), Valle (85), Norte (60), Sur (50).
The other half is doubt. An estimate drawn as a single point or a single bar claims a precision it rarely has. Error bars, bands and ranges tell the reader how much to trust the number, and they are also how you stop yourself from over-reading small differences. Regression & Statistical Modeling (36/33) shows where those intervals come from.
A chart is an argument made of choices: what to encode as position, where to start the axis, which dates to show, which colours to use, what the title says, what to divide by. Make each choice so the reader would reach the same conclusion if they saw all the data.
Try this: find one chart in this week's news. Check where the axis starts, what the time window is, whether the numbers are counts or rates, and whether the title states a finding. Write down what you would change.
Sources. Playfair, The Commercial and Political Atlas (1786) and Statistical Breviary (1801); Minard, "Carte figurative des pertes successives en hommes de l'armée française dans la campagne de Russie 1812-1813" (1869); Tufte, The Visual Display of Quantitative Information (1983); Cleveland and McGill, "Graphical perception," Journal of the American Statistical Association 79 (1984); Heer and Bostock, "Crowdsourcing graphical perception," CHI 2010; Correll, Bertini and Franconeri, "Truncating the y-axis: threat or menace?," CHI 2020; Machado, Oliveira and Fernandes, "A physiologically-based model for simulation of color vision deficiency," IEEE Transactions on Visualization and Computer Graphics 15(6), 2009; Okabe and Ito, "Color Universal Design" (2002, revised 2008), jfly.uni-koeln.de/color; standard clinical references for the prevalence figures (about 8% of males, 0.5% of females); Bateman, Mandryk, Gutwin, Genest, McDine and Brooks, "Useful junk? The effects of visual embellishment on comprehension and memorability of charts," CHI 2010.