Reading Graphs Critically

Opening Hook

Imagine you are watching a news programme. A chart appears on screen. It shows two bars, side by side. One bar is labelled “This Year.” The other is labelled “Last Year.” The “This Year” bar looks roughly five times taller than the “Last Year” bar. You absorb this in about half a second, before you have read anything.

Now imagine you look more carefully. The vertical axis does not start at zero. It starts at 92. The “This Year” bar reaches 97. The “Last Year” bar reaches 94. The actual difference between the two numbers is three percentage points. But the picture showed you something that looked like one bar dwarfing another. The numbers were accurate. The picture was not.

This is how most graph manipulation works. No numbers are changed. No data is fabricated. The manipulation happens entirely in the gap between what the numbers say and what the picture shows to a viewer who spends three seconds on it. Most viewers spend three seconds.

Once you know to look for this gap, you will find it in newspaper charts, government reports, financial advertisements, and political presentations. It is not rare. It is routine.

The Concept

Every graph translates numbers into a visual impression. That translation can be done honestly or it can be done to serve a conclusion. There are five main ways the translation gets corrupted.

The truncated y-axis is the most common trick. The y-axis is the vertical axis, the one with numbers running up the side. Normally it starts at zero. When it starts somewhere above zero instead, any change in the data gets visually amplified. A line that moved from 96 to 99 looks, on a chart where the axis starts at 94, like it has roughly tripled. On a chart that starts at zero, it barely moves.

This is not always dishonest. If you are charting a person’s body temperature over the course of an illness, a range from 36 to 40 degrees Celsius might be the only meaningful window to show. The question is whether the axis choice is serving the data or serving a conclusion. The tell is simple: find where the axis starts, and ask yourself whether the visual impression you just had is proportionate to the actual size of the change.

The compressed x-axis distorts time rather than size. The x-axis is the horizontal one, usually showing time. If you want a trend to look steady and gradual, you stretch the time axis out across a wide chart. If you want it to look steep and dramatic, you compress it. A market recovery that happened over ten years looks very different when it is squeezed into a chart three centimetres wide. Conversely, a sharp drop that happened in a single month can be made to look gentle by spacing the x-axis very broadly. The actual data is the same. The visual impression changes entirely.

Area distortion exploits the way human vision estimates size. When we see two shapes, we judge their relative size by area, not by height alone. A designer who wants to represent a quantity that has doubled might draw a shape twice as tall. But if the shape also gets twice as wide, its area has quadrupled. The viewer’s eye reads the area, not the height, and concludes that something has grown four times rather than two. This is why pictograms showing two oil barrels, or two figures, or two houses, consistently mislead: doubling the height of the image doubles the width too, and the visual impression is of a four-to-one difference. Three-dimensional charts do something similar by adding depth that has no meaning in the data but influences how the eye reads the shapes.

Dual axes are the most flexible manipulation tool because they can be tuned after the fact to show almost any relationship. A dual-axis chart places two different datasets on the same graph, with one dataset measured against the left axis and the other against the right, each with its own scale. By adjusting either scale, the designer can make the two lines converge, diverge, cross, or move in perfect parallel, regardless of whether the underlying data supports any of those impressions. Two completely unrelated trends can be made to look like they rise and fall together. The tell is the presence of two y-axes, one on each side of the chart. When you see one, treat any implied relationship between the two lines with real scepticism until you have checked the actual numbers.

The missing baseline is the trick of showing change without showing context. A chart that shows a variable rising over the past three years, without showing what happened in the ten years before that, or without showing how the current level compares to any reference point, creates the impression that the current direction is the only direction that has ever existed. Which period is being shown, and why does it start there? That question alone will catch a large proportion of misleading trend charts.

Why It Matters

These tricks are not curiosities confined to bad actors. They appear in government reports, in campaign literature, in newspaper graphics, and in financial marketing. The domain does not matter as much as the incentive structure: whenever the person presenting a graph has a reason to prefer one impression over another, the techniques above are available.

In political communication, the governing party and the opposition will take identical economic data and, by choosing different axis ranges, different start dates, and different chart types, each produce a picture that supports their case. Neither is technically lying. Both are engineering an impression.

In financial marketing, investment fund performance charts routinely use time periods that start just before a strong run and end at a peak. The scale is adjusted to make the rise look steeper than competitors. The Financial Conduct Authority in the UK has issued explicit guidance on misleading financial promotions graphs because the pattern is so consistent.

In health communications, graphs used to show drug efficacy in advertisements frequently use truncated axes to amplify the visual impression of benefit. A study published in the Annals of Internal Medicine examined graphs in pharmaceutical advertisements and found that nearly a third contained design features that distorted the data, with improperly scaled axes being one of the three most common distortions.

In political hearings, in 2015, US Congressman Jason Chaffetz used a chart during a congressional hearing on Planned Parenthood that had been produced by Americans United for Life. The chart showed two lines, one for cancer screenings and one for abortion procedures, converging dramatically. The visual impression was clear: abortion numbers were overtaking cancer screenings. What the chart did not disclose was that the two lines used different scales. The cancer screening number, 935,573, was plotted on the same visual axis as the abortion number, 327,000, with no labels showing that these were measured against different values. Statistician and journalist Alberto Cairo, who researches visual communication at the University of Miami, described it as “a damn lie” and “ethically wrong.” PolitiFact rated the chart “Pants on Fire.” The congressman stood by it.

How to Spot It

There is a documented case that shows how these techniques work in combination, and it is instructive for exactly this reason.

In September 2012, Fox Business broadcast a bar chart comparing two tax rates: the then-current top income tax rate of 35 percent, and the rate that would apply if the Bush-era tax cuts were allowed to expire, which was 39.6 percent. The difference between these two numbers is 4.6 percentage points. The chart’s vertical axis started at 34 percent, not zero. The visual result was that the right bar appeared roughly six times taller than the left bar. A viewer absorbing the image at a glance would conclude that the tax rate was about to more than double. The actual change was an increase of just under 13 percent relative to the existing rate. The chart was analysed by the statistics blog Simply Statistics and by Media Matters for America; both documented the axis starting point. Fox Business did not issue a correction.

The tell for each trick follows the same logic:

For a truncated y-axis, find the number where the vertical axis begins. If it is not zero, calculate the actual size of the change in the data and ask whether the picture you saw reflected that magnitude. If the picture made a 4.6 percentage point change look like a five-to-one difference, the axis is doing work that the numbers do not support.

For a compressed x-axis, look at the time span shown and ask what came before and after. A chart showing a rising trend over eighteen months might look entirely different if the preceding five years were included.

For area distortion, when you see two images or shapes being compared, cover one of them with your hand and estimate the other’s height. Then do the same in reverse. If you are comparing two circles or two figures, ask whether the comparison is being made by area or by some linear measure, and which one is proportionate to the underlying data.

For dual axes, look at both sides of the chart. If there are two y-axes with different scales, the visual relationship between the two lines reflects axis-design choices as much as it reflects the data. Redraw the comparison with both series on the same scale before drawing any conclusion about whether they move together.

For a missing baseline, ask what period is shown and why. What would the chart look like if it started ten years earlier? What reference point, if any, would give the current figure meaning?

Your Challenge

A company publishes an annual report. It includes a chart showing sales revenue over the past two years. The chart is a bar chart with two bars. The left bar, representing last year, is roughly half the height of the right bar, representing this year. The headline above the chart reads: “Record Growth.”

Looking more closely, you notice that the y-axis begins at 840. Last year’s revenue was 902. This year’s revenue is 951.

What is the actual percentage increase in revenue? What percentage increase does the visual impression suggest? How many of the five tricks described in this unit are present in this chart? What would you need to add or change to make it honest?

There is no answer on this page.

References

Fox Business Bush tax cuts chart (September 2012): Media Matters for America, “Dishonest Fox Chart: Bush Tax Cut Edition.” URL: https://www.mediamatters.org/fox-business/dishonest-fox-chart-bush-tax-cut-edition. Statistical analysis of the axis starting at 34 percent: Simply Statistics, “The statisticians at Fox News use classic and novel graphical techniques to lead with data” (November 2012). URL: https://simplystatistics.org/posts/2012-11-26-the-statisticians-at-fox-news-use-classic-and-novel-graphical-techniques-to-lead-with-data/

Planned Parenthood / Americans United for Life dual-axis chart (September 2015): PolitiFact, “Chart shown at Planned Parenthood hearing is misleading and ‘ethically wrong’” (October 2015). URL: https://www.politifact.com/factchecks/2015/oct/01/jason-chaffetz/chart-shown-planned-parenthood-hearing-misleading-/. Alberto Cairo quoted in The Boston Globe, “The most misleading chart of 2015” (December 2015). URL: https://www.bostonglobe.com/news/politics/2015/12/29/the-most-misleading-chart/LVHD6M3GK8TFaHzlEc9tUJ/story.html

Graphs in pharmaceutical advertisements: Cooper, R.J., Schriger, D.L., and Wallace, R.C., “The quantity and quality of scientific graphs in pharmaceutical advertisements,” Journal of General Internal Medicine (2003). PMC URL: https://pmc.ncbi.nlm.nih.gov/articles/PMC1494849/

Financial Conduct Authority guidance on misleading graphs in financial promotions: FCA, “FG19/4: Guidance on financial promotions in social media” (2019) and FCA Consumer Duty implementation. URL: https://www.fca.org.uk/publications/finalised-guidance/fg19-4-guidance-financial-promotions-social-media

Truncated bar graphs and persistent viewer misperception: Correll, M., Bertini, E., and Franconeri, S., “Truncating the Y-Axis: Threat or Menace?” CHI Conference on Human Factors in Computing Systems (2020). URL: https://doi.org/10.1145/3313831.3376222. See also: Michael Correll, “Truncating the Y-Axis: Threat or Menace?” Medium (2020). URL: https://mcorrell.medium.com/truncating-the-y-axis-threat-or-menace-d0bce66d4d08

Dual-axis chart problems: Office for National Statistics Digital Blog, “Dueling with axis: the problems with dual axis charts” (July 2019). URL: https://digitalblog.ons.gov.uk/2019/07/03/dueling-with-axis-the-problems-with-dual-axis-charts/

Area distortion and three-dimensional charts: Wilke, C.O., Fundamentals of Data Visualization, Chapter 26 (O’Reilly, 2019). URL: https://clauswilke.com/dataviz/no-3d.html

General reference: Huff, D., How to Lie with Statistics (Victor Gollancz, 1954). The original and still the clearest short treatment of visual manipulation in statistics.