Statistics have a certain level of objectivity. If a news broadcast or news site shows a chart, the viewer assumes its numbers have been taken carefully and are being shown honestly. However, the same facts can be portrayed in completely different ways. The graph isn’t simply a window into the facts, it’s a collection of design choices, with some setting of those choices distorting the understanding of the audience. News reports, advertisers, and political campaigns all have something to communicate and viewers don’t scrutinize a chart. This essay will discuss what makes inaccurate or misleading graphs inaccurate, some recent studies of the effect they have on audiences, and why learning to read the graph properly is essential for the audience of all types of media.
The most popular method used is called axis manipulation. When the y axis does not begin at zero, then the differences at the bottom of the graph will have dramatic significance. Suppose that there are two approval ratings, say 52% and 55%, that you wish to compare using a bar chart. When the second bar begins at 50%, it seems as if it is more than twice the height of the first bar, though in reality it is just 3% higher (see Figure 1, which draws these same two ratings both ways). Other devices operate in the same way. Pie charts with inverted axes will reverse the direction that viewers are accustomed to seeing, irregular time intervals will conceal the true rate of change (see Figure 2), and three-dimensional slices of a pie chart will tend to enlarge the slices that are closest to the viewing person (see Figure 3). Bar charts are particularly susceptible, as viewers take the length of the bars as a direct indicator of the sizes of the numbers and are misled by a cut-off baseline with no actual number appearing on the page.
Misleading: axis starts at 50%
Bar B looks 2.5 times as tall as bar A
Honest: axis starts at 0%
Bar B is only about 6% taller than bar A
Note. The bar charts are created using hypothetical data for illustration purposes. Both charts show the same two values (52% and 55%).
Redrawn by Writers Per Hour from the essay’s own Figure 1. The values, 52% and 55%, and the two axes are the essay’s; the heights in the table are worked out from them.
Show the values behind Figure 1
| Candidate | Approval rating | Bar height, axis from 50% | Bar height, axis from 0% |
|---|---|---|---|
| Candidate A | 52% | 2 points | 52 points |
| Candidate B | 55% | 5 points | 55 points |
| Bar B compared with bar A | 2.5 times as tall | About 1.06 times as tall |
Misleading: points spaced evenly
Looks like steady growth
Honest: true time scale
Growth has sharply slowed since 2016
Note. Hypothetical customer counts created for illustration. The 2016 to 2023 interval is much longer than the earlier intervals.
Redrawn by Writers Per Hour from the essay’s own Figure 2. The four counts are the essay’s; the years between them and the growth per year are worked out from them.
Show the values behind Figure 2
| Year | Customers (thousands) | Years since the previous count | Growth per year (thousands) |
|---|---|---|---|
| 2012 | 20 | ||
| 2014 | 30 | 2 | 5 |
| 2016 | 40 | 2 | 5 |
| 2023 | 50 | 7 | About 1.4 |
Honest: flat pie
Every slice is exactly 25%
Misleading: 3-D pie
Every slice is still exactly 25%, but the front slice (A) looks largest
Note. The pie charts are created using hypothetical data. All four slices represent exactly 25%.
Redrawn by Writers Per Hour from the essay’s own Figure 3. The four equal slices are the essay’s; the labels A to D are the figure’s own.
Show the values behind Figure 3
| Slice | Flat pie | Three-dimensional pie |
|---|---|---|
| Slice A | 25% | 25% |
| Slice B | 25% | 25% |
| Slice C | 25% | 25% |
| Slice D | 25% | 25% |
Experimental research validates that these tricks can work. The authors of this study, Yang et al. (2021), conducted a study that examined the difference judgements made by viewers of bar graphs with truncated and full y-axes. In the overall sample 83.5% rated the differences between truncated graphs as greater than between the graphs starting at zero on the axes. The article exemplifies the difficulty of the problem using a cropped graph from the news media that is inaccessible to laboratories. The authors also said the truncation effect was “surprisingly persistent”. This is important because often people think smart readers will see a cut-off axis but, as the research shows, an impression is built over a fraction of a second about a graph and it is difficult to ‘unsee’.
Once graphs are set in a realistic context, the picture becomes more complicated. Driessen et al. (2022) conducted a randomized controlled trial, in which the participants received a normal line chart and another line chart with a broken y-axis to give an impression of an upward trend. The charts were presented to the participants in two different contexts and the participants provided an opinion regarding the trend, as well as an estimate of the increase. Interestingly, the misleading chart and the graph-literacy of the participants did not show any significant effect on the opinions. The only factor that showed significance was context. There were no significant changes in any of the factors affecting estimates of the increase. The authors concluded that humans could be more immune to being misled by a misleading graph that they might think, and they found that context might have been more important than the skewed axis.
These two studies aren’t so much in opposition to each other as a display of their weaknesses. Yang et al. (2021) eliminated the visual effect of truncation and showed that it consistently leads to an overestimation of the magnitude of a difference. When a graph is presented with a story and a topic, opinions toward the graph can be overshadowed by the opinion about the story and the topic, according to Driessen et al. (2022). In the mind of a media consumer, there are two things that can be the most dangerous. The first is when a graph is the only evidence to substantiate a claim made. The second is when the viewer doesn’t have very much prior knowledge about the context. An unfamiliar chart, with some distortion, can be a quick, perhaps incorrect, avenue to a judgment.
Both producers and audiences have a responsibility, accordingly. Journalists and editors can establish some basic guidelines. This may involve starting the bar chart axes at 0, always “scale labels” clearly, never use “decorative three-dimensional effects” and always include the complete time period. People can develop habits, too. They can read the labels on the axes, see where the scale is starting, ask what data have been omitted and compare the impression created by a graph with the actual numbers. Graph literacy can be taught alongside basic statistics to teach students that graphs can be used to argue, not just to show the truth, thereby encouraging these practices in school.
So, as a summary, there is a point to be understood that statistics can be misleading, again, with no misleading elements! The magnitude of this difference depends upon the technique, and the experimental results suggest that it is not an illusion, but a real phenomenon existing in the long term (Yang et al., 2021). Research also shows that context is as much as a part of an opinion as the distortion is (Driessen et al., 2022). When taken in combination, these results call for a balanced reaction; honest geometry from the graph producers and careful inspection from the graph consumers. In an era of information overload, graph literacy skills can be one of the most applicable means to resist the seductive power of a graph.
