Common ways a graph can exaggerate a change

A graph can make a small change look dramatic without a single wrong number on it. The distortion comes from the drawing itself: how tall a bar stands, how two scales are paired, or how much area an icon covers. The useful question is not whether a chart looks dramatic but how dramatic it is, and that can be measured. Divide the difference you can see by the difference the numbers contain. A ratio near 1 means the picture is fair. A ratio of 6 means the picture shows six times the change the data support.

Most charts are drawn honestly, and some visual emphasis is a legitimate design choice. The point of measuring is to separate a deliberate emphasis from a distortion that changes the message. Three mechanisms account for many exaggerated changes, and each one has its own way to compute the ratio.

Bars that start above zero

When the vertical axis of a bar chart starts above zero, the bars are cut off at the bottom, so their visible heights no longer match their values. Suppose two bars show 60 and 66, a rise of 10 percent. If the axis starts at 50, the first bar is drawn 10 units tall and the second 16 units tall. The taller bar looks 60 percent larger, because 16 is 60 percent more than 10, while the real change is 10 percent. The drawn difference is six times the actual one.

To measure a bar chart, read the top of each bar, subtract the axis floor to get its visible height, and compute the percentage difference between those heights. Then compute the percentage difference between the printed values. Divide the first figure by the second. A chart that starts at zero gives a ratio of 1, because visible heights equal values. A ratio of several times means the axis has been cut to magnify differences, and the bars should be read from their labels.

Two vertical axes with separate scales

A chart with two vertical axes gives each series its own scale. Because the scales are set independently, the drawn steepness of each line depends on its axis as much as on its values. Consider a series that rises from 40 to 44, a 10 percent increase. If its right-hand axis runs from 38 to 46, the line climbs from one quarter of the height of the frame to three quarters of it. That is a climb covering half the chart's height, for a real change of 10 percent.

To measure a line on a dual-axis chart, work out how far it travels as a share of the total chart height, then divide by its percentage change. In the example, half the frame divided by 10 percent gives a ratio of five. Do the same for the second series. If the two ratios differ widely, the lines are drawn at different magnifications, and any crossing or convergence between them describes the scales rather than the data. Compare the two ratios before comparing the two lines, and judge the claim from the printed values.

Three-dimensional shapes and icons

Three-dimensional bars, tilted pie slices and perspective add depth that the data do not contain. Perspective makes nearer parts look larger and distant parts smaller, so equal values can look unequal depending on where they sit in the chart. These effects also make it harder to read the true height or share of each element, and they are hard to measure with a ratio because the drawn shapes are no longer simple lengths. Where the chart prints its values, use them instead.

Icons raise a problem you can measure. When a value is shown by a picture such as a coin or a person, the icon is often scaled in both directions. Doubling an icon's height and width multiplies its area by four, not two. An icon for a value twice as large therefore covers four times the area, and readers judge size largely by area. Dividing the area ratio by the value ratio gives the exaggeration: here, four divided by two, or two. If the icons are all the same size and the number of icons carries the value, the chart is fair.

Rebuild the comparison from the raw numbers

The most reliable check is to set the picture aside and work from the figures. Find the starting and ending values, then calculate the change both as an absolute difference and as a percentage. Compare that result with the visual impression. Two distortions are easy to miss even then. The first is the chart's own proportions. Its width and height set the steepness of its lines: stretch a chart vertically and any line gets steeper, squash it and the same line looks flat. Two charts of identical data drawn at different proportions can seem to show different trends, so compare slopes only between charts drawn to similar proportions, or convert the change to percentages.

The second is the cumulative total. A running total cannot fall while the amounts added are positive, so its line always climbs. The climb looks like growth, but the slope shows only the amount added in each period. A tall, ever-climbing line can come from a modest yearly amount accumulated over many years, and a line that is still rising can hide amounts that have fallen sharply. Look for the per-period figures behind the total and compare those.

The aim of these checks is to read the chart fairly. A designer can have good reasons for a particular scale, and a chart can be honest and still hard to read. When the drawn difference is several times the real one, though, the numbers should win. Put the picture back in its place and read the figures first.