There are numerous ways in which a misleading graph may be constructed.
Excessive usage The use of graphs where they are not needed can lead to unnecessary confusion/interpretation. Generally, the more explanation a graph needs, the less the graph itself is needed.
Fabricated trends Similarly, attempting to draw trend lines through uncorrelated data may mislead the reader into believing a trend exists where there is none. This can be both the result of intentionally attempting to mislead the reader or due to the phenomenon of
illusory correlation.
Pie chart • Comparing pie charts of different sizes could be misleading as people cannot accurately read the comparative area of circles. • The usage of thin slices, which are hard to discern, may be difficult to interpret. • Making a pie chart 3D or adding a slant will make interpretation difficult due to distorted effect of
perspective. Bar-charted pie graphs in which the height of the slices is varied may confuse the reader. In a 3D pie chart, the slices that are closer to the reader appear to be larger than those in the back due to the angle at which they're presented. This effect makes readers less performant in judging the relative magnitude of each
slice when using 3D than 2D : Item C appears to be at least as large as Item A in the misleading pie chart, whereas in actuality, it is less than half as large. Item D looks a lot larger than item B, but they are the same size.
Edward Tufte, a prominent American statistician, noted why tables may be preferred to pie charts in
The Visual Display of Quantitative Information: Tables are preferable to graphics for many small data sets. A table is nearly always better than a dumb pie chart; the only thing worse than a pie chart is several of them, for then the viewer is asked to compare quantities located in spatial disarray both within and between pies – Given their low data-density and failure to order numbers along a visual dimension, pie charts should never be used.
Improper scaling of pictograms Using pictograms in bar graphs should not be scaled uniformly, as this creates a perceptually misleading comparison. The area of the pictogram is interpreted instead of only its height or width. This causes the scaling to make the difference appear to be squared. : The graph of house sales (left) is misleading. It appears that home sales have grown eightfold in 2001 over the previous year, whereas they have actually grown twofold. Besides, the number of sales is not specified. An improperly scaled pictogram may also suggest that the item itself has changed in size. : Assuming the pictures represent equivalent quantities, the misleading graph shows that there are more bananas because the bananas occupy the most area and are furthest to the right.
Confusing use of logarithmic scaling Logarithmic (or log) scales are a valid means of representing data. But when used without being clearly labeled as log scales or displayed to a reader unfamiliar with them, they can be misleading. Log scales put the data values in terms of a chosen number (often 10) to a particular power. For example, log scales may give a height of 1 for a value of 10 in the data and a height of 6 for a value of 1,000,000 (10) in the data. Log scales and variants are commonly used, for instance, for the volcanic explosivity index, the Richter scale for earthquakes, the magnitude of stars, and the pH of acidic and alkaline solutions. Even in these cases, the log scale can make the data less apparent to the eye. Often the reason for the use of log scales is that the graph's author wishes to display vastly different scales on the same axis. Without log scales, comparing quantities such as 1000 (10) versus 10 (1,000,000,000) becomes visually impractical. A graph with a log scale that was not clearly labeled as such, or a graph with a log scale presented to a viewer who did not know logarithmic scales, would generally result in a representation that made data values look of similar size, in fact, being of widely differing magnitudes. Misuse of a log scale can make vastly different values (such as 10 and 10,000) appear close together (on a base-10 log scale, they would be only 1 and 4). Or it can make small values appear to be negative due to how logarithmic scales represent numbers smaller than one. Misuse of log scales may also cause relationships between quantities to appear linear whilst those relationships are exponentials or power laws that rise very rapidly towards higher values. It has been stated, although mainly in a humorous way, that "anything looks linear on a log-log plot with thick marker pen" . : Both graphs show an identical exponential function of
f(x) = 2
x. The graph on the left uses a linear scale, showing clearly an exponential trend. The graph on the right, however uses a logarithmic scale, which generates a straight line. If the graph viewer were not aware of this, the graph would appear to show a linear trend.
Truncated graph A
truncated graph (also known as a
torn graph) has a
y axis that does not start at 0. These graphs can create the impression of important change where there is relatively little change. While truncated graphs can be used to overdraw differences or to save space, their use is often discouraged. Commercial software such as MS Excel will tend to truncate graphs by default if the values are all within a narrow range, as in this example. To show relative differences in values over time, an index chart can be used. Truncated diagrams will always distort the underlying numbers visually. Several studies found that even if people were correctly informed that the y-axis was truncated, they still overestimated the actual differences, often substantially. : These graphs display
identical data; however, in the truncated bar graph on the left, the data
appear to show significant differences, whereas, in the regular bar graph on the right, these differences are hardly visible. There are several ways to indicate
y-axis breaks: :
Axis changes : Changing the
y-axis maximum affects how the graph appears. A higher maximum will cause the graph to appear to have less volatility, less growth, and a less steep line than a lower maximum. : Changing the ratio of a graph's dimensions will affect how the graph appears. More egregiously, a graph may use different Y axes for different data sets, which makes the comparison between the sets misleading (the following graph uses a distinct Y axis for the "U.S." only, making it seem as though the U.S. has been overtaken by China in military expenditures, when it actually spends much more): :
No scale The scales of a graph are often used to exaggerate or minimize differences. : The lack of a starting value for the
y axis makes it unclear whether the graph is truncated. Additionally, the lack of tick marks prevents the reader from determining whether the graph bars are properly scaled. Without a scale, the visual difference between the bars can be easily manipulated. : Though all three graphs share the same data, and hence the actual
slope of the (
x,
y) data is the same, the way that the data is plotted can change the visual appearance of the angle made by the line on the graph. This is because each plot has a different scale on its vertical axis. Because the scale is not shown, these graphs can be misleading.
Improper intervals or units The intervals and units used in a graph may be manipulated to create or mitigate change expression. ==Measuring distortion==