In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the result that an incorrect conclusion may be derived from it. Graphs may be misleading by being excessively complex or poorly constructed. Even when constructed to display the characteristics of their data accurately, graphs can be subject to different interpretations, or unintended kinds of data can seemingly and ultimately erroneously be derived. Misleading graphs may be created intentionally to hinder the proper interpretation of data or accidentally due to unfamiliarity with graphing software, misinterpretation of data, or because data cannot be accurately conveyed. Misleading graphs are often used in false advertising. One of the first authors to write about misleading graphs was Darrell Huff, publisher of the 1954 book How to Lie with Statistics. Data journalist John Burn-Murdoch has suggested that people are more likely to express scepticism towards data communicated within written text than data of similar quality presented as a graphic, arguing that this is partly the result of the teaching of critical thinking focusing on engaging with written works rather than diagrams, resulting in visual literacy being neglected. He has also highlighted the concentration of data scientists in employment by technology companies, which he believes can result in the hampering of the evaluation of their visualisations due to the proprietary and closed nature of much of the data they work with. The field of data visualization describes ways to present information that avoids creating misleading graphs.
Misleading graph methods [A misleading graph] is vastly more effective, however, because it contains no adjectives or adverbs to spoil the illusion of objectivity, there's nothing anyone can pin on you. 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. Graphs do not always convey information better than tables.
Biased labeling The use of biased or loaded words in the graph's title, axis labels, or caption may inappropriately prime the reader.
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. The usage of percentages as labels on a pie chart can be misleading when the sample size is small. 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.
Comparing pie charts Comparing data on barcharts is generally much easier. In the image below, it is very hard to tell where the blue sector is bigger than the green sector on the piecharts.
3D Pie chart slice perspective A perspective (3D) pie chart is used to give the chart a 3D look. Often used for aesthetic reasons, the third dimension does not improve the reading of the data; on the contrary, these plots are difficult to interpret because of the distorted effect of perspective associated with the third dimension. The use of superfluous dimensions not used to display the data of interest is discouraged for charts in general, not only for pie charts. 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.
In the improperly scaled pictogram bar graph, the image for B is actually 9 times as large as A.
The perceived size increases when scaling. The effect of improper scaling of pictograms is further exemplified when the pictogram has 3 dimensions, in which case the effect is cubed.
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.
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