Charts and graphs are very common in statistics. They help visualize data so people will have easy time understanding the results. Pictures are also more appealing than numbers. But charts can be misleading.
Line graph is seen everywhere. It is used mostly to show the change of something overtime. Change of temperature, population or income is often shown in line graphs. But it can be misleading. To demonstrate the possible tricks that can be used in a line graph, I made up data of sales in 6 months and constructed a line graph.
It can be seen that sales are going up slowly. It does not look good. So are there any ways to make it look better without changing the data point?
The answer is yes.
Wow, it looks much better! But no data has changed. The trick here is simply changing the y-axis. Notice this graph has y-axis starting from 18.5 instead of 0. And the whole graph is stretched because of the new y-axis. The graph is still same size a the previous one, but the line on the graph now looks like it is increasing rapidly. The sales is skyrocketing! Without changing any original data point, the graph looks much “nicer” than the original one. This trick appears often to serve the purpose of making results “look good”. So next time you see a chart, pay attention to the axis.
Bar graph is another common graph type that shows the comparison. Bar graph can be misleading by applying the same trick. Here is a real example from Fox News. This bar graph shows the tax rate before and after Bush tax cuts expire. It seems that if the Bush tax cut expires, the tax rate would increase by a lot. It is clearly the message Fox News want to send to the audience. But look at the y-axis. It starts at 34% instead of 0%. The difference of two bars is only 4.6%, but with the new y-axis, the difference is much more visible and thus creates a misleading impression. Such tricks occur often in real life and it is very important to know how to identify the tricks used so you will not be fooled by them.
(Source: http://www.statisticshowto.com/misleading-graphs/)
The next type of graph is called semi-attached figure. It serves similar purposes as bar graph but the main difference is instead of bars, semi-attached figures use pictures. The pictures’ sizes are in proportion to its amount. Below is an example of sales of fast food chains. (Source: http://www.gridgit.com/post_bad-charts-and-graphs_269479/)
It seems that McDonald has significantly more sales compared to other companies. The golden arc is hug in this graph. But here is the problem. The golden arc in this chart is NOT in proportion to its amount. The sales of McDonald is supposed to be 4 times that of Burger King’s but the golden arc is more than 4 times as big as Burger King’s logo. Don’t believe it? Then let’s fill golden arc with Burger King logos.
The golden arc fits roughly 6 Burger King logos. (Notice that the top of golden arc has its top unfilled). The reason is they simply increase the heights of the logos. But to make the logos in the original proportion, they also increase the widths. So the McDonald’s log is more than 4 times as big as Burger Kings’ though the heights are in proportion to the amount of sales. This trick will often make the graph more impressive than it should be.
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A Hitchhiker's Guide to Tricky Statistics 