{"id":761,"date":"2009-03-30T10:46:11","date_gmt":"2009-03-30T10:46:11","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2009\/03\/30\/more-stupid-graphs\/"},"modified":"2009-03-30T10:46:11","modified_gmt":"2009-03-30T10:46:11","slug":"more-stupid-graphs","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2009\/03\/30\/more-stupid-graphs\/","title":{"rendered":"More Stupid Graphs"},"content":{"rendered":"

Remember the post I made a couple of weeks ago, flaming the wall-street idiots for
\na bad graph?<\/a> They were comparing the value of financial firms before and after the current
\nmess. But they way that they drew it was using circles, where the diameter<\/em> of the
\ncircle was proportional to the values, but the way it was drawn strongly suggested that
\nthe area<\/em> was the metric of comparison.<\/p>\n

Well, an astute reader sent me another example of the same error – but it’s even
\nworse. This one is misleading in two ways. Take a look and see if you can figure out
\nwhat the two errors are. I’ll explain beneath the fold.<\/p>\n

\"unem-graph.png\"<\/div<\/p>\n

<\/p>\n

The first problem is exactly the same as the one the Wall Street idiots made: the
\ndiameter<\/em> of the circles is proportional to the actual data – but the use of circles as a visual presentation strongly<\/em> suggests to any reader that the area is the real measure.<\/p>\n

The other error is a bit more subtle. The measure represented in the charge is
\nunemployment rate<\/em> – a percentage figure. But the presentation as a simple area
\nstrongly suggests to the viewer that the area is proportional to the number of unemployed people. So, for example, looking at the chart, you’d think that Florida has many more unemployed people than Texas – from the bubbles, it looks like Florida has about twice as many unemployed as Texas.<\/p>\n

Based on a bit of searching, the number of unemployed people in Texas is has an unemployment rate around 6.6 percent, and a total number of unemployed somewhere around 781,000 according to the Texas Workforce Commission. According to Florida International University, Florida has an unemployment rate of about 8.6 percent, for a total number
\nof unemployed just under 800,000. In other words, Florida and Texas have roughly the same
\nnumber of unemployed people. <\/p>\n

So looking at the graph, you’d guess that the number of unemployed people in Florida is far larger than the number in Texas – which is not true. And even if you know that those bubbles represent percentages, you’d guess the the rate in Florida is roughly double
\nTexas, when in fact, it’s around 25% higher. <\/p>\n

The basic error there is presentational – but still important. The way that you present
\ndata has a significant impact on how that data is going to be interpreted by people who see it. Certain presentations imply certain interpretations.<\/p>\n

A percentage figure is a fraction, and so it should be represented by something that
\nillustrates the fact that it’s a fraction. Presenting percentages via area-bubbles the way
\nthat this chart does is pretty much guaranteed<\/em> to produce misunderstandings. Area
\nbubbles imply that the volume represents a quantity, not a fraction. So most people looking at
\nthat will thing that, for example, the graph is saying that there are more unemployed people
\nin Alaska than there are in Texas – when in fact the opposite is true. The unemployment
\nrate<\/em> is higher in Alaska, but the number of unemployed people in Alaska is
\nmuch<\/em> smaller than the number in Texas. In fact, according to the US census bureau,
\nthe entire population<\/em> of Alaska is smaller than the number of unemployed people in
\nTexas!<\/p>\n

There’s even a third problem with it, but it’s less serious than the other two. The
\ndiameters of the circles represent the state unemployment rates. At the bottom of the chart,
\nthere’s a time-based bar-chart of the national<\/em> unemployment rate. The height of
\nthose bars is directly comparable to the diameter of the circles. But because of the difference in presentation, you would not expect to be able to compare them. In a proper
\nchart, like measures should be presented in like manner. If you’re going to present a measure of a circular area, then everywhere in a particular chart that you present that measure,
\nyou should use a circular area. I don’t think that anyone<\/em> looking at that chart
\nwould have the slightest clue that they’re supposed to compare the diameter<\/em> of the circles on the map to the height of the bars on the timeline. <\/p>\n

If you wanted to do a graph like this, the appropriate presentation would be something
\nlike pie charts: something that clearly illustrates the fact that the relevant measure is a fraction. In fact, if you took that graph, and made the area of the circles proportional to the population of the states, and then used each circle as a pie graph illustrating the unemployment rate, you’d have an extremely<\/em> informative diagram. But as presented,
\nit’s worse than worthless – it’s actively misleading in multiple ways. And I don’t even think that it’s misleading because someone was trying<\/em> to present the data in a skewed way; it’s misleading simply because the person or people who made it was too stupid<\/em> to do it right.<\/p>\n","protected":false},"excerpt":{"rendered":"

Remember the post I made a couple of weeks ago, flaming the wall-street idiots for a bad graph? They were comparing the value of financial firms before and after the current mess. But they way that they drew it was using circles, where the diameter of the circle was proportional to the values, but the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[71],"tags":[],"class_list":["post-761","post","type-post","status-publish","format-standard","hentry","category-bad-economics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4lzZS-ch","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/761","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/comments?post=761"}],"version-history":[{"count":0,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/posts\/761\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/media?parent=761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/categories?post=761"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.goodmath.org\/blog\/wp-json\/wp\/v2\/tags?post=761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}