{"id":448,"date":"2015-02-25T21:35:01","date_gmt":"2015-02-25T21:35:01","guid":{"rendered":"http:\/\/labmath.org\/?p=448"},"modified":"2015-11-18T21:20:35","modified_gmt":"2015-11-18T21:20:35","slug":"graphing-advice","status":"publish","type":"post","link":"http:\/\/labmath.org\/?p=448","title":{"rendered":"Graphing Advice"},"content":{"rendered":"

How to Make Truly Terrible Graphs: A Tutorial by David Streiner<\/h1>\n

Part 4: Where\u2019s the Y?<\/h2>\n

 <\/p>\n

In previous blogs, I described how to make terrible graphs using some of the features of leading graphing packages, such as pie charts and 3-D graphs. But, this is unfair to users of other programs that do not offer these \u201cenhancements\u201d (yes, such programs do exist; in fact, I use them exclusively except when I\u2019m preparing talks for hospital and university administrators).\u00a0 \u201cHow,\u201d I hear them cry, \u201ccan we too make truly terrible graphs?\u201d Well, do not despair; help is at hand. In this blog, I will discuss a very easy way to turn a straightforward graph into a disaster.<\/p>\n

The vast majority of graphs have two axes \u2013 the X-axis (abscissa) along the bottom and the Y-axis (ordinate) running along the left side. There can be variants of this, such as having a secondary Y-axis on the right, or having the Y-axis cross the X-axis in the middle, but these won\u2019t change the basic message. Also in most cases, the Y-axis starts at zero and runs up (or down, in some cases) to the maximum. Simple as this seems, it leaves a lot of room for mischief. The best way to thoroughly distort what the data show is to have a \u201cfloating Y\u201d \u2013 starting the axis at some point other than the natural base, which in most cases is zero. For example, let\u2019s assume that the university\u2019s president is trying to justify his request for an (obscenely high) increase to his (already obscenely high) salary because his workload has gotten so much heavier over the past few years. To bolster his case, he presents the following graph to the board of governors:<\/p>\n

\"blog4<\/a><\/p>\n

Wow! Look at the increase. Of course we have to reward him (although we could ask why he\u2019s still working a shorter week than mere mortals). But wait a second \u2013 the Y-axis doesn\u2019t start at zero; it\u2019s floating up there with a minimum of 30. What would the graph look like if it did start at zero?<\/p>\n

\"blog4<\/a><\/p>\n

That\u2019s more like it and just as we suspected; that \u201cincrease\u201d is barely perceptible without a microscope. By shrinking the range of the Y-axis, small differences are magnified.<\/p>\n

You may object to this graph on esthetic grounds, that most of the graph \u2013 the area below 30 \u2013 is blank, and why waste space showing nothing? That\u2019s a valid point. There are times when it doesn\u2019t make sense to start at zero. In these instances, the honest thing to do is at least alert the reader to that fact by making a break on the axis, like this:<\/p>\n

\"blog4<\/a><\/p>\n

Note that we\u2019ve made a bit of a compromise; there\u2019s less empty real estate, but the increase appears a bit more extreme than it actually is. We\u2019ll discuss in a bit how to determine if there\u2019s too much of a distortion.<\/p>\n

Lest you think that exaggerating differences by having a floating Y-axis is restricted to unscrupulous administrators (if that isn\u2019t a redundancy), here\u2019s a graph taken from an article purportedly showing that the risk of suicide is reduced by attending religious services (Kleiman & Liu, 2014).<\/p>\n

\"blog4<\/a><\/p>\n

For those of you who are unfamiliar with survival analysis, the left axis, \u201cSurvival function,\u201d shows the odds of being alive after a given time for the two groups.<\/p>\n

Again, the first reaction is Wow! Maybe we should all think of attending services a couple of times a week, if not every day, and that\u2019ll really reduce our risk. But let\u2019s take a closer look at the Y-axis. The bottom is not at zero, but at 0.9990. In other words, the entire range is 0.001 rather than 1.0. \u00a0That \u201cdifference\u201d between the groups is actually 0.9998 versus 0.9992 over an 18 year span. I tried plotting it with a true zero, and the lines were perfectly flat and superimposed on one another, as was the case with starting it at 0.80 and 0.90. In fact, I couldn\u2019t see any light between them until I did:<\/p>\n

\"blog4<\/a><\/p>\n

Even here note that the axis extends only from 0.98 to 1.00. Kinda sorta makes you want to reconsider how you spend your weekends, at least insofar as preventing suicides is concerned.<\/p>\n

So, how can you tell if a graph is misrepresenting what\u2019s really going on? You can use the Graph Distortion Index (GDI) proposed by Beattie and Jones (1992). It\u2019s defined as:<\/p>\n

GDI = (% change depicted in graph \u00f7 % change in data) – 1<\/h4>\n

In the first graph, the president\u2019s change in time looks like a 350% increase (from 20% up the Y-axis to 90% up the axis), whereas the actual increase is 15.6%. So, plugging those numbers into the equation we get (350\/15.6) \u2013 1 = 21.4, which is more than a bit higher than the recommended maximum of 0.05.<\/p>\n

Remember what we said in an earlier blog: the main purpose of a graph is not to present numbers, but to allow the viewer to get an immediate visual impression of what\u2019s going on. So don\u2019t despair; even if you can\u2019t make pie charts or 3-D graphs, you can still really distort the data by using a floating Y-axis.<\/p>\n

 <\/p>\n

 <\/p>\n

References<\/p>\n

Beattie, V., & Jones, M. (1992). The use and abuse of graphs in annual reports: Theoretical framework and empirical study. Accounting and Business Research, 22<\/i>, 291\u2013303.<\/p>\n

Kleiman, E. M., & Liu, R. T. (2014). Prospective prediction of suicide in a nationally representative sample: Religious service attendance as a protective factor. British Journal of Psychiatry, 204<\/i>, 262-266.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

How to Make Truly Terrible Graphs: A Tutorial by David Streiner Part 4: Where\u2019s the Y?   In previous blogs, I described how to make terrible graphs using some of the features of leading graphing packages, such as pie charts and 3-D graphs. But, this is unfair to users of other programs that do not […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12,1],"tags":[],"_links":{"self":[{"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/448"}],"collection":[{"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=448"}],"version-history":[{"count":6,"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/448\/revisions"}],"predecessor-version":[{"id":455,"href":"http:\/\/labmath.org\/index.php?rest_route=\/wp\/v2\/posts\/448\/revisions\/455"}],"wp:attachment":[{"href":"http:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=448"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/labmath.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}