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I know that using an origin other than 0 for numeric data is considered misleading. But for plots in academic publications, is it ever a good idea to break an axis so that patterns and outliers can be more easily seen? Or would you always try to find an alternative (e.g., using a logarithmic scale, faceting, using multiple plots with different scales)? I'm looking for a general rule of thumb.

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    A long as it is not bar plot and it is not misleading. – Piotr Migdal Feb 24 '15 at 18:07
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    Honestly, I'm tempted to vote to close as off-topic. This question would be much better at UX.SE, or possibly CV.SE (who also do visualization). There really is nothing very academic about this - this question makes sense for anyone who visualizes data, whether high school student, undergrad, business person or volunteer for a charity. Then again, I just submitted an answer, so I can't very well VTC... – S. Kolassa - Reinstate Monica Feb 24 '15 at 19:35
  • see stats.stackexchange.com/questions/1764/…: this question has been answered on CrossValidated. – cbeleites supports Monica Feb 24 '15 at 20:22
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    I'm voting to close this question as off-topic because it is a duplicate of stats.stackexchange.com/questions/1764/… – cbeleites supports Monica Feb 24 '15 at 20:27
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    I think this should be reopened. The question it supposedly "duplicates" asks about ways to not break an axis, not about situations when it's OK to break an axis. I'm also not sure closing questions just because they have been asked (in a different way) on another SE site is a good idea, either. If they're off topic here, fine, close them, but I don't think on topic questions should be closed just because someone else asked them in a different way on another SE site. – ff524 Feb 25 '15 at 6:02
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In my own experience, the time when it makes sense to break an axis is when you have a mixture of two distributions, such that neither a linear nor a logarithmic scale can represent things clearly. For example, I have done this when dealing with an independent variable in which there was an exponential distribution of conditions, and also zero. (e.g., 0, 1, 10, 100, 1000): this is poorly represented in either log (where zero flies off the chart) or linear (where the lower values are compressed), but well represented by zero, then a break to logarithmic.

For a dependent variable, however, I have found that it is usually better to use two charts with different scales, or a "detail inset," because it is important to give the reader a sense of the full range of the observed values, and a break reduces the visual impact.

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    I would add that it also depends on how many things go off the charts. If it is only one, it can be more acceptable. – Davidmh Feb 24 '15 at 17:37
  • William Cleveland gives pretty much the same advice, see this same question and my answer at the UX site. – Andy W Feb 25 '15 at 12:36
  • Today's xkcd is a good example for this :-) – Bergi Feb 25 '15 at 21:34
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I used to be a "don't break the axis" purist. I like to think that I have learned better. Nowadays, whenever I know that zero does not make sense for the data I am visualizing, I don't hesitate to break the axis.

A little example: I recently started recording my weight (in kg) and reducing my calorie intake. Here is the time series. Does anyone think that the plot on the right is more informative? It isn't. Because zero is not a possible weight for a healthy 39 year old male.

weight

  • It's missing errorbars though ;-) – gerrit Feb 24 '15 at 22:41
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    @gerrit they are there, they are just obscured by the symbols. – StrongBad Feb 25 '15 at 0:46
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I know that using an origin other than 0 for numeric data is considered misleading

You've been told wrong. That's just nonsense. Do use a zero baseline when you're using area to indicate quantity, and a zero baseline gives you an area that's proportional to the quantity. That's typically bar charts, column charts and area charts.

But for line graphs, scatter graphs, sparklines, and any other charts where quantity is indicated by position rather than area, you're absolutely fine with a non-zero baseline.

Have a look at plots of external temperature produced by meteorological organisations: how many of them have a baseline of zero Kelvin? None. Obviously.

  • And note that the zero baseline for logarithmic data (changes are better described as multiples than as difference) is at 1. – cbeleites supports Monica Feb 24 '15 at 20:24
11

Sometimes, breaking an axis is the least bad alternative.

In one of my publications, reviewers were complaining that some of my lines were off the graph. But I didn't want to compress the y-axis so much that the lower values would be harder to tell apart. So, somewhat reluctantly, the final version of my graph looked like this:

IWP performances
Source: Holl et al. (2014)

Note the unusual discontinuity around the value of 300%.

Is it ever a good idea? It is not ideal. But in context, it might be a better choice than any other alternative. In the figure above, I had the choice between (1) extending the entire y-axis normally up to 500% (rendering the difference between 100% and 125% hard to see), cutting off the graph at 300% (with one line going out of the graph), or by stacking two graphs with different y-scales as shown. I originally chose to cut off the graph, but after a reviewer complained, I opted for the solution above.

As long as you make sure that it is entirely unambiguous what set of values each location in the axes relate to, it should be acceptable. As ff524 points out in a comment, you should also point out the discontinuity or break in the figure caption.

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    +1 great example! It's also important that you pointed out the discontinuity and the different scales in the caption, you might want to mention that in the answer. – ff524 Feb 24 '15 at 18:21
  • I think your reviewers helped you out in this case. :^) – J.R. Feb 24 '15 at 18:49
  • @gerrit The plot above looks like pgfplots output. If it is, could you share what keys you specified to get two different scales? – wchargin Feb 24 '15 at 20:03
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    @WChargin It is indeed made with pgfplots. I used the groupplots library with a groupplot, group style={group size=1 by 2,xticklabels at=edge bottom,vertical sep=0pt}, then the first \nextgroupplot with axis x line*=top. See the pgfplots documentation, section 5.5 Grouping plots. – gerrit Feb 24 '15 at 20:14
  • @gerrit cool—thanks for the section reference! That seems like a very versatile feature. – wchargin Feb 24 '15 at 22:22
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It also depends on the variation of the data. If you know, from theory, that your data will change from 10 to 20 and the changes there are the ones you are interested in, you can break the axis and focus on that range. Wherever 0 is is irrelevant, as you know that your data lies between 10 and 20.

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