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I want to submit a manuscript with a journal recommending the APA style guide for formatting.

When looking at my boxplots, a colleague of mine wondered why the whiskers do not represent the 95% confidence interval. So I learned that the default setting for matplotlib is 1.5 IQR, which I did not questioned until that point.

According to the very good Wikipedia article on boxplots there are different possibilities for whiskers representation:

  • the minimum and maximum of all of the data
  • the lowest datum still within 1.5 IQR of the lower quartile, and the highest datum still within 1.5 IQR of the upper quartile (often called the Tukey boxplot)
  • one standard deviation above and below the mean of the data
  • the 9th percentile and the 91st percentile
  • the 2nd percentile and the 98th percentile

Does anybody know what is the most common whisker boundary and if there is a recommendation in the APA style?

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  • P.S.: I am surprised to see there is no APA-style tag on Academia yet. I do not have enough reputation to create it.
    – n1000
    Mar 20, 2015 at 11:39
  • This might be a better question for Cross Validated.
    – Bill Barth
    Mar 20, 2015 at 12:15
  • @BillBarth Yeah, I was hesitant. But then I was thinking it might be more about the APA style and scientific writing. If the community thinks it should be over there, this would be fine for me.
    – n1000
    Mar 20, 2015 at 12:35
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    Technicality: the confidence interval is referring to parameter estimates. What you have is the percentiles of the distribution, I suppose.
    – StasK
    Mar 20, 2015 at 14:10
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3 Answers 3

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Major statistical software such as Stata, SPSS, SAS, and R all use John Tukey's definition (hyperlinks are to the related technical documents), with various degrees of customizability. Some of them also cite William Cleveland's scheme, which is the same as Tukey's.

one standard deviation above and below the mean of the data

This does not make sense as box plot is largely a device to display the central tendency of data using the more robust percentile statistics and I have a hard time pairing it with standard deviations (and its related statistics standard error and 95% CI), which based on the actual value of the data rather than their rank. If showing mean and SD (or SE) is the motive, there are error bar plots for this purpose.

the minimum and maximum of all of the data

While min and max also indicate spread, they are also sensitive to extreme values, and hence a less robust indicator of dispersion. So also not making much sense.

the 9th percentile and the 91st percentile & the 2nd percentile and the 98th percentile

I have less opposition against these schemes, the only reason I'd opt for not using them is just we don't need any more schemes.

So, my bet is on Tukey's. And if you're uncertain if readers may be confused, by all means in the footnote state that the scheme is based on Tukey's box plot.

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  • Thanks. Seems like the Wikipedia article could need an edit.
    – n1000
    Mar 20, 2015 at 13:28
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I don't think this has anything in particular to do with APA style. Rather, it has to do with what you want to communicate about your data: the reason that there are different uses of box-plots is that there are different structures of data distributions, for which different representations are valuable.

The main thing that you are communicating with a box-plot is that your data has a structure that may not be well-represented by a simple parametric distribution, such as a normal distribution or a Poisson distribution. A box plot allows you to show five points on the (likely highly variable and asymmetric) cumulative distribution curve, and those points just need to be chosen in some reasonably principled manner, such as the in examples listed.

You then just need to explain in your text what it is that the box-and-whiskers represents in your particular usage.

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  • Sounds reasonable - thanks. In your opinion, is there a "most common" version? I guess the 1.5 IQR was chosen for a reason.
    – n1000
    Mar 20, 2015 at 13:15
  • It depends on your data set size and structure, but I think I have most commonly seen min/max and Tukey. Min/max is most common for very small sample sizes (e.g., in cognitive science or animal experiments), Tukey for larger.
    – jakebeal
    Mar 20, 2015 at 14:04
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@jakebeal already gave a good answer, but let me impress this in different but more direct words:

You create figures because you want to illustrate something. What the figure shows and how it displays data must be driven by what it is you want to illustrate, not based on a style guide. In other words, the correct answer to your question is: Chose that format that best illustrates the facts you want to demonstrate with the figure.

It is obvious that if a figure allows for multiple interpretations (such as what the whiskers represent), then you need to disambiguate this in the caption or the text. This is appropriate even if the style guide were to specify, say, 95% intervals, as this fact may not be obvious to the casual reader unaware of the style guide.

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