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I decided to give box and whiskers plots a try with my data. However, the produced box plots look a bit abnormal. I have not been able to find such cases online. For example, my "T" value has no box at all, while the median of "R" value is actually the same as first quartile. Is this normal? I'm not sure I want to include it in my class presentation like that.

I played around with the percentile range and set it to 20-80 (instead of 25-75) and then I DID get a more "typical" box plot. How common is it to use 20 and 80 percentiles?

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mydataset

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    $\begingroup$ the box is usually constructed via the first and third quartile of the dataset. the line inside the box is just the median (second quartile). in your case, for group "T", there is nothing wrong with the boxplot. the box not beeing visible just tells you that the the second and third quartile of the data coincide with its median. this is a perfectly fine boxplot and it gives you all the information you want to extract from a boxplot. $\endgroup$ – BloXX Jan 19 '18 at 11:37
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    $\begingroup$ For a similar question, see stats.stackexchange.com/questions/68069/… $\endgroup$ – Nick Cox Jan 19 '18 at 14:12
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@BioXX explains the main point clearly: with data like yours, all small integers, ties of two or more of minimum, median, quartiles and maximum are likely, with inevitable side-effects that boxes and/or whiskers may be of zero length and thus not visible as such.

You would in broad terms get similar problems with other quantile summaries with your kind of data. Using quartiles as box ends rather than say 20 and 80% points is largely a convention, but you would certainly need to explain and justify something different.

I would go further and say that a box plot is not especially useful for such data, not least because important detail is either hidden altogether or cryptic at best. Some kind of histogram or bar chart display is not only much simpler and easier to explain, but considerably more useful in showing the data directly. Here is a token example.

enter image description here

I've not addressed the missing values in your data. This is just every recorded value, regardless of whether there is a recorded value for other variables in the same observation.

Whether the bars should touch is partly a matter of taste, and partly a matter of ideas about the variables. Anyone wanting to see the points as measured on an approximate continuum might well be happy with touching bars; anyone wanting to emphasise the discrete or even ordinal nature of the data might prefer gaps. Here we have precisely no information on what the variables are.

A more subtle variant might be to use square root scale for the counts, a rootogram in J.W. Tukey's terms.

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  • $\begingroup$ The bar chart really does look like a better approach for what I want to present, thank you. Now I just have to figure out how to stack everything (in Statistica) they way you did above. The (environmental) variables are, for example, L = light, M = Moisture, N = Nitrogen, S = salinity etc. $\endgroup$ – nut_kernel Jan 19 '18 at 16:20
  • $\begingroup$ Sorry, I've never used Statistica. Presumably there is a Statistica forum somewhere. $\endgroup$ – Nick Cox Jan 19 '18 at 21:54

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