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How to properly label graphs that can be dimensionless?

One of reviewers of my document strongly emphasised on labelling plots with which I generally strongly agree. On this occasion, however, I was explaining a general mathematical model on generated time series and by time series I mean an observation (value of a variable) that changes. Non of the variables I'm plotting has any units and the only reason why I added label Time [s] on x axis so that reader doesn't have to think too much what is there. Reviewer suggested adding units to all other labels, such as dimensionless amplitude, amplitude square and inverse of amplitude square. It seems that adding Density [1/|1|^2] or making up a unit might be considered a bit offensive.

Here are examples, where I am supposed to label axes. None of used variables requires a unit.

Density of dimensionless variable.

Time series

  • This should be your response to the reviewer. BTW if your variable is changing, then there should be a frame with respect to which it changes. Otherwise is constant everywhere and always. This clearly implies some kind of unit. – PsySp May 19 '17 at 12:34
  • @PsySp It seems so, but odd as it sounds, I'm not sure whether I am allowed to communicate with the reviewer until next submission, so in order to decrease my chances on prolonged communication I thought that asking wider audience might be helpful. (I've edited question: variable is no longer changing, but its value ;-) ) – Dawid Laszuk May 19 '17 at 17:54
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Lack of a unit never implies that a clear label isn't necessary. How can time not have an appropriate, non misleading label? How about "Index" or "sample number"? Just because it doesn't have a unit doesn't mean that you can't come up with an appropriate label? Even "Normalized Amplitude" or something. If the lack of a unit isn't immediately apparent, sometimes "unitless" where you would normally include a unit will clear things up.

Lastly, look toward your literature. If you can't find an example close to what you're doing, you may be reading the wrong literature, or not reading enough of the right literature. Having to ask about something like this is somewhat of a red flag on your due diligence.

  • I'm sorry, seems I have made it clear enough. I am using labels such as "Amplitude", "Power" or "Density" next to most of axes. Most, because there are figures with 16 side-by-side graphs and adding labels to each decreases readability. In all cases, however, caption and text explains the meaning of the variable and I do emphasis where appropriate that values are normalised. In all honesty, the literature that I've been reading uses often same labels. – Dawid Laszuk May 19 '17 at 17:46
  • Maybe more appropriate question would be: should I add "normalised" to each label, despite that it obscures the graph? – Dawid Laszuk May 19 '17 at 17:48
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If the number is dimensionless, you clearly can't add a unit. Even adding "seconds" to time is rather spurious if there aren't tick marks on the axis.

If the reviewer is finding things unclear, it's an indication that some of your readers will as well. You could make sure to explain in the caption that the axes are dimensionless and exactly what each axis represents, or if that can't be put simply, provide a reference to the section of the text in which it is explained. You could consider writing "Dimensionless density" or "Density (arbitrary units)" as the axis label.

  • Thank you for your answer. I'll do what you've mentioned, using the "arbitrary units." Unfortunately, due to my reputation, I cannot upvote your answer. – Dawid Laszuk May 26 '17 at 17:54
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If the unit or even the label is not important at all then arbitrary unit might be a possibility.

  • This seems to be appropriate answer, but I cannot upvote it. I've ended up with adding 'arbitrary unit' and extending explanation both in caption and text. – Dawid Laszuk May 26 '17 at 17:52

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