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I have a series of left-skewed/heavy tailed distributions that I would like to show. There are 42 distributions across three factors (labeled as A, B and C below). Also, the variation is shrinking across factor B.

The issue I have is that the distributions are hard to differentiate across the scale of the outcome (a ratio or fold-change):

enter image description here

Logging the data seems to over-emphasizes the left skewness and moves more samples into the tails (creating a mash of outlier points):

enter image description here

Does anyone have suggestions on other techniques for visualizing these data?

mkt
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topepo
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    Logging is often used to reduce right-skewness, so it can be expected to increase left-skewness. The exp() transformation is its inverse, but that is probably far too strong here. Squaring is a milder alternative. You don't say what sample size(s) you have. It is not obvious that the main problem is really left skewness, rather than a few moderate outliers in the left tail in B1. Is there no science here to throw light on this? – Nick Cox Mar 25 '14 at 00:55
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    The sample size per box plot is about 100. The values are speed-ups achieved by a new computational algorithm (i.e. old run-time/new run time). There are occasions where it does not produce significant time savings so the distributions tend to trail off to the left. – topepo Mar 25 '14 at 01:25
  • Thanks. The number of points beyond the whiskers seems to be rather small then. – Nick Cox Mar 25 '14 at 01:49
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    What is it about these distributions that you want to see better? The current plot looks good to me: C makes very little, if any, difference; higher B makes tighter & lower distributions; & higher A goes w/ higher values. – gung - Reinstate Monica Nov 30 '16 at 18:20
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    If you are looking at something multiplicative, like fold change, then a logarithmic scale often makes sense. (See also https://stats.stackexchange.com/a/361263) It might increase "outliers" but maybe that's just what you have and you should not hide this with transformations (if you want to hide them then you can just as well not plot them). To me the log scale graph looks more intuitive because it shows that the variance is more or less equal. (The lower variance for larger factor b on the linear scale seems partly because it is a smaller value and the smaller values have all lower variance) – Sextus Empiricus Sep 25 '21 at 19:17

2 Answers2

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Just an idea: if you can describe the distributions you got relatively well with a normal distribution, you can do 2-dimensional plots showing the impact of A, B and C on the fitted distributions parameters: mean and standart deviation.

Or you try to find other describing measures for the distribution that you got and show the impact of the three variables on them.

If you find that two variables have interactions, you can do a 3d plot. Lets hope they do not all interact with one another. ;)

Elmar Macek
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As noted in the comments, especially by Sextus Empiricus, fold change is often depicted on a logarithmic scale (specifically log2). It appears to work well in your case because the variances are much more similar when shown on the log scale.

I don't see any real evidence in the plots that skewness is a meaningful problem. There's a small handful of extreme values but those don't really call for a change in your visualisation.

That said, there are probably nicer ways to plot this (while retaining the general design and the log2 scale). If you have a small number of points, you could just plot the data directly or perhaps use a beeswarm plot instead of using boxplots. If you have a large number, violin plots, ridgeline plots (as Shawn Hemelstrand's answer shows), or density plots would all be good options.

mkt
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