# Visualizing many left-skewed distributions

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):

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

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

• 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? Commented Mar 25, 2014 at 0:55
• 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. Commented Mar 25, 2014 at 1:25
• Thanks. The number of points beyond the whiskers seems to be rather small then. Commented Mar 25, 2014 at 1:49
• 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. Commented Nov 30, 2016 at 18:20
• If you are looking at something multiplicative, like fold change, then a logarithmic scale often makes sense. (See also 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) Commented Sep 25, 2021 at 19:17

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.