# 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? – Nick Cox Mar 25 '14 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. – topepo Mar 25 '14 at 1:25
• Thanks. The number of points beyond the whiskers seems to be rather small then. – Nick Cox Mar 25 '14 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. – gung - Reinstate Monica Nov 30 '16 at 18:20

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.