You ask
I would like to compare these three distributions. By compare I mean
that I want to see if there are any large shifts in either the shape
or spread of the distribution
and your question implies you are also interested in shift of location.
Then there are really three things you want to compare: 1. Location, 2) Spread and 3) Shape.
For 1., you can compare means, medians or other quantiles. There are statistical tests of these, or you could bootstrap. One problem, though, is your sample sizes: They are small and varying. So, as often, you have to look at effect size, not just p value. For comparing 3 means, you can use a linear model (ANOVA/regression) provided the assumptions are met. For comparing quantiles (including the median) you could use quantile regression (fewer assumptions than linear model). Or you could just list them and say "Look!"
For 2, again, there are different measures of spread: Most common are probably standard deviation and inter quartile range. Do either of these appeal?
For 3, things are trickier. You could look at measures of skewness and kurtosis across the three groups, but 1) These don't fully capture "shape" and 2) They are less intuitive than measures of location or spread (in particular, kurtosis doesn't really match intuition for any particular aspect of shape). So, you'd have to say what about the shape you are interested in.
Visual inspection gives you more information; looking at 400 beanplots is a lot; but so is looking at 400 quantile regressions or ANOVAs.
Best Answer
For multiple groups with 10-30 data points per group, I like "dot plots" (as I call them), which you can create with
stripchart()in R. I always usemethod="jitter"andpch=1.You might also check out the beeswarm package, which makes similar plots but with deterministic placement of points.