# Violin plots interpretation

I am comparing the distrubution of different groups using the violin plots, however most of the online resources I found are just related to how to make the plots and very basic interpretation of the results (the median variation, the data is clustered or not).

I am looking for detailed examples that I can follow as my guideline to correctly interpret the violin plots.

A violin plot is just a histogram (or more often a smoothed variant like a kernel density) turned on its side and mirrored. Any textbook that teaches you how to interpret histograms should give you the intuition you seek. Edit per Nick Cox's suggestion: Freedman, Pisani, Purves, Statistics covers histograms.

As far as interpreting them in a more formal way, the whole point of graphing the distribution is to see things that statistical tests might be fooled by.

One thing I like to do with violin plots is add lines for the median, mean, etc. Sometimes I'll superimpose a boxplot so I can see even more in the way of summary statistics.

At very least, you should be able to pick out any gross deviations in the first few moments (mean, dispersion, skewness, kurtosis) as well as bimodality and outliers.

• +1, a similar plot is a population pyramid, the reflected distribution is just a different category (and it uses more typical histogram type estimators instead of kde). – Andy W Aug 12 '13 at 20:00
• Neither Tukey, Exploratory data analysis, nor Cleveland, Elements of graphing data, says much about histograms: both are more interested in and more impressed by other representations. Are those are the books alluded to here? One book that does cover histograms as basic is Freedman, Pisani, Purves, Statistics. – Nick Cox Aug 12 '13 at 20:11
• Actually, Cleveland does say something about histograms. He says that they are poor graphs and that they won't be used in his book. :-). And F, P and P is a wonderful book. – Peter Flom Aug 12 '13 at 21:07
• I've taught from FPP. They wouldn't explicitly use OLS to predict the area of a rectangle, because they don't explicitly do multivariate regression. They do have a few examples in this spirit, though. For example, what if Galileo had tried to predict the time t that it takes an object to fall from height h by linear regression? You get a nice least squares fit, but of course the truth is $t = c\sqrt{h}$ - the moral of the story is to always look at the residuals. – Michael Lugo Aug 12 '13 at 23:10
• @TrevorAlexander That's a good question. I'm unaware of any literature showing interpretation is better when mirrored, but they do look nicer than histograms in a vertical orientation, to my eye at least. – Ari B. Friedman Sep 6 '14 at 11:08