# Boxplot for data with a large number of zero values

Is there a recommended way to illustrate a heavily skewed distribution using a boxplot? For example, my boxplot looks like so:

It's very difficult to know what the median value is for the green boxplot. If I specify the range using ylim(0, 1), as far as I can tell ggplot2 removes points outside of the range in the boxplot calculation. I'm creating my plot using the following R code:

ggplot(df, aes(x=x, y=y)) + geom_boxplot(aes(colour=status))


I am aware that I can plot this using a histogram, but it's difficult to visuallly compare the two groups using a histogram.

• What about a qqplot or a relative distribution plot? When the goal is to compare the distributions, it might be better with a plot specially made for distribution comparison, than with two parallell plots. Dec 12, 2016 at 10:54
• Zero-skewed is not a good term for "skewed because there are lots of zeros" as zero skewness otherwise means skewness of zero. But it's not difficult to determine the median on the right at all: it's zero, as clearly at least 75% of values are zero. I'd use a quantile plot for these data. Can you post them? Dec 12, 2016 at 10:56
• @kjetilbhalvorsen - good idea, I have used geom_freqpoly() previously. @nickcox thanks for explaining - did not realize I was using incorrect term. I'll prepare a sample of data to post Dec 12, 2016 at 11:01
• See stats.stackexchange.com/questions/140090/… for a quantile-box plot for a dataset with several zeros. But your data appear more skewed yet. Dec 12, 2016 at 11:02
• Independently of other suggestions, using a transformed scale might also help, say cube root or square root. Dec 12, 2016 at 12:14

You can use violin plots and logarithmic transformation (of course you should add some constant to avoid $$log(0)$$) to compare the distributions and their quantiles at different levels of some factor.

For the sake of illustration please see below zero-inflated data of the number of the cod parasite (A Beginner’s Guide to R, A.F. Zuur et al., 2009) in dependence of its sex:

df <- structure(list(Sex = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 1L, 1L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L,
1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 0L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L,
1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L,
1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L,
2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
1L, 2L, 2L, 1L, 0L, 0L, 0L, 0L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 0L, 0L, 1L, 2L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 0L, 0L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L,
0L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L,
2L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 0L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 0L, 1L, 1L, 2L, 1L,
2L, 2L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 0L, 0L,
2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 0L, 2L, 1L, 0L, 0L, 1L, 1L, 0L,
2L, 0L, 2L, 0L, 1L, 0L, 0L, 2L, 2L, 1L, 0L, 0L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L,
2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 2L, 1L,
2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 2L,
2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L,
1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L), Intensity = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 10L, 10L, 10L,
10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L,
12L, 12L, 12L, 13L, 13L, 13L, 14L, 14L, 14L, 14L, 15L, 15L, 15L,
16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 19L, 19L,
20L, 20L, 21L, 21L, 21L, 22L, 22L, 23L, 23L, 24L, 25L, 25L, 26L,
27L, 28L, 28L, 28L, 32L, 33L, 35L, 35L, 36L, 38L, 39L, 41L, 41L,
45L, 50L, 51L, 52L, 56L, 65L, 68L, 73L, 84L, 86L, 126L, 160L,
183L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L,
9L, 9L, 9L, 10L, 10L, 11L, 11L, 12L, 12L, 12L, 12L, 13L, 14L,
14L, 14L, 15L, 17L, 19L, 20L, 20L, 22L, 26L, 26L, 27L, 28L, 30L,
30L, 30L, 31L, 31L, 35L, 39L, 40L, 43L, 43L, 44L, 45L, 45L, 49L,
52L, 56L, 56L, 58L, 67L, 67L, 71L, 81L, 186L, 210L, 223L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 10L,
10L, 10L, 10L, 10L, 11L, 13L, 13L, 13L, 14L, 14L, 14L, 16L, 17L,
17L, 18L, 18L, 18L, 19L, 20L, 20L, 30L, 34L, 36L, 40L, 42L, 45L,
46L, 46L, 49L, 50L, 55L, 75L, 84L, 89L, 90L, 104L, 125L, 128L,
257L)), class = "data.frame", row.names = c(1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L,
19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L,
32L, 33L, 34L, 35L, 36L, 37L, 38L, 39L, 40L, 41L, 42L, 43L, 44L,
45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L,
58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 69L, 70L,
71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 82L, 83L,
84L, 85L, 86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 95L, 96L,
97L, 98L, 99L, 100L, 101L, 102L, 103L, 104L, 105L, 106L, 107L,
108L, 109L, 110L, 111L, 112L, 113L, 114L, 115L, 116L, 117L, 118L,
119L, 120L, 121L, 122L, 123L, 124L, 125L, 126L, 127L, 128L, 129L,
130L, 131L, 132L, 133L, 134L, 135L, 136L, 137L, 138L, 139L, 140L,
141L, 142L, 143L, 144L, 145L, 146L, 147L, 148L, 149L, 150L, 151L,
152L, 153L, 154L, 155L, 156L, 157L, 158L, 159L, 160L, 161L, 162L,
163L, 164L, 165L, 166L, 167L, 168L, 169L, 170L, 171L, 172L, 173L,
174L, 175L, 176L, 177L, 178L, 179L, 180L, 181L, 182L, 183L, 184L,
185L, 186L, 187L, 188L, 189L, 190L, 191L, 192L, 193L, 194L, 195L,
196L, 197L, 198L, 199L, 200L, 201L, 202L, 203L, 204L, 205L, 206L,
207L, 208L, 209L, 210L, 211L, 212L, 213L, 214L, 215L, 216L, 217L,
218L, 219L, 220L, 221L, 222L, 223L, 224L, 225L, 226L, 227L, 228L,
229L, 230L, 231L, 232L, 233L, 234L, 235L, 236L, 237L, 238L, 239L,
240L, 241L, 242L, 243L, 244L, 245L, 246L, 247L, 248L, 249L, 250L,
251L, 252L, 253L, 254L, 255L, 256L, 257L, 258L, 259L, 260L, 261L,
262L, 263L, 264L, 265L, 266L, 267L, 268L, 269L, 270L, 271L, 272L,
273L, 274L, 275L, 276L, 277L, 278L, 279L, 280L, 281L, 282L, 283L,
284L, 285L, 286L, 287L, 288L, 289L, 290L, 291L, 292L, 293L, 294L,
295L, 296L, 297L, 298L, 299L, 300L, 301L, 302L, 303L, 304L, 305L,
306L, 307L, 308L, 309L, 310L, 311L, 312L, 313L, 314L, 315L, 316L,
317L, 318L, 319L, 320L, 321L, 322L, 323L, 324L, 325L, 326L, 327L,
328L, 329L, 330L, 331L, 332L, 333L, 334L, 335L, 336L, 337L, 338L,
339L, 340L, 341L, 342L, 343L, 344L, 345L, 346L, 347L, 348L, 349L,
350L, 351L, 352L, 353L, 354L, 355L, 356L, 357L, 358L, 359L, 360L,
361L, 362L, 363L, 364L, 365L, 366L, 367L, 368L, 369L, 370L, 371L,
372L, 373L, 374L, 375L, 376L, 377L, 378L, 379L, 380L, 381L, 382L,
383L, 384L, 385L, 386L, 387L, 388L, 389L, 390L, 391L, 392L, 393L,
394L, 395L, 396L, 397L, 398L, 399L, 400L, 401L, 402L, 403L, 404L,
405L, 406L, 407L, 408L, 409L, 410L, 411L, 412L, 413L, 414L, 415L,
416L, 417L, 418L, 419L, 420L, 421L, 422L, 423L, 424L, 425L, 426L,
427L, 428L, 429L, 430L, 431L, 432L, 433L, 434L, 435L, 436L, 437L,
438L, 439L, 440L, 441L, 442L, 443L, 444L, 445L, 446L, 447L, 448L,
449L, 450L, 451L, 452L, 453L, 454L, 455L, 456L, 457L, 458L, 459L,
460L, 461L, 462L, 463L, 464L, 465L, 466L, 467L, 468L, 469L, 470L,
471L, 472L, 473L, 474L, 475L, 476L, 477L, 478L, 479L, 480L, 481L,
482L, 483L, 484L, 485L, 486L, 487L, 488L, 489L, 490L, 491L, 492L,
493L, 494L, 495L, 496L, 497L, 498L, 499L, 500L, 501L, 502L, 503L,
504L, 505L, 506L, 507L, 508L, 509L, 510L, 511L, 512L, 513L, 514L,
515L, 516L, 517L, 518L, 519L, 520L, 521L, 522L, 523L, 524L, 525L,
526L, 527L, 528L, 529L, 530L, 531L, 532L, 533L, 534L, 535L, 536L,
537L, 538L, 539L, 540L, 541L, 542L, 543L, 544L, 545L, 546L, 547L,
548L, 549L, 550L, 551L, 552L, 553L, 554L, 555L, 556L, 557L, 558L,
559L, 560L, 561L, 562L, 563L, 564L, 565L, 566L, 567L, 568L, 569L,
570L, 571L, 572L, 573L, 574L, 575L, 576L, 577L, 578L, 579L, 580L,
581L, 582L, 583L, 584L, 585L, 586L, 587L, 588L, 589L, 590L, 591L,
592L, 593L, 594L, 595L, 596L, 597L, 598L, 599L, 600L, 601L, 602L,
603L, 604L, 605L, 606L, 607L, 608L, 609L, 610L, 611L, 612L, 613L,
614L, 615L, 616L, 617L, 618L, 619L, 620L, 621L, 622L, 623L, 624L,
625L, 626L, 627L, 628L, 629L, 630L, 631L, 632L, 633L, 634L, 635L,
636L, 637L, 638L, 639L, 640L, 641L, 642L, 643L, 644L, 645L, 646L,
647L, 648L, 649L, 650L, 651L, 652L, 653L, 654L, 655L, 656L, 657L,
658L, 659L, 660L, 661L, 662L, 663L, 664L, 665L, 666L, 667L, 668L,
669L, 670L, 671L, 672L, 673L, 674L, 675L, 676L, 677L, 678L, 679L,
680L, 681L, 682L, 683L, 684L, 685L, 686L, 687L, 688L, 689L, 690L,
691L, 692L, 693L, 694L, 695L, 696L, 697L, 698L, 699L, 700L, 701L,
702L, 703L, 704L, 705L, 706L, 707L, 708L, 709L, 710L, 711L, 712L,
713L, 714L, 715L, 716L, 717L, 718L, 719L, 720L, 721L, 722L, 723L,
724L, 725L, 726L, 727L, 728L, 729L, 730L, 731L, 732L, 733L, 734L,
735L, 736L, 737L, 738L, 739L, 740L, 741L, 742L, 743L, 744L, 745L,
746L, 747L, 748L, 749L, 750L, 751L, 752L, 753L, 754L, 755L, 756L,
757L, 758L, 759L, 760L, 761L, 762L, 763L, 764L, 765L, 766L, 767L,
768L, 769L, 770L, 771L, 772L, 773L, 774L, 775L, 776L, 777L, 778L,
779L, 780L, 781L, 782L, 783L, 784L, 785L, 786L, 787L, 788L, 789L,
790L, 791L, 792L, 793L, 794L, 795L, 796L, 797L, 798L, 799L, 800L,
801L, 802L, 803L, 804L, 805L, 806L, 807L, 808L, 809L, 810L, 811L,
812L, 813L, 814L, 815L, 816L, 817L, 818L, 819L, 820L, 821L, 822L,
823L, 824L, 825L, 826L, 827L, 828L, 829L, 830L, 831L, 832L, 833L,
834L, 835L, 836L, 837L, 838L, 839L, 840L, 841L, 842L, 843L, 844L,
845L, 846L, 847L, 848L, 849L, 850L, 851L, 852L, 853L, 854L, 855L,
856L, 857L, 858L, 859L, 860L, 861L, 862L, 863L, 864L, 865L, 866L,
867L, 868L, 869L, 870L, 871L, 872L, 873L, 874L, 875L, 876L, 877L,
878L, 879L, 880L, 881L, 882L, 883L, 884L, 885L, 886L, 944L, 945L,
946L, 947L, 948L, 949L, 950L, 951L, 952L, 953L, 954L, 955L, 956L,
957L, 958L, 959L, 960L, 961L, 962L, 963L, 964L, 965L, 966L, 967L,
968L, 969L, 970L, 971L, 972L, 973L, 974L, 975L, 976L, 977L, 978L,
979L, 980L, 981L, 982L, 983L, 984L, 985L, 986L, 987L, 988L, 989L,
990L, 991L, 992L, 993L, 994L, 995L, 996L, 997L, 998L, 999L, 1000L,
1001L, 1002L, 1003L, 1004L, 1005L, 1006L, 1007L, 1008L, 1009L,
1010L, 1011L, 1012L, 1013L, 1014L, 1015L, 1016L, 1017L, 1018L,
1019L, 1020L, 1021L, 1022L, 1023L, 1024L, 1025L, 1026L, 1027L,
1028L, 1029L, 1030L, 1031L, 1032L, 1033L, 1034L, 1035L, 1036L,
1037L, 1038L, 1039L, 1040L, 1041L, 1042L, 1043L, 1044L, 1045L,
1046L, 1047L, 1048L, 1049L, 1050L, 1051L, 1052L, 1053L, 1054L,
1055L, 1056L, 1057L, 1058L, 1059L, 1060L, 1061L, 1062L, 1063L,
1064L, 1065L, 1066L, 1067L, 1068L, 1069L, 1070L, 1071L, 1072L,
1073L, 1074L, 1075L, 1076L, 1077L, 1078L, 1079L, 1080L, 1081L,
1082L, 1083L, 1084L, 1085L, 1086L, 1087L, 1088L, 1089L, 1090L,
1091L, 1092L, 1093L, 1094L, 1095L, 1096L, 1097L, 1098L, 1099L,
1100L, 1101L, 1102L, 1103L, 1104L, 1105L, 1106L, 1107L, 1108L,
1109L, 1110L, 1111L, 1112L, 1113L, 1114L, 1115L, 1116L, 1117L,
1118L, 1119L, 1120L, 1121L, 1122L, 1123L, 1124L, 1125L, 1126L,
1127L, 1128L, 1129L, 1130L, 1131L, 1132L, 1133L, 1134L, 1135L,
1136L, 1137L, 1138L, 1139L, 1140L, 1141L, 1142L, 1143L, 1144L,
1145L, 1146L, 1147L, 1148L, 1149L, 1150L, 1151L, 1152L, 1153L,
1154L, 1155L, 1156L, 1157L, 1158L, 1159L, 1160L, 1161L, 1162L,
1163L, 1164L, 1165L, 1166L, 1167L, 1168L, 1169L, 1170L, 1171L,
1172L, 1173L, 1174L, 1175L, 1176L, 1177L, 1178L, 1179L, 1180L,
1181L, 1182L, 1183L, 1184L, 1185L, 1186L, 1187L, 1188L, 1189L,
1190L, 1191L, 1192L, 1193L, 1194L, 1195L, 1196L, 1197L, 1198L,
1199L, 1200L, 1201L, 1202L, 1203L, 1204L, 1205L, 1206L, 1207L,
1208L, 1209L, 1210L, 1211L, 1212L, 1213L, 1214L, 1215L, 1216L,
1217L, 1218L, 1219L, 1220L, 1221L, 1222L, 1223L, 1224L, 1225L,
1226L, 1227L, 1228L, 1229L, 1230L, 1231L, 1232L, 1233L, 1234L,
1235L, 1236L, 1237L, 1238L, 1239L, 1240L, 1241L, 1242L, 1243L,
1244L, 1245L, 1246L, 1247L, 1248L, 1249L, 1250L, 1251L, 1252L,
1253L, 1254L))


Then using ggplot2 package together with logarithmic transformation $$ln(x + 1)$$ you can draw violin-plot and show quantiles:

library(ggplot2)
ggplot(df, aes(x = factor(Sex), y = log(Intensity + 1))) +
geom_violin(draw_quantiles = c(.25, .5, .75, .95))


The result is:

• A square or cube root transformation works well too. Both allow you to skip the workaround of adding 1 before taking the log. Cube roots also work well with negative numbers.
– mkt
Sep 25, 2019 at 19:30