Violin plot: How is the adjacent value range determined, and why is it different from boxplot?

Question

In theory the violinplot of vioplot package is a boxplot + density function.

In the "boxplot part",

• the black box corresponds to the IQR (indeed, see below), and

• the midline should correspond to the same range (adjacent values, default 1.5 IQR), yet it is not (see below). Anyone can explain why are they different?

  require("vioplot")
  a = rnorm(100)
  range (a)
  a = c(a,2,8,2.9,3,4, -3, -5) # add some outliers
  
  par ( mfrow = c(1,2))
  boxplot(a, range=1.5)
  vioplot(a, range=1.5 )
  

Benerated by above:

Hintze, J. L. and R. D. Nelson (1998). Violin plots: a box plot-density trace synergism. The American Statistician, 52(2):181-4.

Answer 1

Let me illustrate this with a simple example:

b <- c(1:10, 20)

par(mfrow = c(1,2))
boxplot(b, range=1.5)
vioplot(b, range=1.5 )

The definition of R's boxplot is (borrowing from ggplot's help on the topic):

The upper whisker extends from the hinge to the highest value that is within 1.5 * IQR of the hinge, where IQR is the inter-quartile range, or distance between the first and third quartiles.

Browsing the source code of vioplot, we see upper[i] <- min(q3[i] + range*iqd, data.max).

Therefore, let us try to reproduce the upper whisker value:

# vioplot draws
quantile(b, 0.75) + 1.5 * IQR(b)
# 16

# boxplot draws
max(b[b <= quantile(b, 0.75) + 1.5 * IQR(b)])
# 10