Differing quantiles: Boxplot vs. Violinplot

Question

require(ggplot2)
require(cowplot)
d = iris

ggplot2::ggplot(d, aes(factor(0), Sepal.Length)) + 
    geom_violin(fill="black", alpha=0.2, draw_quantiles = c(0.25, 0.5, 0.75)
                , colour = "red", size = 1.5) +
    stat_boxplot(geom ='errorbar', width = 0.1)+
    geom_boxplot(width = 0.2)+
    facet_grid(. ~ Species, scales = "free_x") +
    xlab("") + 
    ylab (expression(paste("Value"))) +
    coord_cartesian(ylim = c(3.5,9.5)) + 
    scale_y_continuous(breaks = seq(4, 9, 1)) + 
    theme(axis.text.x=element_blank(),
          axis.text.y = element_text(size = rel(1.5)),
          axis.ticks.x = element_blank(),
          strip.background=element_rect(fill="black"),
          strip.text=element_text(color="white", face="bold"),
          legend.position = "none") +
    background_grid(major = "xy", minor = "none")

To my knowledge box ends in boxplots represent the 25% and 75% quantile, respectively, and the median = 50%. So they should be equal to the 0.25/0.5/0.75 quantiles which are drawn by geom_violin in the draw_quantiles = c(0.25, 0.5, 0.75) argument.

Median and 50% quantile fit. However, both 0.25 and 0.75 quantile do not fit the box ends of the boxplot (see figure, especially 'virginica' facet).

References:

user_570918 · Answer

The second factor that @coffeinjunky raised seems to be the main cause. Here is some more evidence to bolster that.

By switching to geom_ydensity, one can empirically confirm that the difference is due to the geom_violin using the kernel density estimate to compute the quantiles, rather than the actual observations. For example, if we force a wide bandwidth (bw=1), then the estimated densities will be over-smoothed and deviate further from the observation-based quantiles used in the boxplots:

require(ggplot2)
require(cowplot)

theme_set(cowplot::theme_cowplot())

d = iris

ggplot2::ggplot(d, aes(factor(0), Sepal.Length)) + 
  stat_ydensity(bw=1, fill="black", alpha=0.2, draw_quantiles = c(0.25, 0.5, 0.75)
              , colour = "red", size = 1.5) +
  stat_boxplot(geom ='errorbar', width = 0.1)+
  geom_boxplot(width = 0.2)+
  facet_grid(. ~ Species, scales = "free_x") +
  xlab("") + 
  ylab (expression(paste("Value"))) +
  coord_cartesian(ylim = c(3.5,9.5)) + 
  scale_y_continuous(breaks = seq(4, 9, 1)) + 
  theme(axis.text.x=element_blank(),
        axis.text.y = element_text(size = rel(1.5)),
        axis.ticks.x = element_blank(),
        strip.background=element_rect(fill="black"),
        strip.text=element_text(color="white", face="bold"),
        legend.position = "none") +
  background_grid(major = "xy", minor = "none")

enter image description here

So, yes, be careful with this one - the parameters of the density estimation can impact the results!

Differing quantiles: Boxplot vs. Violinplot

2 Answers