Bootstrap confidence intervals for the median

Grammar of graphics plots provide a simple way of adding confidence intervals for the mean to any boxplot. Let's set up some grouped data.

d <- data.frame(group = rep(c("A", "B", "C", "D"), each = 100), mean = rep(c(10, 
    12, 15, 20), each = 100))
d$value <- d$mean + rnorm(400, 0, 5)

Standard box plot

library(ggplot2)
library(boot)
g0 <- ggplot(d, aes(x = group, y = value))
g_box <- g0 + geom_boxplot(fill = "grey", colour = "black") + theme_bw()
g_box

Boxplot with confidence intervals for the mean added.

g_box <- g_box + stat_summary(fun.data = mean_cl_boot, geom = "errorbar", colour = "red") + 
    stat_summary(fun.y = mean, geom = "point", colour = "red")
g_box

It is possible to add some text to display the value of the mean.

g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = mean, geom = "text", 
    size = 6, col = "red")
g_box

More can be added

g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = function(x) quantile(x, 
    0.75), geom = "text", size = 4, vjust = -1)
g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = function(x) quantile(x, 
    0.25), geom = "text", size = 4, vjust = 2)
g_box

Confidence intervals for the median

One way of adding approximate confidence intervals is to use notch=TRUE.

g_box <- g0 + geom_boxplot(fill = "grey", colour = "black", notch = TRUE) + 
    theme_bw()
g_box

Bootstrapping the median

We need a function that returns a data frame in the same format as mean_cl_boot.

median_cl_boot <- function(x, conf = 0.95) {
    lconf <- (1 - conf)/2
    uconf <- 1 - lconf
    require(boot)
    bmedian <- function(x, ind) median(x[ind])
    bt <- boot(x, bmedian, 1000)
    bb <- boot.ci(bt, type = "perc")
    data.frame(y = median(x), ymin = quantile(bt$t, lconf), ymax = quantile(bt$t, 
        uconf))
}

Now we can add the bootstrapped confidence intervals for the median in the same way.

g_box <- g_box + stat_summary(fun.data = median_cl_boot, geom = "errorbar", 
    colour = "red") + stat_summary(fun.y = median, geom = "point", colour = "red")
g_box

The values for the median can also be added as text.

g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = median, 
    geom = "text", size = 4, vjust = -0.5)
g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = function(x) quantile(x, 
    0.75), geom = "text", size = 4, vjust = -1)
g_box <- g_box + stat_summary(aes(label = round(..y.., 1)), fun.y = function(x) quantile(x, 
    0.25), geom = "text", size = 4, vjust = 2)
g_box

Changing the confidence interval.

g_box + stat_summary(fun.data = median_cl_boot, conf = 0.99, geom = "errorbar", 
    colour = "blue")