Question

In R, how to use ellipses to represent error bars (standard deviation) for x and y variables if only summary data, i.e. mean and SD for different data sets, are available. Any feedback is appreciated.

Answer 1

You can write your own function like this one:

draw_ellipse = function (mean_x, mean_y, sd_x, sd_y)
{
    ellipse <- function (x) { sin(acos(x)) }
    t = seq(-1, 1, length.out = 100)
    el_y = sd_y*ellipse(t)
    newx = mean_x + sd_x * t
    polygon(c(newx, rev(newx)), c(mean_y + el_y, rev(mean_y - el_y)), col = "grey", border = NA)
}

You can use it very easily using apply():

x = runif(10)
y = runif(10)
sd_x = abs(rnorm(10, 0.1, 0.02))
sd_y = abs(rnorm(10, 0.05, 0.01))
plot(x, y)
df = data.frame(x, y, sd_x, sd_y)
apply(df, 1, function (x) { draw_ellipse(x[1], x[2], x[3], x[4]) })
points(x, y, pch = 3)

Solution for plotting ellipses with different colors:

draw_ellipse = function (mean_x, mean_y, sd_x, sd_y, colidx)
{
    ellipse <- function (x) { sin(acos(x)) }
    t = seq(-1, 1, length.out = 100)
    el_y = sd_y*ellipse(t)
    newx = mean_x + sd_x * t
    polygon(c(newx, rev(newx)), c(mean_y + el_y, rev(mean_y - el_y)), col = as.character(colors[colidx]), border = NA)
}

x = runif(10)
y = runif(10)
sd_x = abs(rnorm(10, 0.1, 0.02))
sd_y = abs(rnorm(10, 0.05, 0.01))
plot(x, y)
colors = rainbow(length(x))
df = data.frame(x, y, sd_x, sd_y, colidx = 1:length(x))
apply(df, 1, function (x) { draw_ellipse(x[1], x[2], x[3], x["sd_y"], x["colidx"]) })
points(x, y, pch = 3)