Diagnostic plots
Quantile-Quantile plots (Q'Q plots)
(Theoretical) Q'Q Plots

This type of diagnostic tools plots quantiles (fractiles) of an empirical distribution against the corresponding quantiles of a theoretical distribution, frequently the normal distribution (in this case the Q'Q-plots are often called "Normal probability plot").

Empirical Q'Q plots

Plots quantiles of two empirical distributions.

Other diagnostic plots
Symmetry plots
Spread-and-Level plot (package car)

There is also a similar spread.level.plot function in package LearnEDA.

Program your own symmetry plots
Example 1

In the programming envrionment provided by R, it is not very difficult to build your own diagnostic graphics. Let us first look at the R code of a symmetry diagnostic proposed by Ross Ihaka,

symplot1= function(x) 
    { n=length(x)
      n2=n %/% 2
      sx = sort(x)
      mx = median(x)
      plot(mx-sx[1:n2], rev(sx)[1:n2]-mx,
      xlab="Distance below median",   ylab="Distance above median")

By the way this code is not very different form the code of the symplot function from the LearnEDA (You can see the code of functions programmed in S, by simply typing the name of the function, without parentheses, and the code is displayed.

Example 2

A second example produces a symmetry plot where you plot on y the sorted variable of interest and the corresponding fractions on x. You will get a nicely linear trend if the observations are regularly spaced over the whole range from the mimimum and the maximum.

n = length(gnpserv)
plot((1:n - 1)/(n - 1), sort(gnpserv), type="l",
main = "Quantiles of variable gnpserv",
xlab = "Fractions", ylab = " Quantiles")
Example 3

Symmetry plot where you plot the sorted x values the following way: (x1,xn:), (x2,xn-1:), (x3,xn-2:),...

plot(sort(x)[1:ceiling(length(x)/2)],sort(x,decreasing = TRUE)[1:ceiling(length(x)/2)])