Here is how Hamilton and Cleveland frame their use of the qq plots.

Lawrence Hamilton's book stresses analytical graphics. In the intro he states, “Regression
summarizes (or models)complex data in a compact way...” and then, with respect to graphics,
he says, “...Graphs are not compact: if they are 'worth a thousand words,' we cannot easily
describe or compare them. Graphs show data rather than summarize them.” Hamilton's first
chapter presents the exploratory tools and graphical tools,

mean+variance -> normal distribution -> median+interquartile -> boxplot
-> symmetry plots -> quantile plots -> quantile-quantile -> quantile normal

Lawrence's theme is a restatement of Tukey's exploratory data analysis.

For the quantile plot Lawrence places the fraction of data, 0 to 1, on the x axis, and quartiles on
the y-axis. For the qq plots he plots observations on both the x-axis and y-axis. He notes that
qq plots are for comparing two empirical distributions or for comparing an empirical distribution
against a theoretical distribution. For qn, quantile-normal plots (aka quantile probability plots), he
plots quantiles on the vertical axis “against the corresponding quantiles of a theoretical Gaussian
(normal) distribution with the same mean and standard deviation).

Cleveland refers to the goal of comparing to distributions, “usually to rank the categories according
to how much each has of the variable being measured.” His example plots male verbal SAT on one
axis, female verbal SAT scores on the other. Next to that qq plot he also provides a Tukey mean-
difference plot showing mean on the horizontal and difference on the vertical.

peter schrieb:
  

Two references that may be some help,

William Cleveland, The Elements of Graphing Data, Hobart Press, NJ, pgs
143  to 149
Lawrence C Hamilton, Regression with Graphics, Duxbury Press, CA, pgs 11
through 17

    

Peter, could you summarize their argument? Most of us will not have
access to these.

thanks,
sven

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