## Construction of Quantile-Quantile and Probability Plots

Figure 10.6 illustrates how a Q-Q plot is constructed.
First, the *n* nonmissing values of the variable are ordered from
smallest to largest:

`
`

Then
the *i*^{ th} ordered value *x*_{(i)} is represented on the plot
by a point whose *y*-coordinate is *x*_{(i)} and whose
*x*-coordinate is *F*^{-1}( [(*i*- 0.375 )/(*n* + 0.25)] ),
where *F*(·) is the theoretical distribution
with zero location parameter
and unit scale parameter.

**Figure 10.6:** Construction of a Q-Q Plot

You can modify the adjustment constants -0.375 and 0.25
with the RANKADJ= and NADJ= options.
This default combination is recommended by Blom (1958).
For additional information, refer to
Chambers and others (1983).
Since *x*_{(i)} is a quantile of the
empirical cumulative distribution function (ecdf),
a Q-Q plot compares quantiles of the ecdf with quantiles
of a theoretical distribution.
Probability plots (see Chapter 9, "PROBPLOT Statement")
are constructed the same way, except that the *x*-axis
is scaled nonlinearly in percentiles.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.