Normal Plot

The normal plot is a graphical procedure used to assess normality. It is provided by proc univariate when the plot option is specified. Unfortunately, as produced by proc univariate, this plot is not really usable since it is hard to read.

Fortunately, we do not have to rely on proc univariate. A readable normal plot may be quite easily produced from scratch by using proc rank in conjunction with proc plot.

The following code produces a normal plot for the variable "time". Notice that two options have been specified, normal=blom and out=new2. The first option tells proc rank to use a procedure developed by the statistician Blom to produce normal scores (i.e. z-values). The second option specifies the name of a dataset which will contain all the original data plus a new variable called nscores. This is the variable which will contain normal scores for the variable "time".

proc rank computes z-values (i.e. normal scores) for the values of "time" but it bases its computation on the ranks of these values. Statistical theory tells us that if a set of values are drawn from a normal population we can estimate the z-scores if we know their ranks. This is the theory being applied here. Hence, if the values of "time" are drawn from a normal population we should expect a straight line when we plot these values against their estimated normal scores. We use proc plot to produce this plot.

A plot that is nearly linear suggests agreement with normality, whereas a plot that departs substantially from linearity suggests that the values are not drawn from a normal distribution.

Code:

proc rank normal=blom out=new2;
 var time;
 ranks nscores;
proc plot;
 plot time*nscores='*';
 label nscores='Normal Scores';

                Plot of TIME*NSCORES.  Symbol used is '*'.

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         ---+-------------+-------------+-------------+-------------+--
           -2            -1             0             1             2

                                  Normal Scores