Example 10.1: Interpreting a Normal Q-Q Plot of Nonnormal Data

QQPLOT Statement

Example 10.1: Interpreting a Normal Q-Q Plot of Nonnormal Data

See CAPQQ2 in the SAS/QC Sample Library

The following statements produce the normal Q-Q plot in Output 10.1.1:

   data measures;
      input diameter @@;
      label diameter='Diameter in mm';
      datalines;
    5.501  5.251  5.404  5.366  5.445  5.576  5.607
    5.200  5.977  5.177  5.332  5.399  5.661  5.512
    5.252  5.404  5.739  5.525  5.160  5.410  5.823
    5.376  5.202  5.470  5.410  5.394  5.146  5.244
    5.309  5.480  5.388  5.399  5.360  5.368  5.394
    5.248  5.409  5.304  6.239  5.781  5.247  5.907
    5.208  5.143  5.304  5.603  5.164  5.209  5.475
    5.223
   ;

   title 'Normal Q-Q Plot for Diameters';
   proc capability data=measures noprint;
      qqplot diameter / normal 
                        square 
                        vaxis=axis1
                        cframe = ligr;
      axis1 label=(a=90 r=0);
   run;

Output 10.1.1: Normal Quantile-Quantile Plot of Nonnormal Data

The nonlinearity of the points in Output 10.1.1 indicates a departure from normality. Since the point pattern is curved with slope increasing from left to right, a theoretical distribution that is skewed to the right, such as a lognormal distribution, should provide a better fit than the normal distribution. The mild curvature suggests that you should examine the data with a series of lognormal Q-Q plots for small values of the shape parameter, as illustrated in the next example.

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