Creating a Normal Quantile-Quantile Plot

QQPLOT Statement

Creating a Normal Quantile-Quantile Plot

See CAPQQ1 in the SAS/QC Sample Library

Measurements of the distance between two holes cut into 50 steel sheets are saved as values of the variable DISTANCE in the following data set:

   data sheets;
      input distance @@;
      label distance='Hole Distance in cm';
      datalines;
    9.80 10.20 10.27  9.70  9.76
   10.11 10.24 10.20 10.24  9.63
    9.99  9.78 10.10 10.21 10.00
    9.96  9.79 10.08  9.79 10.06
   10.10  9.95  9.84 10.11  9.93
   10.56 10.47  9.42 10.44 10.16
   10.11 10.36  9.94  9.77  9.36
    9.89  9.62 10.05  9.72  9.82
    9.99 10.16 10.58 10.70  9.54
   10.31 10.07 10.33  9.98 10.15
   ;

The cutting process is in control, and you decide to check whether the process distribution is normal. The following statements create a Q-Q plot for DISTANCE, shown in Figure 10.1, with lower and upper specification lines at 9.5 cm and 10.5 cm:^*

   title 'Normal Quantile-Quantile Plot for Hole Distance';
   legend1 frame cframe=ligr cborder=black position=center;
   proc capability data=sheets noprint;
      spec lsl=9.5   clsl=red
           usl=10.5  cusl=blue;
      qqplot distance / cframe = ligr
                        legend = legend1;
   run;

The plot compares the ordered values of DISTANCE with quantiles of the normal distribution. The linearity of the point pattern indicates that the measurements are normally distributed. Note that a normal Q-Q plot is created by default. If you specify the LINEPRINTER option in the PROC CAPABILITY statement, the plot is created using a line printer, as shown in Figure 10.2. The specification lines are requested with the LSL= and USL= options in the SPEC statement.

Figure 10.1: Normal Quantile-Quantile Plot Created with Graphics Device

Normal Quantile-Quantile Plot for Hole Distance

          -------------------------------------------------------------------   
 H 10.75 +                                                                   |  
 o       |                                                          +        |  
 l       |                                                   + +             |  
 e 10.50 +UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU+UUUUUUUUUUUUUUUUU|  
         |                                                +                  |  
 D       |                                            +++                    |  
 i 10.25 +                                         +++                       |  
 s       |                                      +++                          |  
 t       |                                 +++++                             |  
 a 10.00 +                              +++                                  |  
 n       |                            ++                                     |  
 c       |                          ++                                       |  
 e  9.75 +                     +++++                                         |  
         |                  + +                                              |  
 i       |                 +                                                 |  
 n  9.50 +LLLLLLLLLLLLLLL+LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL|  
         |             +                                                     |  
 c       |        +                                                          |  
 m  9.25 +                                                                   |  
          +----------+----------+----------+----------+----------+----------+   
         -3         -2         -1          0          1          2          3   
                                                                                
                                   Normal Quantiles                             
                                                                                
 Specifications:   LLL Lower = 9.5    UUU Upper = 10.5                          
 Observations:     +   (13 Hidden)

Figure 10.2: Normal Quantile-Quantile Plot Created with Line Printer

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