## Example 4.36 Creating a P-P Plot

The distances between two holes cut into 50 steel sheets are measured and 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
;
run;

It is decided to check whether the distances are normally distributed. The following statements create a P-P plot, shown in Output 4.36.1, which is based on the normal distribution with mean and standard deviation :

title 'Normal Probability-Probability Plot for Hole Distance';
ods graphics on;
proc univariate data=Sheets noprint;
ppplot Distance / normal(mu=10 sigma=0.3)
square;
run;

The NORMAL option in the PPPLOT statement requests a P-P plot based on the normal cumulative distribution function, and the MU= and SIGMA= *normal-options* specify and . Note that a P-P plot is always based on a *completely specified* distributionâ€”in other words, a distribution with specific parameters. In this example, if you did not specify the MU= and SIGMA= *normal-options*, the sample mean and sample standard deviation would be used for and .

**
Output 4.36.1
Normal P-P Plot with Diagonal Reference Line**

The linearity of the pattern in Output 4.36.1 is evidence that the measurements are normally distributed with mean 10 and standard deviation 0.3. The SQUARE option displays the plot in a square format.

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