# PROC CAPABILITY and General Statements

#### Computing Descriptive Statistics

See CAPPROC in the SAS/QC Sample LibraryThe fluid weights of 100 drink cans are measured in ounces. The filling process is assumed to be in statistical control. The measurements are saved in a SAS data set named `Cans`.

```data Cans;
label Weight = "Fluid Weight (ounces)";
input Weight @@;
datalines;
12.07  12.02  12.00  12.01  11.98  11.96  12.04  12.05  12.01  11.97
12.03  12.03  12.00  12.04  11.96  12.02  12.06  12.00  12.02  11.91
12.05  11.98  11.91  12.01  12.06  12.02  12.05  11.90  12.07  11.98
12.02  12.11  12.00  11.99  11.95  11.98  12.05  12.00  12.10  12.04
12.06  12.04  11.99  12.06  11.99  12.07  11.96  11.97  12.00  11.97
12.09  11.99  11.95  11.99  11.99  11.96  11.94  12.03  12.09  12.03
11.99  12.00  12.05  12.04  12.05  12.01  11.97  11.93  12.00  11.97
12.13  12.07  12.00  11.96  11.99  11.97  12.05  11.94  11.99  12.02
11.95  11.99  11.91  12.06  12.03  12.06  12.05  12.04  12.03  11.98
12.05  12.05  12.11  11.96  12.00  11.96  11.96  12.00  12.01  11.98
;

```

You can use the PROC CAPABILITY and VAR statements to compute summary statistics for the weights.

```title 'Process Capability Analysis of Fluid Weight';
proc capability data=Cans normaltest;
var Weight;
run;
```

The input data set is specified with the DATA= option. The NORMALTEST option requests tests for normality. The VAR statement specifies the variables to analyze. If you omit the VAR statement, all numeric variables in the input data set are analyzed.

The descriptive statistics[7] for `Weight` are shown in Figure 5.1. For instance, the average weight (labeled Mean) is 12.0093. The Shapiro-Wilk test statistic labeled W is 0.987876, and the probability of a more extreme value of W (labeled Pr < W) is 0.499. Compared to the usual cutoff value of 0.05, this probability (referred to as a p-value) indicates that the weights are normally distributed.

Figure 5.1: Descriptive Statistics

 Process Capability Analysis of Fluid Weight

The CAPABILITY Procedure
Variable: Weight (Fluid Weight (ounces))

Moments
N 100 Sum Weights 100
Mean 12.0093 Sum Observations 1200.93
Std Deviation 0.04695269 Variance 0.00220456
Skewness 0.05928405 Kurtosis -0.1717404
Uncorrected SS 14422.5469 Corrected SS 0.218251
Coeff Variation 0.39096946 Std Error Mean 0.00469527

Basic Statistical Measures
Location Variability
Mean 12.00930 Std Deviation 0.04695
Median 12.00000 Variance 0.00220
Mode 12.00000 Range 0.23000
Interquartile Range 0.07000

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 2557.745 Pr > |t| <.0001
Sign M 50 Pr >= |M| <.0001
Signed Rank S 2525 Pr >= |S| <.0001

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.987876 Pr < W 0.4991
Kolmogorov-Smirnov D 0.088506 Pr > D 0.0522
Cramer-von Mises W-Sq 0.079055 Pr > W-Sq 0.2179
Anderson-Darling A-Sq 0.457672 Pr > A-Sq >0.2500

Quantiles (Definition 5)
Quantile Estimate
100% Max 12.130
99% 12.120
95% 12.090
90% 12.065
75% Q3 12.050
50% Median 12.000
25% Q1 11.980
10% 11.955
5% 11.935
1% 11.905
0% Min 11.900

Extreme Observations
Lowest Highest
Value Obs Value Obs
11.90 28 12.09 59
11.91 83 12.10 39
11.91 23 12.11 32
11.91 20 12.11 93
11.93 68 12.13 71

[7] In SAS 7, the Moments table was reorganized. Tables for Basic Statistical Measures, Tests for Location, and Tests for Normality have been added.