Computing Statistical Intervals

INTERVALS Statement

Computing Statistical Intervals

See CAPINT1 in the SAS/QC Sample Library

The following statements create the data set CANS, which contains measurements (in ounces) of the fluid weights of 100 drink cans. The filling process is assumed to be in statistical control.

   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
   ;

Note that this data set is introduced in "Computing Descriptive Statistics" of Chapter 1, "PROC CAPABILITY and General Statements." The analysis in that section provides evidence that the weight measurements are normally distributed.

By default, the INTERVALS statement computes and prints the six intervals described in the entry for the METHODS= option. The following statements tabulate these intervals for the variable WEIGHT:

   title 'Statistical Intervals for Fluid Weight';
   proc capability data=cans noprint;
      intervals weight;
   run;

The intervals are displayed in Figure 6.1.

Statistical Intervals for Fluid Weight

The CAPABILITY Procedure

Two-Sided Statistical Intervals for weight Assuming Normality

Approximate Prediction Interval Containing All of k Future Observations
Confidence	k	Prediction Limits
99.00%	1	11.89	12.13
99.00%	2	11.87	12.14
99.00%	3	11.87	12.15
95.00%	1	11.92	12.10
95.00%	2	11.90	12.12
95.00%	3	11.89	12.12
90.00%	1	11.93	12.09
90.00%	2	11.92	12.10
90.00%	3	11.91	12.11

Approximate Prediction Interval Containing the Mean of k Future Observations
Confidence	k	Prediction Limits
99.00%	1	11.89	12.13
99.00%	2	11.92	12.10
99.00%	3	11.94	12.08
95.00%	1	11.92	12.10
95.00%	2	11.94	12.08
95.00%	3	11.95	12.06
90.00%	1	11.93	12.09
90.00%	2	11.95	12.06
90.00%	3	11.96	12.05

Approximate Tolerance Interval Containing At Least Proportion p of the Population
Confidence	p	Tolerance Limits
99.00%	0.900	11.92	12.10
99.00%	0.950	11.90	12.12
99.00%	0.990	11.86	12.15
95.00%	0.900	11.92	12.10
95.00%	0.950	11.90	12.11
95.00%	0.990	11.87	12.15
90.00%	0.900	11.92	12.09
90.00%	0.950	11.91	12.11
90.00%	0.990	11.88	12.14

Figure 6.1: Statistical Intervals for WEIGHT

The CAPABILITY Procedure

Two-Sided Statistical Intervals for weight Assuming Normality

Confidence Limits Containing the Mean
Confidence	Confidence Limits
99.00%	11.997	12.022
95.00%	12.000	12.019
90.00%	12.002	12.017

Prediction Interval Containing the Standard Deviation of k Future Observations
Confidence	k	Prediction Limits
99.00%	2	0.0003	0.1348
99.00%	3	0.0033	0.1110
95.00%	2	0.0015	0.1069
95.00%	3	0.0075	0.0919
90.00%	2	0.0030	0.0932
90.00%	3	0.0106	0.0825

Confidence Limits Containing the Standard Deviation
Confidence	Confidence Limits
99.00%	0.040	0.057
95.00%	0.041	0.055
90.00%	0.042	0.053

Figure 6.2: Statistical Intervals for WEIGHT

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