This example, which is a continuation of Example 4.9, illustrates how to compute confidence limits for quantiles and percentiles. A second researcher is more interested in summarizing the heights with quantiles than the mean and standard deviation. He is also interested in computing 90% confidence intervals for the quantiles. The following statements produce estimated quantiles and confidence limits for the population quantiles:
title 'Analysis of Female Heights'; ods select Quantiles; proc univariate data=Heights ciquantnormal(alpha=.1); var Height; run;
The ODS SELECT statement restricts the output to the “Quantiles” table; see the section ODS Table Names. The CIQUANTNORMAL option produces confidence limits for the quantiles. As noted in Output 4.10.1, these limits assume that the data are normally distributed. You should check this assumption before using these confidence limits. See the section ShapiroWilk Statistic for information about the ShapiroWilk test for normality in PROC UNIVARIATE; see Example 4.19 for an example that uses the test for normality.
Output 4.10.1: NormalBased Quantile Confidence Limits
Analysis of Female Heights 
Quantiles (Definition 5)  

Quantile  Estimate  90% Confidence Limits Assuming Normality 

100% Max  70.0  
99%  70.0  68.94553  70.58228 
95%  68.6  67.59184  68.89311 
90%  67.5  66.85981  68.00273 
75% Q3  66.0  65.60757  66.54262 
50% Median  64.4  64.14564  64.98770 
25% Q1  63.1  62.59071  63.52576 
10%  61.6  61.13060  62.27352 
5%  60.6  60.24022  61.54149 
1%  60.0  58.55106  60.18781 
0% Min  60.0 
It is also possible to use PROC UNIVARIATE to compute confidence limits for quantiles without assuming normality. The following statements use the CIQUANTDF option to request distributionfree confidence limits for the quantiles of the population of heights:
title 'Analysis of Female Heights'; ods select Quantiles; proc univariate data=Heights ciquantdf(alpha=.1); var Height; run;
The distributionfree confidence limits are shown in Output 4.10.2.
Output 4.10.2: DistributionFree Quantile Confidence Limits
Analysis of Female Heights 
Quantiles (Definition 5)  

Quantile  Estimate  Order Statistics  
90% Confidence Limits Distribution Free 
LCL Rank  UCL Rank  Coverage  
100% Max  70.0  
99%  70.0  68.6  70.0  73  75  48.97 
95%  68.6  67.5  70.0  68  75  94.50 
90%  67.5  66.6  68.6  63  72  91.53 
75% Q3  66.0  65.7  66.6  50  63  91.77 
50% Median  64.4  64.1  65.1  31  46  91.54 
25% Q1  63.1  62.7  63.7  13  26  91.77 
10%  61.6  60.6  62.7  4  13  91.53 
5%  60.6  60.0  61.6  1  8  94.50 
1%  60.0  60.0  60.5  1  3  48.97 
0% Min  60.0 
The table in Output 4.10.2 includes the ranks from which the confidence limits are computed. For more information about how these confidence limits are calculated, see the section Confidence Limits for Percentiles. Note that confidence limits for quantiles are not produced when the WEIGHT statement is used.
A sample program for this example, uniex07.sas, is available in the SAS Sample Library for Base SAS software.