In order to improve service, the San Francisco Municipal Railway (MUNI) conducts a survey to estimated passenger’s average waiting time for MUNI’s subway system.
The study uses a stratified cluster sample design. Each MUNI subway line is a stratum. The subway lines included in the study are 'JChurch,' 'KIngleside,' 'LTaraval,' 'MOcean View,' 'NJudah,' and the street car 'FMarket & Wharves.' The MUNI vehicles in service for these lines during a day are primary sampling units. Within each stratum, two vehicles (PSUs) are randomly selected. Then the waiting times of passengers for a selected MUNI vehicle are collected.
Table 96.7 shows the number of passengers that are interviewed in each of the selected MUNI vehicles.
Table 96.7: The Sample of the MUNI Waiting Time Study
MUNI Line 
Vehicle 
Number of Passengers 

FMarket & Wharves 
1 
65 
2 
102 

JChurch 
1 
101 
2 
142 

KIngleside 
1 
145 
2 
180 

LTaraval 
1 
135 
2 
185 

MOcean View 
1 
139 
2 
203 

NJudah 
1 
306 
2 
234 
The collected data are saved in the SAS data set MUNIsurvey
. The variable Line
indicates which MUNI line a passenger is riding. The variable vehicle
identifies the vehicle that a passenger is boarding. The variable Waittime
is the time (in minutes) that a passenger waited. The variable weight
contains the sampling weights, which are determined by selection probabilities within each stratum.
Output 96.5.1 displays the first 10 observations of the data set MUNIsurvey
.
Output 96.5.1: First 10 Observations in the Data Set from the MUNI Subway Survey
MUNI Subway Passenger Waiting Time Survey Data 
Obs  line  vehicle  passenger  waittime  weight 

1  FMarket & Wharves  1  1  18  59 
2  FMarket & Wharves  1  2  0  59 
3  FMarket & Wharves  1  3  16  59 
4  FMarket & Wharves  1  4  13  59 
5  FMarket & Wharves  1  5  5  59 
6  FMarket & Wharves  1  6  13  59 
7  FMarket & Wharves  1  7  7  59 
8  FMarket & Wharves  1  8  5  59 
9  FMarket & Wharves  1  9  16  59 
10  FMarket & Wharves  1  10  5  59 
Using the VARMETHOD=BRR option, the following SAS statements analyze the MUNI subway survey by using the BRR method to estimate the variance:
title 'MUNI Passenger Waiting Time Analysis Using BRR'; proc surveymeans data=MUNIsurvey mean varmethod=brr mean clm; strata line; cluster vehicle; var waittime; weight weight; run;
The STRATUM variable is line
, which corresponds to MUNI lines. The two clusters within each stratum are identified by the variable vehicle
. The sampling weights are stored in the variable weight
. The mean and confident limits for passenger waiting time (in minutes) are requested statistics.
Output 96.5.2 summarizes the data and indicates that the variance estimation method is BRR with 8 replicates.
Output 96.5.2: MUNI Passenger Waiting Time Analysis Using the BRR Method
MUNI Passenger Waiting Time Analysis Using BRR 
Data Summary  

Number of Strata  6 
Number of Clusters  12 
Number of Observations  1937 
Sum of Weights  143040 
Variance Estimation  

Method  BRR 
Number of Replicates  8 
Output 96.5.3 reports that the average passenger waiting time for a MUNI vehicle is 7.33 minutes, with an estimated standard of 0.24 minutes, using the BRR method. The 95% confident limits for the mean are estimated as 6.75 to 7.91 minutes.
Output 96.5.3: MUNI Passenger Waiting Time Analysis Using the BRR Method
Statistics  

Variable  Mean  Std Error of Mean  95% CL for Mean  
waittime  7.333012  0.237557  6.75172983  7.91429366 
Alternatively, the variance can be estimated using the jackknife method if the VARMETHOD=JACKKNIFE option is used. The following SAS statements analyze the MUNI subway survey by using the jackknife method to estimate the variance:
title 'MUNI Passenger Waiting Time Analysis Using Jackknife'; proc surveymeans data=MUNIsurvey mean varmethod=jackknife mean clm; strata line; cluster vehicle; var waittime; weight weight; run;
Output 96.5.4 summarizes the data and indicates that the variance estimation method is jackknife with 12 replicates.
Output 96.5.4: MUNI Passenger Waiting Time Analysis Using the Jackknife Method
MUNI Passenger Waiting Time Analysis Using Jackknife 
Data Summary  

Number of Strata  6 
Number of Clusters  12 
Number of Observations  1937 
Sum of Weights  143040 
Variance Estimation  

Method  Jackknife 
Number of Replicates  12 
Output 96.5.5 reports the statistics computed using the jackknife method. Although the average passenger waiting time remains the same (7.33 minutes), the standard error is slightly smaller 0.23 minutes when the jackknife method is used, as opposed to 0.24 minutes when the BRR method is used. The 95% confidence limits are between 6.76 and 7.90 minutes when the jackknife method is used.
Output 96.5.5: MUNI Passenger Waiting Time Analysis Using the Jackknife Method
Statistics  

Variable  Mean  Std Error of Mean  95% CL for Mean  
waittime  7.333012  0.232211  6.76481105  7.90121244 