Example 86.5 Variance Estimation Using Replication Methods

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 'J-Church,' 'K-Ingleside,' 'L-Taraval,' 'M-Ocean View,' 'N-Judah,' and the street car 'F-Market & 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 86.5 shows the number of passengers that are interviewed in each of the selected MUNI vehicles.

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 86.5.1 displays the first 10 observations of the data set MUNIsurvey.

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 of passenger waiting time (in minutes) are requested statistics.

Output 86.5.2 summarizes the data and indicates that the variance estimation method is BRR with 8 replicates.

Output 86.5.3 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.

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 86.5.4 summarizes the data and indicates that the variance estimation method is jackknife with 12 replicates.

Output 86.5.5 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.