Example 87.3 PPS (Dollar-Unit) Sampling

A small company wants to audit employee travel expenses in an effort to improve the expense reporting procedure and possibly reduce expenses. The company does not have resources to examine all expense reports and wants to use statistical sampling to objectively select expense reports for audit.

The data set TravelExpense contains the dollar amount of all employee travel expense transactions during the past month:

   data TravelExpense;
      input ID$ Amount @@;
      if (Amount < 500) then Level='1_Low ';
         else if (Amount > 1500) then Level='3_High';
         else Level='2_Avg ';   
      datalines;
   110  237.18   002  567.89   234  118.50
   743   74.38   411 1287.23   782  258.10
   216  325.36   174  218.38   568 1670.80
   302  134.71   285 2020.70   314   47.80
   139 1183.45   775  330.54   425  780.10
   506  895.80   239  620.10   011  420.18
   672  979.66   142  810.25   738  670.85
   192  314.58   243   87.50   263 1893.40
   496  753.30   332  540.65   486 2580.35
   614  230.56   654  185.60   308  688.43
   784  505.14   017  205.48   162  650.42
   289 1348.34   691   30.50   545 2214.80
   517  940.35   382  217.85   024  142.90
   478  806.90   107  560.72
   ;

In the SAS data set TravelExpense, the variable ID identifies the travel expense report. The variable Amount contains the dollar amount of the reported expense. The variable Level equals '1_Low', '2_Avg', or '3_High', depending on the value of Amount.

In the sample design for this audit, expense reports are stratified by Level. This ensures that each of these expense levels is included in the sample and also permits a disproportionate allocation of the sample, selecting proportionately more of the expense reports from the higher levels. Within strata, the sample of expense reports is selected with probability proportional to the amount of the expense, thus giving a greater chance of selection to larger expenses. In auditing terms, this is known as monetary-unit sampling. See Wilburn (1984) for details.

PROC SURVEYSELECT requires that the input data set be sorted by the STRATA variables. The following PROC SORT statements sort the TravelExpense data set by the stratification variable Level.

   proc sort data=TravelExpense;
      by Level;
   run;

Output 87.3.1 displays the sampling frame data set TravelExpense, which contains 41 observations.

The following PROC SURVEYSELECT statements select a probability sample of expense reports from the TravelExpense data set by using the stratified design with PPS selection within strata:

   title1 'Travel Expense Audit';
   title2 'Stratified PPS (Dollar-Unit) Sampling';
   proc surveyselect data=TravelExpense
         method=pps n=(6 10 4)
         seed=47279 out=AuditSample;
      size Amount;
      strata Level;
   run;

The STRATA statement names the stratification variable Level. The SIZE statement specifies the size measure variable Amount. In the PROC SURVEYSELECT statement, the METHOD=PPS option requests sample selection with probability proportional to size and without replacement. The N=(6 10 4) option specifies the stratum sample sizes, listing the sample sizes in the same order as the strata appear in the TravelExpense data set. The sample size of 6 corresponds to the first stratum, Level = '1_Low'; the sample size of 10 corresponds to the second stratum, Level = '2_Avg'; and 4 corresponds to the last stratum, Level = '3_High'. The SEED=47279 option specifies '47279' as the initial seed for random number generation.

Output 87.3.2 displays the output from PROC SURVEYSELECT. A total of 20 expense reports are selected for audit. The data set AuditSample contains the sample of travel expense reports.