sampled and completely measured strata. If a stratum for the largest units is required 

 to satisfy the above inequality, all the units assigned to this stratum can be given a 

 sampling probability of exactly unity. Thus, the estimated population total can be 

 seen to be the sum of the estimated total for all the sampled stratum plus the total of 

 the stratum of excessively large units. 



To provide the proper elements for the variance estimate based on the units in the 

 sampled stratum, PPSORT returns values of the total size of the sampled stratum and the 

 number of units selected from it for measurement along with their identification and 

 probability of inclusion. Certain other values depending on the distribution of the 

 inclusion probabilities over the entire population are also saved by PPSORT for later 

 use in calculating the variance estimate. 



CALLING PPSORT 



To use PPSORT, a computer program would be prepared that enters the data describing 

 the entire population, calls PPSORT, and then displays the identification and sampling 

 probabilities for each member of the sample drawn by PPSORT, and the values required 

 for the subsequent variance estimate. A simple version of such a program with test 

 data that can be used to verify the functioning of the PPSORT program is provided in 

 appendix II. Three random odd integers must be assigned to the variables KR, LR, and 

 MR to start the pseudorandom number generator used in PPSORT (Marsaglia and Bray 1968) . 



The subroutine is executed by the statement 



CALL PPSORT (NP,ID,CHAR,NSAM,IDSAM,PP,TX,TS,TP,NRS,N,LR,MR,KR) 



in which the first four and the last three arguments of the calling sequence are estab- 

 lished prior to the execution of the CALL statement. 



NP contains the number of units in the population. (If NP exceeds 498, 

 the DIMENSION statement in the PPSORT program should be changed 

 accordingly.) 



ID is a vector of NP elements identifying the units of the population. 



CHAR is a vector of NP elements containing the sizes of the units of the 

 population corresponding to the same sequence as the ID vector. 



NSAM contains the number of units to be measured (sample units plus those 

 that may be designated for measurement with absolute certainty). 



The intervening seven arguments contain information about the sampling as it was 

 accomplished by PPSORT. 



IDSAM is a vector of NSAM elements containing the values copied from the ID 

 vector for only those units selected for measurement. 



PP is a vector of NSAM elements containing the value of the probability 

 with which each unit was selected for measurement. Their sequence is 

 the same as the sequence of ID's in IDSAM. (PP(I) = P.) 



2 



