How do I analyze survey data with a two-stage cluster with unequal probabilities design? | SAS FAQ

This example is taken from Levy and Lemeshow’s Sampling of Populations.

page 350 cluster sampling with unequal probabilities:  probability proportional to size sampling
This example uses the hospslect data set.

proc surveymeans data = hospslct n = 4672 sum mean;
  weight wstar;
  cluster drawing;
  var lifethrt dxdead;
run;

The SURVEYMEANS Procedure

            Data Summary

Number of Clusters                 5
Number of Observations            50
Sum of Weights                 50056

                               Statistics

                               Std Error
Variable            Mean         of Mean             Sum         Std Dev
------------------------------------------------------------------------
LIFETHRT        0.120000        0.019989     6006.720000     1000.584155
DXDEAD          0.040000        0.024482     2002.240000     1225.460312
------------------------------------------------------------------------

Page 353 cluster sampling with unequal probabilities:   probability proportional to size sampling

data hspslct2;
  set hospslct;
  /*n is 50*/
  /*N_i is admiss*/
  /* X is 7087, the total number of life-threating conditions across all the hospitals*/
  /*X_i is tl, the total number of life-threating conditions for each hospital*/
  if hospno = 2 then  tl = 785; 
  if hospno = 5 then  tl = 3404; 
  if hospno = 9 then  tl = 778; 
  w2star = (admiss/50)*(7087/tl);
run;

proc surveymeans data = hspslct2 n = 4672 mean sum;
  weight w2star;
  cluster drawing;
  var lifethrt dxdead;
run;

The SURVEYMEANS Procedure

            Data Summary

Number of Clusters                 5
Number of Observations            50
Sum of Weights            51344.9973

                               Statistics

                               Std Error
Variable            Mean         of Mean             Sum         Std Dev
------------------------------------------------------------------------
LIFETHRT        0.121904        0.021404     6259.175814     1276.638273
DXDEAD          0.034287        0.022991     1760.471466     1078.465840
------------------------------------------------------------------------