Unrestricted Random Sampling

The method of unrestricted random sampling (METHOD=URS) selects units with equal probability and with replacement. Because units are selected with replacement, a unit can be selected for the sample more than once. The expected number of selections or hits for each unit equals when sampling without stratification. For stratified sampling, the expected number of hits for a unit in stratum equals . Note that the expected number of hits exceeds one when the sample size is greater than the population size .

For unrestricted random sampling, by default, the output data set contains one observation for each distinct unit selected for the sample, together with a variable NumberHits that gives the number of times the observation was selected. But if you specify the OUTHITS option, then the output data set contains a separate observation for each selection, so that a unit selected three times, for example, is represented by three observations in the output data set. For information about the contents of the output data set, see the section Sample Output Data Set.