List sampling
If sampling with unequal selection probabilities is indicated, the probabilities need to be determined for each element before sampling can start. If a size variable is available, the selection probabilities can be calculated proportional to size. This is then called PPS sampling (probability proportional to size).
Table 1. Listed sampling frame as used for „list sampling” where the selection probability is determined proportional to size.
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This sampling approach is also called list sampling because the selection can most easily be explained by listing the size variables and select from the cumulative sum with uniformly distributed random numbers (which perfectly simulates the unequal probability selection process). This is illustrated in Table 1: the size variables of the 5 elements are listed (not necessarily any order!) and the cumulative sums are calculated. The uniformly distributed random number is drawn between the lowest and highest possible value of that range, that is from 0 to the total sum. Assume, for example, the random number 111.11 is drawn; this falls into the range “>60 – 120” so that element 4 is selected. Obviously, the elements have then a selection probability proportional to the size variable.
