Independent random sample
The term “independent” has a different meaning for sample selection than in the context of variables. Independent sample (see also random selection means simply that selecting one sampling element has no influence on the selection of another sampling element. A counter-example of a non-independent selection would be if one selects one element at random and then takes the neighbor to that element as next sample; this is clearly not independent. Also in systematic sampling or cluster sampling the selection of elements or sampling locations is not independent. Independence of sample selection is achieved by randomization for each and every sampling element.
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