Independent random sample
From AWF-Wiki
General information
The term “independent” has a different meaning for sample selection than in the context of variables. Independent sample means simply that selecting one sampling element does nothing have to do with 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. Independence of sample selection is achieved by randomization for each and every sampling element.