What defines the independence of selection in a random sample?

Independence of selection in a random sample is defined by the idea that each selection does not affect other selections. This means that the outcome of one selection is completely unrelated to the outcomes of previous or future selections. In a process where selections are independent, knowing the result of one selection gives no information about the others. This characteristic is fundamental to the concept of random sampling, as it ensures that each sample drawn from a population is representative and that the probability of selecting any particular item remains constant for each selection.

In contrast, if each selection were to affect the next, it would indicate a dependence that can introduce bias and skew the results, rendering the sample unrepresentative of the population. Similarly, selecting from different populations (rather than a single population) or requiring all selections to be made at once would disrupt the underlying principles of individual randomness and independence, potentially compromising the validity of the sampling method. Hence, the correct definition of independence in this context is that each selection does not affect other selections.