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When data for a variable are gathered from a finite population and that variable is regarded to be a random variable, then the finite population is referred to as being “a realization from a superpopulation.” A superpopulation is the infinite population that elementary statistical textbooks often describe as part of the enumeration of a finite population. It is because sampling theory is based on making inference for a well-defined finite population that the concept of superpopulation is needed to differentiate between a finite population and an infinite superpopulation.

This distinction is important for two reasons: (1) Sampling theory estimation and inference can be based entirely on a finite population (in the absence of nonsampling errors), with no recourse to a superpopulation; and (2) even when ...

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