On statistical inference in sample surveys and the underlying role of randomization
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Assuming only the existence of a universe and a frame that identifies its members (ultimate sampling units), and a minimum number of necessary but nonrestrictive assumptions, the writer derives a basic proposition which shows that for sample surveys any form of inference about any universe characteristic must depend on the sampling distribution of estimates generated by randomization, and, by direct implication, the sampling design. Unbiasedness is validated by this proposition, but likelihood appears to be in conflict with it, and by implication with randomization. The relation between high or low variance and correspondingly low or high probability for an estimator is also investigated in the paper. Finally it is argued that restrictions on randomization may be injurious to normality.
KeywordsSampling Design Statistical Inference Sample Survey Finite Population Distinct Sample
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