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Sampling Random Variables: A Paradigm Shift for Opinion Polling
Volume 3, Issue 4 (2005), pp. 439–448
Gordon G. Bechtel  

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https://doi.org/10.6339/JDS.2005.03(4).214
Pub. online: 4 August 2022      Type: Research Article      Open accessOpen Access

Published
4 August 2022

Abstract

Abstract: Conventional sampling in biostatistics and economics posits an individual in a fixed observable state (e.g., diseased or not, poor or not, etc.). Social, market, and opinion research, however, require a cognitive sampling theory which recognizes that a respondent has a choice between two options (e.g., yes versus no). This new theory posits the survey re spondent as a personal probability. Once the sample is drawn, a series of independent non-identical Bernoulli trials are carried out. The outcome of each trial is a momentary binary choice governed by this unobserved proba bility. Liapunov’s extended central limit theorem (Lehmann, 1999) and the Horvitz-Thompson (1952) theorem are then brought to bear on sampling unobservables, in contrast to sampling observations. This formulation reaf firms the usefulness of a weighted sample proportion, which is now seen to estimate a different target parameter than that of conventional design-based sampling theory

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