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Wednesday, July 2, 2008

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Thursday, December 6, 2007

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Successful statistical practice is based on focused problem definition. Typically, we seek to take action on some population, for example when a batch of material from production must be released to the customer or sentenced for scrap or rework.
Alternatively, we seek knowledge about the cause system of which the population is an outcome, for example when a researcher performs an experiment on rats with the intention of gaining insights into biochemistry that can be applied for the benefit of humans. In the latter case, the population of concern can be difficult to specify, as it is in the case of measuring some physical characteristic such as the electrical conductivity of copper.
However, in all cases, time spent in making the population of concern precise is often well spent, often because it raises many issues, ambiguities and questions that would otherwise have been overlooked at this stage.In the most straightforward case, such as the sentencing of a batch of material from production (acceptance sampling by lots), it is possible to identify and measure every single item in the population and to include any one of them in our sample. However, in the more general case this is not possible. There is no way to identify all rats in the set of all rats. There is no way to identify every voter at a forthcoming election (in advance of the election).
These imprecise populations are not amenable to sampling in any of the ways below and to which we could apply statistical theory.
As a remedy, we seek a sampling frame which has the property that we can identify every single element and include any in our sample. For example, in an opinion poll, possible sampling frames include:
Electoral register Telephone directory Shoppers in Anytown, High Street on the Monday afternoon before the election. The sampling frame must be representative of the population and this is a question outside the scope of statistical theory demanding the judgment of experts in the particular subject matter being studied. All the above frames omit some people who will vote at the next election and contain some people who will not. People not in the frame have no prospect of being sampled. Statistical theory tells us about the uncertainties in extrapolating from a sample to the frame. In extrapolating from frame to population, its role is motivational and suggestive.
There is, however, a strong division of views about the acceptability of representative sampling across different domains of study. To the philosopher, the representative sampling procedure has no justification whatsoever because it is not how truth is pursued in philosophy. "To the scientist, however, representative sampling is the only justified procedure for choosing individual objects for use as the basis of generalization, and is therefore usually the only acceptable basis for ascertaining truth." (Andrew A. Marino) . It is important to understand this difference to steer clear of confusing prescriptions found in many web pages.



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