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Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement. Sampling done without replacement is no longer independent, but still satisfies exchangeability, hence most results of mathematical statistics still hold. Further ...
Sampling schemes may be without replacement ('WOR' – no element can be selected more than once in the same sample) or with replacement ('WR' – an element may appear multiple times in the one sample). For example, if we catch fish, measure them, and immediately return them to the water before continuing with the sample, this is a WR design ...
In a sense, AI can give each of us a job promotion, not be a job replacement. There will be short-term displacement but it will self-correct. Of course, the widescale adoption of Gen AI will have ...
The design effect is rarely applied when constructing confidence intervals. Ideally, one would be able to determine, for an estimator of a particular parameter, both the variance under Simple Random Sample (SRS) with replacement and the design effect (which accounts for all elements of the sampling design that change the variance).
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Lane Kiffin works the spin room, furiously trying to position Ole Miss for a CFP bracket bid. It's a tough road, but he's got a case. Lane Kiffin is pushing Ole Miss for College Football Playoff ...
An autosampler for liquid or gaseous samples based on a microsyringe. Autosamplers for liquids work along many kinds of machines that perform different kinds of chemical measurements, like titrators, gas chromatographers, liquid chromatographers, water analyzers (like total carbon analyzers, dissolved inorganic carbon analyzers, nutrient analyzers) and many others.