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Since sampling is almost always done to estimate population parameters that are unknown, by definition exact measurement of the sampling errors will not be possible; however they can often be estimated, either by general methods such as bootstrapping, or by specific methods incorporating some assumptions (or guesses) regarding the true ...
The sampling distribution of a mean is generated by repeated sampling from the same population and recording the sample mean per sample. This forms a distribution of different means, and this distribution has its own mean and variance .
Sampling error, which occurs in sample surveys but not censuses results from the variability inherent in using a randomly selected fraction of the population for estimation. Nonsampling error, which occurs in surveys and censuses alike, is the sum of all other errors, including errors in frame construction, sample selection, data collection ...
Non-sampling errors are other errors which can impact final survey estimates, caused by problems in data collection, processing, or sample design. Such errors may include: Over-coverage: inclusion of data from outside of the population; Under-coverage: sampling frame does not include elements in the population.
This interval is called the confidence interval, and the radius (half the interval) is called the margin of error, corresponding to a 95% confidence level. Generally, at a confidence level , a sample sized of a population having expected standard deviation has a margin of error
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.
The difference between the height of each man in the sample and the observable sample mean is a residual. Note that, because of the definition of the sample mean, the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).