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All colored circles are included in the target population. Green and Orange colored circles are included in the sample frame. Green colored circles are a randomly generated sample from the sample frame. The sample frame includes overcoverage because John and Jack are the same person, but he is included more than once in the sample frame.
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, data processing and estimation methods.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test (the ability of its results to be generalized to the entire population), while selection bias mainly addresses internal validity for differences or similarities found in the sample at hand. In this sense, errors occurring in ...
Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed. [1] It is sometimes referred to as the selection effect.
In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. [1] Type I error: an innocent person may be convicted. Type II error: a guilty person may be not convicted.
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.