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In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample [ 1 ] of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected ...
This can also be termed selection effect, sampling bias and Berksonian bias. [3] Spectrum bias arises from evaluating diagnostic tests on biased patient samples, leading to an overestimate of the sensitivity and specificity of the test. For example, a high prevalence of disease in a study population increases positive predictive values, which ...
Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more). All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias ...
¯ is the sample mean; σ 2 is the population variance; s n 2 is the biased sample variance (i.e., without Bessel's correction) s 2 is the unbiased sample variance (i.e., with Bessel's correction) The standard deviations will then be the square roots of the respective variances.
One way of seeing that this is a biased estimator of the standard deviation of the population is to start from the result that s 2 is an unbiased estimator for the variance σ 2 of the underlying population if that variance exists and the sample values are drawn independently with replacement. The square root is a nonlinear function, and only ...
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.
Although an unbiased estimator is usually favored over a biased one, a more efficient biased estimator can sometimes be more valuable than a less efficient unbiased estimator. For example, this can occur when the values of the biased estimator gathers around a number closer to the true value.
In reality, obtaining an unbiased sample can be difficult as many parameters (in this example, country, age, gender, and so on) may strongly bias the estimator and it must be ensured that none of these factors play a part in the selection process.