Sampling bias
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.[2] If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.
"Spotlight fallacy" redirects here. For the psychological effect, see Spotlight effect.Distinction from selection bias[edit]
Sampling bias is usually classified as a subtype of selection bias,[7] sometimes specifically termed sample selection bias,[8][9][10] but some classify it as a separate type of bias.[11]
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 the process of gathering the sample or cohort cause sampling bias, while errors in any process thereafter cause selection bias.
However, selection bias and sampling bias are often used synonymously.[12]
Problems due to sampling bias[edit]
Sampling bias is problematic because it is possible that a statistic computed of the sample is systematically erroneous. Sampling bias can lead to a systematic over- or under-estimation of the corresponding parameter in the population. Sampling bias occurs in practice as it is practically impossible to ensure perfect randomness in sampling. If the degree of misrepresentation is small, then the sample can be treated as a reasonable approximation to a random sample. Also, if the sample does not differ markedly in the quantity being measured, then a biased sample can still be a reasonable estimate.
The word bias has a strong negative connotation. Indeed, biases sometimes come from deliberate intent to mislead or other scientific fraud. In statistical usage, bias merely represents a mathematical property, no matter if it is deliberate or unconscious or due to imperfections in the instruments used for observation. While some individuals might deliberately use a biased sample to produce misleading results, more often, a biased sample is just a reflection of the difficulty in obtaining a truly representative sample, or ignorance of the bias in their process of measurement or analysis. An example of how ignorance of a bias can exist is in the widespread use of a ratio (a.k.a. fold change) as a measure of difference in biology. Because it is easier to achieve a large ratio with two small numbers with a given difference, and relatively more difficult to achieve a large ratio with two large numbers with a larger difference, large significant differences may be missed when comparing relatively large numeric measurements. Some have called this a 'demarcation bias' because the use of a ratio (division) instead of a difference (subtraction) removes the results of the analysis from science into pseudoscience (See Demarcation Problem).
Some samples use a biased statistical design which nevertheless allows the estimation of parameters. The U.S. National Center for Health Statistics, for example, deliberately oversamples from minority populations in many of its nationwide surveys in order to gain sufficient precision for estimates within these groups.[15] These surveys require the use of sample weights (see later on) to produce proper estimates across all ethnic groups. Provided that certain conditions are met (chiefly that the weights are calculated and used correctly) these samples permit accurate estimation of population parameters.
Statistical corrections for a biased sample[edit]
If entire segments of the population are excluded from a sample, then there are no adjustments that can produce estimates that are representative of the entire population. But if some groups are underrepresented and the degree of underrepresentation can be quantified, then sample weights can correct the bias. However, the success of the correction is limited to the selection model chosen. If certain variables are missing the methods used to correct the bias could be inaccurate.[21]
For example, a hypothetical population might include 10 million men and 10 million women. Suppose that a biased sample of 100 patients included 20 men and 80 women. A researcher could correct for this imbalance by attaching a weight of 2.5 for each male and 0.625 for each female. This would adjust any estimates to achieve the same expected value as a sample that included exactly 50 men and 50 women, unless men and women differed in their likelihood of taking part in the survey.