Problems Caused By Sampling Bias
A biased sample causes problems because any statistic computed from that sample has the potential to be consistently erroneous. The bias can lead to an over- or underrepresentation of the corresponding parameter in the population. Almost every sample in practice is biased because it is practically impossible to ensure a perfectly random sample. If the degree of underrepresentation is small, the sample can be treated as a reasonable approximation to a random sample. Also, if the group that is underrepresented does not differ markedly from the other groups in the quantity being measured, then a random sample can still be a reasonable approximation.
The word bias in common usage has a strong negative word connotation, and implies a deliberate intent to mislead or other scientific fraud. In statistical usage, bias merely represents a mathematical property, no matter if it is deliberate or either 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.
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. These surveys require the use of sample weights (see below) to produce proper estimates across all racial and ethnic groups. Provided that certain conditions are met (chiefly that the sample is drawn randomly from the entire sample) these samples permit accurate estimation of population parameters.
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