Abstract
Sampling bias means that the samples of a stochastic variable that are collected to determine its distribution are selected incorrectly and do not represent the true distribution because of non-random reasons. Let us consider a specific example: we might want to predict the outcome of a presidential election by means of an opinion poll. Asking 1000 voters about their voting intentions can give a pretty accurate prediction of the likely winner, but only if our sample of 1000 voters is 'representative' of the electorate as a whole (i.e. unbiased). If we only poll the opinion of, 1000 white middle class college students, then the views of many important parts of the electorate as a whole (ethnic minorities, elderly people, blue-collar workers) are likely to be underrepresented in the sample, and our ability to predict the outcome of the election from that sample is reduced.
In an unbiased sample, differences between the samples taken from a random variable and its true distribution, or differences between the samples of units from a population and the entire population they represent, should result only from chance. If their differences are not only due to chance, then there is a sampling bias. Sampling bias often arises because certain values of the variable are systematically under-represented or over-represented with respect to the true distribution of the variable (like in our opinion poll example above). Because of its consistent nature, sampling bias leads to a systematic distortion of the estimate of the sampled probability distribution. This distortion cannot be eliminated by increasing the number of data samples and must be corrected for by means of appropriate techniques, some of which are discussed below. In other words, polling an additional 1000 white college students will not improve the predictive power of our opinion poll, but polling 1000 individuals chosen at random from the electoral roll would. Obviously, a biased sample may cause problems in the measure of probability functionals (e.g., the variance or the entropy of the distribution), since any statistics computed from that sample has the potential to be consistently erroneous.
