Bias is defined as the difference between the expected value of a statistic and the true value of the corresponding parameter. Therefore the bias is a measure of the systematic error of an estimator. The bias indicates the distance of the estimator from the true value of the parameter. For example, if we calculate the mean of large number of unbiased estimators, we will find the correct value.
Gauss, C.F. (1821) during his work on the least squares method gave the concept of an unbiased estimator.
Bias of an estimator of a parameter should not be confused with its degree of precision as degree of precision is a measure of the sampling error.
There are several types of bias which should not be considered as mutually exclusive
- Selection Bias (arise due to systematic differences between the groups compared)
- Exclusion Bias (arise due to the systematic exclusion of certain individuals from the study)
- Analytical Bias (arise due to the way that the results are evaluated)
Mathematically Bias can be Defined as
Let statistics T used to estimate a parameter θ, if E(T)=θ + b(θ) then b(θ) is called the bias of the statistic T, where E(T) represents the expected value of the statistics T. Note that if b(θ)=0, then E(T)=θ. So T is an unbiased estimator of θ.
Gauss, C.F. (1821, 1823, 1826). Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Parts 1, 2 and suppl. Werke 4, 1-108.