Editing Consistency (statistics) (section)

== Relationship to unbiasedness ==
An estimator or test may be consistent without being unbiased.<ref>{{Cite book |last=Vaart |first=A. W. van der |url=http://dx.doi.org/10.1017/cbo9780511802256 |title=Asymptotic Statistics |date=1998-10-13 |publisher=Cambridge University Press |isbn=978-0-511-80225-6}}</ref> A classic example is the [[sample standard deviation]] which is a biased estimator, but converges to the expected [[standard deviation]] almost surely by the [[law of large numbers]]. Phrased otherwise, unbiasedness is not a requirement for consistency, so [[Biased estimator|biased estimators]] and tests may be used in practice with the expectation that the outcomes are reliable, especially when the sample size is large (recall the definition of consistency). In contrast, an estimator or test which is not consistent may be difficult to justify in practice, since gathering additional data does not have the asymptotic guarantee of improving the quality of the outcome.