Bias

Bias, in estimation, is the systematic gap between an estimator's expected value and the true population parameter.

Also known asestimator bias

ByHoang TruongUpdated June 30, 2026

See it move

Loading infographic...

A two-column comparison contrasts an unbiased estimator, where the expected value E[θ̂] equals the true parameter θ and the bias is zero, with a biased estimator, where E[θ̂] differs from θ by a non-zero amount and estimates land systematically off-centre. The comparison notes that omitted variable bias — leaving a relevant correlated regressor out of a regression model — is the most common source of such systematic error.

Where it fits

SubjectData Analysis & StatisticsCoreTopicEstimation & Sampling DistributionsCore

The formula

LaTeX

\text{Bias}(\hat{\theta}) = \mathbb{E}[\hat{\theta}] - \theta

Variables

$\hat{θ}$: Estimator
$E (\hat{θ})$: Expected value of the estimator across all possible samples
$θ$: True population parameter

An unbiased estimator has E(θ̂) = θ, making the bias exactly zero.

Check yourself

PracticeCORE

An estimator of the population mean consistently overestimates the true value by exactly €120, regardless of which sample is drawn. Which statement correctly characterises this estimator?

Select an answer to check your understanding.