An Illuminating Counterexample

because S is “unbiased” and T 2 is “biased.” That means E(S) = σ 6= E(T ), i.e., an “unbiased estimator” is a statistic whose expected value is the quantity to be estimated. The goodness of an estimator is sometimes measured by the smallness of its “mean squared error,” defined as E ( ([estimator]− [quantity to be estimated]) ) . By that criterion the biased estimator T 2 would be better than the unbiased estimator S, since E((T 2 − σ)) < E((S − σ)),