1.8 Unbiased Estimator

An unbiased estimator is an estimator that has an expected value equal to the parameter being estimated. For example, The sample variance/mean is an unbiased estimator of the population variance/mean. We calculate the sample variance by dividing the sum of squared deviations by n-1, where n is the sample size. The variance is naturally slightly bigger when (n-1) is used as the denominator than when n is used, suggesting that if we were to (incorrectly) use n instead, it might result in an underestimate of the population variance. The population variance may be calculated accurately with n in the denominator and yield the same results as using (n-1) in the sample calculations’ denominators. This is what statisticians mean when they refer to the sample variance (with n-1) as an unbiased estimator. In 20 out of our 27 samples, the sample mean was wrong (i.e., not equal to the population mean)—either too low or too high— making the variance incorrect as well. This uncertainty in the sample is taken into account in the variance calculation by using (n-1) as the denominator.