Revisiting Bessel’s Correction and the Bias-Variance Tradeoff in Variance Estimation

When estimating the variance from a sample, usually the so-called Bessel’s correction is used, i.e., unintuitively each term is weighted by the sample size n minus one. Although this is an unbiased estimator, it does not necessarily yield the best accuracy in terms of bias-variance tradeoff. To this end, we conducted bibliometric work and observe that many statistics textbooks recommend Bessel’s correction for somewhat spurious reasons. Furthermore, we address the bias-variance tradeoff in variance estimation from a theoretical perspective and show that usually the uncorrected version of the sample variance is a better choice. We back this up with a simulation study that can be conducted in a classroom setting, where students can learn about unbiasedness, bias-variance tradeoff, conducting simulation studies, and estimation in general from an easy example.