Correcting for Systematic Bias in Sample Estimates of Population Variances: Why Do We Divide by n-1?

Mittag, K. C.

An important topic presented in introductory statistics courses is the estimation of population parameters using samples. Students learn that when estimating population variances using sample data, we always get an underestimate of the population variance if we divide by n rather than n-1. One implication of this correction is that the degree of bias gets smaller as the sample gets larger and larger. This paper explains the nature of bias and correction in the estimated variance and discusses the properties of a good estimator (unbiasedness, consistency, efficiency, and sufficiency). A BASIC computer program that is based on Monte Carlo methods is introduced, which can be used to teach students the concept of bias in estimating variance. The program is included in this paper. This type of treatment is needed because surprisingly few students or researchers understand this bias and why a correction for bias is needed. One table and three graphs summarize the analyses. A 10-item list of references is included, and two appendices present the computer program and five examples of its use. (Author/SLD)

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education