The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

48 CHAPTER 3 Graphics and Summary Statistics

Figure 3.8. Properties of the sample mean and sample standard deviation
(taken from the Cartoon Guide to Statistics with permission).

unbiased estimate of the population variance. So this means that
E ( V ) = ( n − 1 ) σ 2 / n , which means that V is biased on the side of under-
estimating σ 2. Hence, it is more common to use S 2 for the estimate. But
sometimes, I think too much is made of this, because for large n , the
bias is small (i.e., ( n − 1)/ n is close to 1). Furthermore, since we esti-
mate the standard deviation by taking the square root of an unbiased
estimate of the variance, that will give us a slightly biased estimate of
the standard deviation anyway.
Although we have only discussed the unbiasedness property for the
variance estimate S 2 when the observations come from a random sample