Thursday, October 10, 2013

Variance of the mean

Bessel says that the larger is your sample, the larger is the variance (see Bessel correction) but sample mean $\overline x$ is closer to the population mean (see Standard error), $\mu$, and, therefore, the variance goes down. How can it decrease and increase at the same time?

The answer is that the decrease in variation when sample size is reduced is achieved at cost of higher mean variation. Your mean will vary more seriously when your sample sizes are smaller and, thus, have lower variability within them. But, which correction should you choose to get to the population variance, given the sample variance?