Next section: Estimating variance

Statistics are used to estimate parameters. Three important attributes of statistics as estimators are covered in this text: unbiasedness, consistency, and relative efficiency.

Most statistics you will see in this text are unbiased estimates of the parameter they estimate. For example, the sample mean, M, is an unbiased estimate of the population mean, μ.

All statistics covered will be consistent estimators. It is hard to imagine a reasonably-chosen statistic that is not consistent.

When more than one statistic can be used to estimate a parameter, one will naturally be more efficient than the other(s). In general the relative efficiency of two statistics differs depending on the shape of the distribution of the numbers in the population. Statistics that minimize the sum of squared deviations such as the mean are generally the most efficient estimators for normal distributions but may not be for highly skewed distributions.

Next section: Estimating variance