Confidence Intervals

A confidence interval gives us a whole range of plausible values for an unknown quantity, rather than a single numerical estimate.

The key idea is to construct a random interval which contains the true value we are looking for with some known probability, before the data are collected. Once we observe the data, this random interval becomes a numerical confidence interval.

To do this, we introduce the important idea of a pivot: a random quantity whose probability distribution is known, even though the pivot itself may involve unknown parameters.

We then show how probability statements about a pivot can be rearranged to produce interval estimators, and spend some time on the equally important question of how the resulting confidence intervals should be interpreted.

Confidence intervals will appear repeatedly in statistics and econometrics, so getting the underlying logic straight here is well worth the effort.