Confidence Interval - Alternatives and Critiques

Alternatives and Critiques

Main article: Interval estimation See also: Prediction interval, Tolerance interval, and Credible interval

Confidence intervals are one method of interval estimation, and the most widely used in frequentist statistics. An analogous concept in Bayesian statistics is credible intervals, while an alternative frequentist method is that of prediction intervals which, rather than estimating parameters, estimate the outcome of future samples. For other approaches to expressing uncertainty using intervals, see interval estimation.

There is disagreement about which of these methods produces the most useful results: the mathematics of the computations are rarely in question–confidence intervals being based on sampling distributions, credible intervals being based on Bayes' theorem–but the application of these methods, the utility and interpretation of the produced statistics, is debated.

Users of Bayesian methods, if they produced an interval estimate, would in contrast to confidence intervals, want to say "My degree of belief that the parameter is in fact in this interval is 90%," while users of prediction intervals would instead say "I predict that the next sample will fall in this interval 90% of the time."

Confidence intervals are an expression of probability and are subject to the normal laws of probability. If several statistics are presented with confidence intervals, each calculated separately on the assumption of independence, that assumption must be honoured or the calculations will be rendered invalid. For example, if a researcher generates a set of statistics with intervals and selects some of them as significant, the act of selecting invalidates the calculations used to generate the intervals.