Interval estimate

In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number. Jerzy Neyman (1937) identified interval estimation ("estimation by interval") as distinct from point estimation ("estimation by unique estimate"). In doing so, he recognised that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.

The most prevalent forms of interval estimation are:

Other common approaches to interval estimation, which are encompassed by statistical theory, are:

There is another approach to statistical inference, namely fiducial inference, that also considers interval estimation. Non-statistical methods that can lead to interval estimates include fuzzy logic.

An interval estimate is one type of outcome of a statistical analysis. Some other types of outcome are point estimates and decisions.

The scientific problems associated with interval estimation may be summarised as follows:

Severini (1991) discusses conditions under which credible intervals and confidence intervals will produce similar results, and also discusses both the coverage probabilities of credible intervals and the posterior probabilities associated with confidence intervals.

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