Our German »Streuspanne Lexicon« is not a regular series, but a section to refer to small explanations without having to go on and on in a separate series. Today we continue with »C for Confidence Interval«. The Streuspanne team briefly and concisely explains the confidence interval.
Today we explain the confidence interval in the »Streuspanne Lexicon« – in under five minutes.
In short, a confidence interval is a confidence interval. If you determine a single value for an estimator, then this value depends on the sample and would change if the experiment were repeated. How an estimator works is explained in our encyclopaedia series »E for Estimation«, which you should listen to beforehand.
The confidence interval is a range in which an unknown parameter is assumed to lie. The wider this range – or interval – is, the more likely it is that the unknown value will be covered by the interval. At the same time, the wider the interval, the less meaningful it becomes, as the example of body sizes in the podcast makes clear.
If the interval is too wide, more effort must be made and the sample size must be increased in order to make a more precise statement about the result and thus select a narrower confidence interval. A square root law applies here – if the confidence interval is to be halved, four times the amount of data is required.
Specific figures are often given for the confidence interval, e.g. 95 percent confidence interval. In general, the greater the confidence, the wider the interval. Confidence is therefore a measure of whether an unknown but fixed value is recorded by chance with an interval.
The interval limits are determined from the sample according to a precise calculation rule. They therefore depend on chance and can be »good« or »bad« – i.e. contain or do not contain the true value.
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Fraunhofer Institute for Industrial Mathematics ITWM