Simulation for Data Science with R by Matthias Templ

Author:Matthias Templ [Templ, Matthias]
Language: eng
Format: azw3, pdf
Publisher: Packt Publishing
Published: 2016-06-30T04:00:00+00:00

Confidence intervals

Along with point estimates, confidence intervals are commonly reported to show the reliability of the point estimates. For example, a confidence interval can be used to describe how reliable estimates from surveys are. The average hourly wages of employees taken from a simple random sample survey of 1000 respondents might be 31 Euros. A 99% confidence interval for the average income of the population might be 25 to 37 Euros. However, since there is no negative income, the confidence intervals must not be always symmetric, as is the case also for voting-intentions, for example. We will not cover these special cases, but refer to Hron, Templ, and Filzmoser (2013).

Generally, from the observed data, a lower and upper bound—an estimated interval—for the parameter is estimated. is unknown but fixed (an actual parameter in the population). The estimated interval, however, depends on the observations in the sample and is therefore random. Often, is contained therein, but sometimes, it is not. The calculation formula should be such that, for example, = 95% (significance level = 0.05) of all samples provide a covering interval. Increased coverage ( small) means the larger the estimated confidence intervals.

In a nutshell: We are looking for two estimates, U and O, specifying the limits of the confidence interval for a given coverage of percent:

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