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Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated. More specifically, given a confidence level (95% and 99% are typical values), a CI is a random interval which contains the parameter being estimated % of the time.[1][2] The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.[3]
Factors affecting the width of the CI include the sample size, the variability in the sample, and the confidence level.[4] All else being the same, a larger sample produces a narrower confidence interval, greater variability in the sample produces a wider confidence interval, and a higher confidence level produces a wider confidence interval.[5]
^Zar, Jerrold H. (199). Biostatistical Analysis (4th ed.). Upper Saddle River, N.J.: Prentice Hall. pp. 43–45. ISBN978-0130815422. OCLC39498633.