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Confidence interval

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The Confidence interval (CI) is a "range of values for a variable of interest, e.g., a rate, constructed so that this range has a specified probability of including the true value of the variable."[1]

In large samples, calculations for the CI for rates and proportions may be based on the normal distribution.[2][3]

The equation using the normal distribution is:[4]

\begin{align} \mbox{CI lower limit} &= \bar X - \mbox{Z} * \mbox{SE} \\ \mbox{CI upper limit} &= \bar X + \mbox{Z} * \mbox{SE} \end{align}

Where

\bar X = \mbox{sample mean}\,\!
\mbox{Z} = 1.96\,(\mbox{if}\, \alpha = 0.05 \,\mbox{for}\,95%\,\mbox{confidence intervals})\,\!
\mbox{Z} = 3.29\,(\mbox{if}\, \alpha = 0.001 \,\mbox{for}\,99.9%\,\mbox{confidence intervals})\,\!
\mbox{SE} = \mbox{standard error} = \frac{\mbox{standard deviation}}{\sqrt{n}}

For small samples, calculations should be made using the binomial distribution or the Poisson distribution.

References

  1. ↑ Anonymous, (2008) Confidence interval (English). Medical Subject Headings. U.S. National Library of Medicine.
  2. ↑ Fleiss, Joseph L. (1973). Statistical methods for rates and proportions. New York: Wiley, 13. ISBN 0-471-26370-2. 
  3. ↑ Cochran, William Cox; Snedecor, George W. (1980). Statistical methods. Ames: Iowa State University Press, 118. ISBN 0-8138-1560-6. 
  4. ↑ Gardner MJ, Altman DG (March 1986). "Confidence intervals rather than P values: estimation rather than hypothesis testing". Br Med J (Clin Res Ed) 292 (6522): 746–50. PMID 3082422.
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