Confidence interval: Difference between revisions
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The '''Confidence interval''' 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."<ref>{{MeSH}}</ref> | 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."<ref>{{MeSH}}</ref> | ||
In large samples, calculations for the CI for rates and proportions may be based on the [[normal distribution]].<ref name="isbn0-471-26370-2">{{cite book |author=Fleiss, Joseph L. |title=Statistical methods for rates and proportions |publisher=Wiley |location=New York |year=1973 |pages=13 |isbn=0-471-26370-2 |oclc= |doi=}}</ref><ref name="isbn0-8138-1560-6">{{cite book |author=Cochran, William Cox; Snedecor, George W. |title=Statistical methods |publisher=Iowa State University Press |location=Ames |year=1980 |pages=118 |isbn=0-8138-1560-6 |oclc= |doi=}}</ref> | |||
The equation using the normal distribution is:<ref name="pmid3082422">{{cite journal |author=Gardner MJ, Altman DG |title=Confidence intervals rather than P values: estimation rather than hypothesis testing |journal=Br Med J (Clin Res Ed) |volume=292 |issue=6522 |pages=746–50 |year=1986 |month=March |pmid=3082422 |doi= |url= |issn=}}</ref> | |||
:<math>\begin{align} | |||
\mbox{CI lower limit} &= \bar X - \mbox{Z} * \mbox{SE} \\ | |||
\mbox{CI upper limit} &= \bar X + \mbox{Z} * \mbox{SE} | |||
\end{align} </math> | |||
Where | |||
:<math>\bar X = \mbox{sample mean}\,\!</math> | |||
:<math>\mbox{Z} = 1.96\,(\mbox{if}\, \alpha = 0.05 \,\mbox{for}\,95%\,\mbox{confidence intervals})\,\!</math> | |||
:<math>\mbox{Z} = 3.29\,(\mbox{if}\, \alpha = 0.001 \,\mbox{for}\,99.9%\,\mbox{confidence intervals})\,\!</math> | |||
:<math>\mbox{SE} = \mbox{standard error} = \frac{\sigma}{\sqrt{n}}</math> | |||
:<math>\sigma = \mbox{standard deviation}\,\!</math> | |||
For small samples, calculations should be made using the binomial distribution or the Poisson distribution. | For small samples, calculations should be made using the binomial distribution or the Poisson distribution. | ||
==References== | ==References== | ||
<references/> | <references/>[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 07:00, 1 August 2024
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]
Where
For small samples, calculations should be made using the binomial distribution or the Poisson distribution.
References
- ↑ Anonymous (2024), Confidence interval (English). Medical Subject Headings. U.S. National Library of Medicine.
- ↑ Fleiss, Joseph L. (1973). Statistical methods for rates and proportions. New York: Wiley, 13. ISBN 0-471-26370-2.
- ↑ Cochran, William Cox; Snedecor, George W. (1980). Statistical methods. Ames: Iowa State University Press, 118. ISBN 0-8138-1560-6.
- ↑ 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. [e]