Confidence interval

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."

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

The equation using the normal distribution is:

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

Where

${\bar {X}}={\mbox{sample mean}}\,\!$

${\mbox{Z}}=1.96\,({\mbox{if}}\,\alpha =0.05\,{\mbox{for}}\,95\%\,{\mbox{confidence intervals}})\,\!$

${\mbox{Z}}=3.29\,({\mbox{if}}\,\alpha =0.001\,{\mbox{for}}\,99.9\%\,{\mbox{confidence intervals}})\,\!$

${\mbox{SE}}={\mbox{standard error}}={\frac {\sigma }{\sqrt {n}}}$

$\sigma ={\mbox{standard deviation}}\,\!$

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