When a certain event occurs several times in a series of observations, then its proportion and confidence interval can be calculated.
Variables:
(1) N observations
(2) X events of interest
Distribution used
(1) F distribution, with F = 0.975 for the 95% confidence interval
(2) uses m and n as degrees of freedom
proportion of events =
= X / N
lower limit for the 95% confidence interval =
= X / (X + ((N - X + 1) * (F distribution for m and n)))
where
• m = 2 * (N - X + 1)
• n = 2 * X
upper limit for the 95% confidence interval =
= ((X + 1) * (F distribution for m and n)) / (N - X + ((X + 1) * (F distribution for m and n)))
where:
• m = 2 * (X + 1) = n + 2
• n = 2 * (N - X) = m - 2
