Wald interval (aka one proportion z-interval): + z*

 

Score interval (aka Wilson) inverts

The midpoint of the Score interval can be rewritten as: (n /(n + z2)) + .5(z2/(n+z2)), a weighted average of and 0.50.

 

Adjusted Wald interval: + z*where=  (X+.5z*2)/(n+z*2), = n+z*2

For 95% confidence this is approximately: = (X+2)/(n+4) and = n+4 which adds two successes and two failures to the sample (plus four method)

 

Finite Population Correction Factor (N = population size)

+ z*