Why is does StatsDirect give slightly different confidence intervals to the ones I calculate by hand for proportions?
Many text books contain poorly performing formulae for approximation of confidence intervals for binomial proportions and differences between them. StatsDirect improves upon these formulae, especially in the presence of small numbers, by using methods that have good coverage properties. For more detailed discussion of the reasons behind the choices of methods used in StatsDirect, please see the following series of excellent papers by Robert Newcombe: Newcombe R. Improved confidence intervals for the difference between binomial proportions based on paired data. Statistics in Medicine 1998;17:2635-2650. Newcombe R. Interval estimation for the difference between independent proportions. Statistics in Medicine 1998;17:873-890. Newcombe R. Two sided confidence intervals for the single proportion: a comparative evaluation of seven methods. Statistics in Medicine 1998;17:857-872.
