Why 95%CIs of One sample tests of proportions were different in Stata and R

Question

R

 > prop.test(x =44, n = 63, p = 0.8, alternative = "two.sided", correct = FALSE)

    95 percent confidence interval:
    **0.5763963 0.7976231**

Stata

. prtesti 63 44 0.8, count

  95% Conf. Interval
 **.5850839    .8117415**

Why 95%CIs of One sample tests of proportions were different in Stata and R，Thanks!

Answer 1

http://www.stata.com/manuals13/rprtest.pdf suggests that Stata is using the normal approximation. The epitools package provides a range of binomial CI calculators:

Normal approximation (matches Stata):

binom.approx(44,63)
   x  n proportion     lower     upper conf.level
1 44 63  0.6984127 0.5850839 0.8117415       0.95

Exact (matches binom.test() in base R):

binom.exact(44,63)
   x  n proportion     lower     upper conf.level
1 44 63  0.6984127 0.5697502 0.8076894       0.95

Wilson's formula (matches prop.test() in base R):

binom.wilson(44,63)
   x  n proportion     lower     upper conf.level
1 44 63  0.6984127 0.5763963 0.7976231       0.95

EDIT (Nick Cox) Some further Stata results, here from cii which accepts input calculator-style:

. cii 63 44, wald

                                                     -- Binomial Wald ---
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |         63    .6984127    .0578219        .5850839    .8117415

The default is so-called "exact" (Clopper-Pearson):

. cii 63 44

                                                     -- Binomial Exact --
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |         63    .6984127    .0578219        .5697502    .8076894


. cii 63 44, wilson

                                                     ------ Wilson ------
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |         63    .6984127    .0578219        .5763963    .7976231

. cii 63 44, jeffreys

                                                     ----- Jeffreys -----
    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]
-------------+---------------------------------------------------------------
             |         63    .6984127    .0578219        .5781254    .8009394

The moral is simple. In any decent statistical software, several options are available for binomial confidence intervals. Just read the documentation to know what is the default for your software, and pay attention to other options that are available.

END OF EDIT