invbinomial(), cci proportions, and confidence intervals

[daniel klein]

I'm puzzled:

. version 18 : display invbinomial(10,4,.025)
.73762192

. version 18 : display invbinomial(10,4,1-.025)
.18708603

. version 9 : display invbinomial(10,4,.025)
.12155226

. version 9 : display invbinomial(10,4,1-.025)
.73762192

. version 18 : cii proportion 10 4

                                                            Binomial exact  
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |         10          .4    .1549193        .1215523    .7376219

. version 9 : cii 10 4

                                                            Binomial exact  
    Variable |        Obs        Mean    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |         10          .4    .1549193        .1215523    .7376219

The behavior of invbinomial() has been changed from Stata 9 to Stata 10. The respective entry in whatsnew9to10 says:

[...]
d. invbinomial(n, k, p), [...] are more accurate for small values of p or for returned values close to zero.

implying that results from Stata 18 should be "better". Yet, cii still uses ancient results from before Stata 10. Why? And, should I or should I not use the modern, "improved" invbinomial()?


Edit: Title should say cii not cci (a related command) sorry.

[daniel klein]

Private conversation with Mike Lacy made me realize I missed a very basic point: The binomial distribution isn't symmetric (unless P=.5). Therefore

invbinomial(10,4,1-.025)

is not supposed to match

invbinomialtail(10,4,.975)

This makes all the difference when constructing confidence intervals. Older versions of Stata didn't have invbinomialtail(), and invbinomial() switched tails automatically for P>=.5.

cii's confidence intervals were and still are accurate.

[edit]
To spell things out, the upper bound should be obtained as

invbinomial(10,4,.025)

and the lower bound as

invbinomialtail(10,4,.025)

[/edit]

Sorry for the confusion. Hopefully, this post helps others avoid the same mistake.