[R] Small p from binomial probability function.

Rolf Turner rolf.turner at vodafone.co.nz
Fri Oct 11 03:36:35 CEST 2013

I've figured it out.  It ***is*** "obvious" why Evert's procedure works.
Once you hold your head at the correct angle, as my first year calculus 
used to say.

The binom.test() confidence interval gives you the value of a random 
say "U" (for "upper") such that

     Pr(U < p) = p0

where U is a function of the observed binomial random variable, say U = 

The observed value of U is h(x), where x is the observed value of X.

Now we want p such that Pr(X <= x) = p0 where X ~ Binom(N,p).

But when X ~ Binom(N,p),

     Pr(U <= p) = p0, i.e
     Pr(h(X) <= p) = p0, so if we take p = h(x) we have
     Pr(h(X) <= h(x)) = p0, whence
     Pr(X <= x) = p0 as desired.

Still twists my head, but.


     Rolf Turner

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