[R] binom.test and small N
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Fri Mar 22 23:45:05 CET 2002
Tony Long <tdlong at uci.edu> writes:
> running R 1.4.1 on MAC and 1.2.2 on Linux
>
> When I use run binom.test with small N the results are a little
> perplexing to me
>
> >binom.test(9,20,p=0.5)
>
> gives the below plus other stuff
>
> 95 percent confidence interval:
> 0.2305779 0.6847219
>
> Now:
>
> >pbiom(9,20,0.6847219)
> [1] 0.02499998 # i.e., lower 2.5% of distribution
> >pbinom(9,20,0.2305779)
> [1] 0.9923132
> >pbinom(8,20,0.2305779)
> [1] 0.975 # i.e., upper 2.5% of distribution
>
> I would think I generally want a 95% CI on the observed 9 out of 20,
> not 8 out of 20 LB and 9 out of 20 UB. I am missing something or is
> this strictly a function of the beta approximation used in the source
> code??
The devil is lurking in de tails...
Notice that you want "this or worse" in both cases, i.e. solve
P(X <= 9) = 2.5% for the upper bound and
P(X >= 9) = 2.5% for the lower bound
now, P(X >= 9) = 1 - P(X <= 8) for integer X.
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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