[R] confidence intervals for multinomial

Drescher, Michael (MNR) michael.drescher at ontario.ca
Thu Jul 19 00:31:11 CEST 2007

Hi All,

I want to test an H0 hypothesis about the proportions of observed counts
in k classes. I know that I can do this with the chisq.test.

However, besides of the overall acceptance or rejection of the H0, I
would like to know which of the k classes cause(s) rejection and I would
like to know the observation-based confidence envelopes for the
proportions for the k classes.

My quick-and-dirty approach thus far is to do an initial chisq.test on
the original k classes and then to lump data into two classes (=one of
the original classes and all other original classes lumped into one new
class) and do a binom.test. I interpret the result of the binom.test as
indicating whether the current class might be the reason for the
rejection of the overall H0. Additionally, it gives me a confidence
envelope for this class.

This approach seems fairly straightforward, but I just do not feel
totally comfortable with it. I would feel so much better if there was
something like a multinom.test, but to my knowledge there is none.

Do you have any suggestions what I could rather do? For instance, I
might follow a Monte Carlo-like approach:
I simulate proportions for the k classes based on the proportions of
observed counts with rmultinom. After exclusion of the most extreme
values I construct my confidence envelope based on the remaining
simulated proportions. Based on whether the hypothesized proportions
fall into the observation-based confidence envelopes, I accept or

Do you think that either of these approaches is better or would you
suggest doing something totally different?

All comments and suggestions are highly appreciated.

Kind regards, Michael

PS: I guess my request parallels that of Matthias Schmidt from Apr 5,
2004, that was answered by Brian Ripley ...

Michael Drescher
Ontario Forest Research Institute
Ontario Ministry of Natural Resources
1235 Queen St East
Sault Ste Marie, ON, P6A 2E3
Tel: (705) 946-7406
Fax: (705) 946-2030

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