# [R] Power of a single sample binomial test

From: Chris Evans <chris_at_psyctc.org>
Date: Mon 31 Jul 2006 - 04:53:46 EST

The only references to this I can find searching the archives are to a student who asked in relation to his course work on a stats course. Promise I'm not doing that!

I have a situation in which we want to test proportions against an expected proportion, binom.test() is great. I'd like to do some post hoc power tests (the x and n were beyond our control in the survey as all we could set was an overall n.max where n < n.max, n is between 1 and 44).

I would love to work out our power to have detected a proportions different from the expected (.307). I've run two-tailed binomial tests as we were interested in both high and low. We can not unreasonably confine to the directional prediction of observed x/n << .307, say <.15 if that makes the maths easier. I can't see functions in R that will do this for me. The only book I seem to have to hand that addresses this is: Kraemer, H. C. & Thiemann, S. (1988) How many subjects? Statistical power analysis in research. Newbury Park California, Sage Publications, Inc. which I appreciate is ageing but I assume still correct. The problem I have is that I can use R to get Kraemer's upper case delta (p.77) and look up in their "Master table" but I'd love a more flexible function that would say solve for power where p1, n, p0 and alpha are given. I think I ought to be able to work out how their master table was calculated and work from that but I'm finding the mathematics a bit opaque for my ageing brain. Their model is clearly one-tailed. I'm not sure how one works a two-tailed power.

A search around for web calculators etc. turns up all manner of things, some probably good, some dead etc. I'd hugely appreciate if someone here could share anything they may have in R or point me to R solutions I may have missed.

TIA, Chris

```--
Chris Evans <chris@psyctc.org>
Professor of Psychotherapy, Nottingham University;
Consultant Psychiatrist in Psychotherapy, Rampton Hospital;
Research Programmes Director, Nottinghamshire NHS Trust;
Hon. SL Institute of Psychiatry, Hon. Con., Tavistock & Portman Trust

**If I am writing from one of those roles, it will be clear. Otherwise**

**my views are my own and not representative of those institutions    **

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