Proper power computation for one-sided binomial tests.
Collin Lynch wrote:
Hi, I trying to determine the best way to compute the power for a one-sample one-sided binomial test. Specifically I need to sample a population of individuals and ask whether a sample rate of 0% is compatable with a minimum threshold of 3% and how many samples are needed. I have made use of power.prop.test but I am not sure if a) that is the correct (or best) function to use and b) if the output is quite right. Here is a sample run:
power.prop.test(p1=0, p2=0.03, sig.level=0.05, power=0.90,
alt="one.sided")
Two-sample comparison of proportions power calculation
n = 279.3004
p1 = 0
p2 = 0.03
sig.level = 0.05
power = 0.9
alternative = one.sided
NOTE: n is number in *each* group
This is an attempt to test whether a sample of 0% occurrance is compatable
with an a-priori probability of 3% at the specified significance levels.
My questions are those above, and, as a followup whether the caveat about
n being the number in each group means that I need to sample twice that
number in a single group. I don't believe so but I want to be sure.
Yes, that's wrong. Now you can be sure ;-)
For this kind of problem I'd go directly for the binomial distribution.
If the actual probability is 0, this is essentially deterministic and
you can look at
> binom.test(0,99,p=.03, alt="less")
Exact binomial test
data: 0 and 99
number of successes = 0, number of trials = 99, p-value = 0.04902
alternative hypothesis: true probability of success is less than 0.03
95 percent confidence interval:
0.00000000 0.02980667
sample estimates:
probability of success
0
So you have significance at n=99, which I think we can easily agree is
less than two times 249....
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