# poisson.test

0th

Percentile

##### Exact Poisson tests

Performs an exact test of a simple null hypothesis about the rate parameter in Poisson distribution, or for the ratio between two rate parameters.

Keywords
htest
##### Usage
poisson.test(x, T = 1, r = 1,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95)
##### Arguments
x
number of events. A vector of length one or two.
T
time base for event count. A vector of length one or two.
r
hypothesized rate or rate ratio
alternative
indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less". You can specify just the initial letter.
conf.level
confidence level for the returned confidence interval.
##### Details

Confidence intervals are computed similarly to those of binom.test in the one-sample case, and using binom.test in the two sample case.

##### Value

• A list with class "htest" containing the following components:
• statisticthe number of events (in the first sample if there are two.)
• parameterthe corresponding expected count
• p.valuethe p-value of the test.
• conf.inta confidence interval for the rate or rate ratio.
• estimatethe estimated rate or rate ratio.
• null.valuethe rate or rate ratio under the null, r.
• alternativea character string describing the alternative hypothesis.
• methodthe character string "Exact Poisson test" or "Comparison of Poisson rates" as appropriate.
• data.namea character string giving the names of the data.

##### Note

The rate parameter in Poisson data is often given based on a time on test or similar quantity (person-years, population size, or expected number of cases from mortality tables). This is the role of the T argument.

The one-sample case is effectively the binomial test with a very large n. The two sample case is converted to a binomial test by conditioning on the total event count, and the rate ratio is directly related to the odds in that binomial distribution.

binom.test
library(stats) ### These are paraphrased from data sets in the ISwR package ## SMR, Welsh Nickel workers poisson.test(137, 24.19893) ## eba1977, compare Fredericia to other three cities for ages 55-59 poisson.test(c(11, 6+8+7), c(800, 1083+1050+878))