# poisson.test

##### 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:

the number of events (in the first sample if there are two.)

the corresponding expected count

the p-value of the test.

a confidence interval for the rate or rate ratio.

the estimated rate or rate ratio.

the rate or rate ratio under the null,
`r`

.

a character string describing the alternative hypothesis.

the character string `"Exact Poisson test"`

or
`"Comparison of Poisson rates"`

as appropriate.

a 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.

##### See Also

##### Examples

`library(stats)`

```
# NOT RUN {
### 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))
# }
```

*Documentation reproduced from package stats, version 3.5.0, License: Part of R 3.5.0*