poisson.test {stats} | R Documentation

## Exact Poisson tests

### Description

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

### 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:

`statistic` | the number of events (in the first sample if there are two.)
`parameter` | the corresponding expected count
`p.value` | the p-value of the test.
`conf.int` | a confidence interval for the rate or rate ratio.
`estimate` | the estimated rate or rate ratio.
`null.value` | the rate or rate ratio under the null, `r`.
`alternative` | a character string describing the alternative hypothesis.
`method` | the character string `"Exact Poisson test"` or `"Comparison of Poisson rates"` as appropriate.
`data.name` | 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

`binom.test`

### Examples

    ### 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))

[Package stats version 3.4.3 Index]