poisson.exact {exactci} | R Documentation |
Performs an exact test of a simple null hypothesis about the
rate parameter in Poisson distribution, or for the
ratio between two rate parameters. This is different from poisson.test
in that 3 different types of exact two-sided tests (and the matching confidence intervals)
are offered. The one-sided tests are the same as in poisson.test
.
poisson.exact(x, T = 1, r = 1, alternative = c("two.sided", "less", "greater"), tsmethod=c("central","minlike","blaker"), conf.level = 0.95, control=binomControl())
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. |
tsmethod |
character giving two-sided method, one of "central", "minlike" or "blaker", ignored if alternative not equal "two.sided" |
conf.level |
confidence level for the returned confidence interval. |
control |
list with settings to avoid problems with ties, etc, should not need to change this for normal use,
see binomControl |
Confidence intervals are computed similarly to those of
binom.exact
in the one-sample case, in that there are three two-sided options depending on the
tsmethod
. For the one-sample case the
default intervals use tsmethod="central"
giving the Garwood (1936) exact central confidence intervals.
For the two-sample case we condition on the total counts and then use binomial methods,
see Lehmann and Romano (2005) for that motivation and vignette("exactci")
for description
of the three different two-sided methods for calculating p-values and confidence intervals.
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. |
The rate parameter in Poisson data is often given based on a
“time on test” or similar quantity (person-years, population
size). This is the role of the T
argument.
Garwood, F (1936). Fiducial limits for the Poisson distribution. Biometrika, 437-442.
Lehmann, EL, and Romano, JP (2005). Testing Statistical Hypotheses, third edition. Springer:New York.
### Suppose you have observed rates of 2 out of 17877 in group A ### and 10 out of 20000 in group B ### poisson.test gives non-matching confidence intervals ### i.e., p-value using 'minlike' criteria but confidence interval using 'central' criteria poisson.test(c(2,10),c(17877,20000)) ### poisson.exact gives matching CI to the p-values ### defaults to 'central' two-sided method poisson.exact(c(2,10),c(17877,20000)) ### other options poisson.exact(c(2,10),c(17877,20000),tsmethod="minlike") poisson.exact(c(2,10),c(17877,20000),tsmethod="blaker")