binom.test {stats}  R Documentation 
Exact Binomial Test
Description
Performs an exact test of a simple null hypothesis about the probability of success in a Bernoulli experiment.
Usage
binom.test(x, n, p = 0.5,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95)
Arguments
x 
number of successes, or a vector of length 2 giving the numbers of successes and failures, respectively. 
n 
number of trials; ignored if 
p 
hypothesized probability of success. 
alternative 
indicates the alternative hypothesis and must be
one of 
conf.level 
confidence level for the returned confidence interval. 
Details
Confidence intervals are obtained by a procedure first given in
Clopper and Pearson (1934).
This guarantees that the confidence level
is at least conf.level
, but in general does not give the
shortestlength confidence intervals.
Value
A list with class "htest"
containing the following components:
statistic 
the number of successes. 
parameter 
the number of trials. 
p.value 
the pvalue of the test. 
conf.int 
a confidence interval for the probability of success. 
estimate 
the estimated probability of success. 
null.value 
the probability of success under the null,

alternative 
a character string describing the alternative hypothesis. 
method 
the character string 
data.name 
a character string giving the names of the data. 
References
Clopper, C. J. & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404–413. doi:10.2307/2331986.
William J. Conover (1971), Practical nonparametric statistics. New York: John Wiley & Sons. Pages 97–104.
Myles Hollander & Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 15–22.
See Also
prop.test
for a general (approximate) test for equal or
given proportions.
Examples
## Conover (1971), p. 97f.
## Under (the assumption of) simple Mendelian inheritance, a cross
## between plants of two particular genotypes produces progeny 1/4 of
## which are "dwarf" and 3/4 of which are "giant", respectively.
## In an experiment to determine if this assumption is reasonable, a
## cross results in progeny having 243 dwarf and 682 giant plants.
## If "giant" is taken as success, the null hypothesis is that p =
## 3/4 and the alternative that p != 3/4.
binom.test(c(682, 243), p = 3/4)
binom.test(682, 682 + 243, p = 3/4) # The same.
## => Data are in agreement with the null hypothesis.