mosaic (version 1.1.0)

binom.test: Exact Tests for Proportions

Description

The binom.test function performs an exact test of a simple null hypothesis about the probability of success in a Bernoulli experiment from summarized data or from raw data. The mosaic binom.test provides wrapper functions around the function of the same name in stats. These wrappers provide an extended interface (including formulas).

Usage

binom.test(x, n = NULL, p = 0.5, alternative = c("two.sided", "less",
  "greater"), conf.level = 0.95, ci.method = c("Clopper-Pearson",
  "binom.test", "Score", "Wilson", "prop.test", "Wald", "Agresti-Coull",
  "Plus4"), data = NULL, success = NULL, ...)

Arguments

x

count of successes, length 2 vector of success and failure counts, a formula, or a character, numeric, or factor vector containing raw data.

n

sample size (successes + failures) or a data frame (for the formula interface)

p

probability for null hypothesis

alternative

type of alternative hypothesis

conf.level

confidence level for confidence interval

ci.method

a method to use for computing the confidence interval (case insensitive and may be abbreviated). See details below.

data

a data frame (if missing, n may be a data frame)

success

level of variable to be considered success. All other levels are considered failure.

...

additional arguments (often ignored)

Value

an object of class htest

Details

binom.test is a wrapper around binom.test() from the base package to simplify its use when the raw data are available, in which case an extended syntax for binom.test is provided. See the examples.

Also, five confidence interval methods are provided:

Clopper-Pearson, binom.test

This is the interval produced when using stats::binom.test() from the stats package. It guarantees a coverage rate at least as large as the nominal coverage rate, but may produce wider intervals than some of the methods below, which may either under- or over-cover depending on the data.

Score, Wilson, prop.test

This is the usual method used by stats::prop.test() and is computed by inverting p-values from score tests. It is often atrributed to Edwin Wilson.

Wald

This is the interval traditionally taught in entry level statistics courses. It uses the sample proportion to estimate the standard error and uses normal theory to determine how many standard deviations to add and/or substract from the sample proportion to determine an interval.

Agresti-Coull

This is the Wald method after setting \(n' = n + z^2\) and \(p'= (x + z^2/2) / n\)' and using \(x' = n' p'\) and \(n'\) in place of \(x\) and \(n\).

Plus4

This is Wald after adding in two artifical success and two artificial failures. It is nearly the same as the Agresti-Coull method when the confidence level is 95 \(z^2\) is approximately 4 and \(z^2/2\) is approximately 2.

See Also

mosaic::prop.test(), stats::binom.test()

Examples

# NOT RUN {
# Several ways to get a confidence interval for the proportion of Old Faithful
# eruptions lasting more than 3 minutes.
data(faithful)
binom.test(faithful$eruptions > 3)
binom.test(97, 272)
binom.test(c(97, 272-97))
faithful$long <- faithful$eruptions > 3
binom.test(faithful$long)
binom.test(resample(1:4, 400), p=.25)
binom.test(~ long, data = faithful)
binom.test(~ long, data = faithful, ci.method = "Wald")
binom.test(~ long, data = faithful, ci.method = "Plus4")
with(faithful, binom.test(~long))
with(faithful, binom.test(long))

# }