binom.pval {corpora}

P-values of the binomial test for frequency counts (corpora)

Description

This function computes the p-value of a binomial test for frequency counts. In the two-sided case, a “central” p-value (Fay 2010) provides better numerical efficiency than the likelihood-based approach of binom.test and is always consistent with confidence intervals.

Usage

binom.pval(k, n, p = 0.5,
           alternative = c("two.sided", "less", "greater"))

Arguments

k

frequency of a type in the corpus (or an integer vector of frequencies)

n

number of tokens in the corpus, i.e. sample size (or an integer vector specifying the sizes of different samples)

p

null hypothesis, giving the assumed proportion of this type in the population (or a vector of proportions for different types and/or different populations)

alternative

a character string specifying the alternative hypothesis; must be one of two.sided (default), less or greater

Details

For alternative="two.sided" (the default), a “central” p-value is computed (Fay 2010: 53f), which differs from the likelihood-based two-sided p-value determined by binom.test (the “minlike” method in Fay's terminology). This approach has two advantages: (i) it is numerically robust and efficient, even for very large samples and frequency counts; (ii) it is always consistent with Clopper-Pearson confidence intervals (see examples below).

Value

The p-value of a binomial test applied to the given data (or a vector of p-values).

Author(s)

Stephanie Evert (https://purl.org/stephanie.evert)

References

Fay, Michael P. (2010). Two-sided exact tests and matching confidence intervals for discrete data. The R Journal, 2(1), 53-58.

See Also

z.score.pval, prop.cint

Examples

# inconsistency btw likelihood-based two-sided binomial test and confidence interval
binom.test(2, 10, p=0.555)

# central two-sided test as implemented by binom.pval is always consistent
binom.pval(2, 10, p=0.555)
prop.cint(2, 10, method="binomial")