corpora (version 0.5)

fisher.pval: P-values of Fisher's exact test for frequency comparisons (corpora)

Description

This function computes the p-value of Fisher's exact test (Fisher 1934) for the comparison of corpus frequency counts (under the null hypothesis of equal population proportions). In the two-sided case, a fast approximation is used that may be inaccurate for small samples.

Usage

fisher.pval(k1, n1, k2, n2, 
            alternative = c("two.sided", "less", "greater"),
            log.p = FALSE)

Arguments

k1

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

n1

the sample size of the first corpus (or an integer vector specifying the sizes of different samples)

k2

frequency of the type in the second corpus (or an integer vector of type frequencies, in parallel to k1)

n2

the sample size of the second corpus (or an integer vector specifying the sizes of different samples, in parallel to n1)

alternative

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

log.p

if TRUE, the natural logarithm of the p-value is returned

Value

The p-value of Fisher's exact test applied to the given data (or a vector of p-values).

Details

When alternative is two.sided, a fast approximation of the two-sided p-value is used (multiplying the appropriate single-sided tail probability by two), which may be inaccurate for small samples. Unlike the exact algorithm of fisher.test, this implementation is memory-efficient and can be applied to large samples and/or large frequency counts.

For one-sided tests, the p-values returned by this functions are identical to those computed by fisher.test on two-by-two contingency tables.

References

Fisher, R. A. (1934). Statistical Methods for Research Workers. Oliver & Boyd, Edinburgh, 2nd edition (1st edition 1925, 14th edition 1970).

See Also

fisher.test, chisq.pval

Examples

# NOT RUN {
  ## Fisher's Tea Drinker (see ?fisher.test)
  TeaTasting <-
  matrix(c(3, 1, 1, 3),
         nrow = 2,
         dimnames = list(Guess = c("Milk", "Tea"),
                         Truth = c("Milk", "Tea")))
  print(TeaTasting)
  ##  - the "corpora" consist of 4 cups of tea each (n1 = n2 = 4)
  ##     => columns of TeaTasting
  ##  - frequency counts are the number of cups selected by drinker (k1 = 3, k2 = 1)
  ##     => first row of TeaTasting
  ##  - null hypothesis of equal type probability = drinker makes random guesses
  fisher.pval(3, 4, 1, 4, alternative="greater")
  fisher.test(TeaTasting, alternative="greater")$p.value # should be the same
  
  fisher.pval(3, 4, 1, 4) # uses fast approximation suitable for small p-values
  fisher.test(TeaTasting)$p.value # approximation is exact for symmetric distribution

# }