fisher.pval {corpora}

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 “central” p-value (Fay 2010) provides better numerical efficiency than the likelihood-based approach of fisher.test and is always consistent with confidence intervals.

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

Details

For alternative="two.sided" (the default), the p-value of the “central” Fisher's exact test (Fay 2010) is computed, which differs from the more common likelihood-based method implemented by fisher.test (and referred to as the “two-sided Fisher's exact test” by Fay). This approach has two advantages: (i) it is numerically robust and efficient, even for very large samples and frequency counts; (ii) it is consistent with Clopper-Pearson type confidence intervals (see examples below).

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

Value

The p-value of Fisher's exact 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). Confidence intervals that match Fisher's exact or Blaker's exact tests. Biostatistics, 11(2), 373-374.

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

## 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)         # central Fisher's exact test is equal to
fisher.test(TeaTasting)$p.value # standard two-sided Fisher's test for symmetric distribution

# inconsistency btw likelihood-based two-sided Fisher's test and confidence interval
# for 4/15 vs. 50/619 successes
fisher.test(cbind(c(4, 11), c(50, 619)))

# central Fisher's exact test is always consistent
fisher.pval(4, 15, 50, 619)