[Rd] Feature request: Fisher's 2x2, binomial (, others?) exact test efficiency improvements

[Chris Chang]

After looking at src/library/stats/R/fisher.test.R, I realize that my
initial guess at why one-sided fisher.test() is slow was incorrect:
phyper() is actually used for the one-sided p-value, it's the logdc
calculation over the entire distribution support (which is unconditionally
needed by the later mle(x) call) that's currently most responsible for the
slowdown.  Sorry about the misdiagnosis.

I will revise my feature request to "have an easily-discoverable fast
p-value-only calculation" for those who aren't using the odds ratio or
confidence interval.

On Sat, May 16, 2026 at 10:54 AM Chris Chang <chrchang using alumni.caltech.edu>
wrote:

> Recent R versions come with accurate and efficient implementations of the
> {d,p,q}hyper() and {d,p,q}binom() functions, which can even handle
> probabilities smaller than DBL_MIN properly.
>
> However, the equivalent Fisher's 2x2 one-sided test is inefficient:
>
>
> > install.packages("microbenchmark")
> trying URL '
> https://cran.rstudio.com/bin/macosx/big-sur-arm64/contrib/4.5/microbenchmark_1.5.0.tgz
> '
> Content type 'application/x-gzip' length 73120 bytes (71 KB)
> ==================================================
> downloaded 71 KB
>
>
> The downloaded binary packages are in
>
> /var/folders/hw/lw9w89gj5jncz6_gcyh0kj1m0000gn/T//RtmprzZbVW/downloaded_packages
> > microbenchmark::microbenchmark(phyper_result <- phyper(1000000, 4000000,
> 7900000, 3000000))
> Unit: microseconds
>                                                   expr   min    lq    mean
> median
>  phyper_result <- phyper(1e+06, 4e+06, 7900000, 3e+06) 2.706 2.706 2.86508
>  2.747
>     uq    max neval
>  2.747 13.161   100
> Warning message:
> In microbenchmark::microbenchmark(phyper_result <- phyper(1e+06,  :
>   less accurate nanosecond times to avoid potential integer overflows
>
> > phyper_result
> [1] 7.446407e-33
> > microbenchmark::microbenchmark(fisher_result <-
> fisher.test(matrix(c(1000000, 2000000, 3000000, 5900000), nr=2),
> alternative="less"))
> Unit: milliseconds
>
> expr
>  fisher_result <- fisher.test(matrix(c(1e+06, 2e+06, 3e+06, 5900000),
>  nr = 2), alternative = "less")
>       min       lq     mean   median      uq      max neval
>  803.6944 810.1379 831.0808 836.1659 845.203 889.8512   100
> > fisher_result
>
> Fisher's Exact Test for Count Data
>
> data:  matrix(c(1e+06, 2e+06, 3e+06, 5900000), nr = 2)
> p-value < 2.2e-16
> alternative hypothesis: true odds ratio is less than 1
> 95 percent confidence interval:
>  0.0000000 0.9856339
> sample estimates:
> odds ratio
>  0.9833322
>
> > fisher_result$p.value
> [1] 7.446407e-33
>
>
> (Yes, fisher.test() is returning some additional values, but that isn't
> the bottleneck.)
>
> The one-sided binom.test() does not have this kind of performance problem,
> but the two-sided test (which can be written in a manner similar to
> qbinom(): instead of searching for minimal k satisfying pbinom(k, ...) >=
> p, search for the innermost opposite-tail k satisfying dbinom(k) <=
> dbinom(x)) does.
>
> I can submit a patch with efficient two-sided binomial and Fisher's 2x2
> exact test implementations if there is interest.
>
> --Chris
>

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