[R] A very small p-value

[Ivan Krylov]

В Sat, 25 Oct 2025 11:45:42 +0200
Christophe Dutang <dutangc using gmail.com> пишет:

> Indeed, the p-value is lower than the epsilon machine
> 
> > pt(t_score, df = n-2, lower=FALSE) < .Machine$double.eps  
> [1] TRUE

Which means that for lower=TRUE, there will not be enough digits in R's
numeric() type to represent the 5*10^-19 subtracted from 1 and
approximately 16 zeroes.

Instead, you can verify your answer by asking for the logarithm of the
number that is too close to 1, thus retaining more significant digits:

print(
 -expm1(pt(t_score, df = n-2, lower=TRUE, log.p = TRUE)),
 digits=16
)
# [1] 2.539746620181249e-19
print(pt(t_score, df = n-2, lower=FALSE), digits=16)
# [1] 2.539746620181248e-19

expm1(.) computes exp(.)-1 while retaining precision for numbers that
are too close to 0, for which exp() would otherwise return 1.

See the links in
https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f
for a more detailed explanation.

-- 
Best regards,
Ivan
(flipping the "days since referring to R FAQ 7.31" sign back to 0)