Jonckheere Terpstra Test asymptotic p value seems to be inconsistent with cor.test(x, g, method="k")

[lijuanyan122]

When we have data with ties, the DescTools::JonckheereTerpstraTest() does not provide the same asymptotic p value as described in the documentation using cor.test(x, g, method="k"). Please see the code below.

https://gist.github.com/lijuanyan122/f0e3a8a520f47b238b44f30fa79d4b2c

[AndriSignorell]

I can't see from your example

# For data with ties
x <- rep(1:4, 4)
g <- c(rep(57, 15), 59)
# The below p values based on normal approximation produced are different
DescTools::JonckheereTerpstraTest(x, g, exact=FALSE)
cor.test(x, g, method="kendall")

why the two functions should yield the same p-value. Are you aware that x is a numeric variable and g a grouping factor for JonckheereTerpstraTest and cor.test expects two variables x, y? Can you explain what you would expect? Thanks

[lijuanyan122]

First of all, thanks for responding to my question and sorry it took long to reply. I edited the code, so to better describe my question: https://gist.github.com/lijuanyan122/f0e3a8a520f47b238b44f30fa79d4b2c

In the documentation of DescTools::JonckheereTerpstraTest(), it is written that "the asymptotic version is equivalent to cor.test(x, g, method="k")." Therefore, I would expect that the p values produced by cor.test() and DescTools::JonckheereTerpstraTest() for the asymptotic version are the same. As expected, the JT test from another R package PMCMRplus::jonckheereTest() actually gives exactly the same result as cor.test(), no matter if the "g" is a grouping factor or integer --> I also checked the results with one standard software used for the statistical analysis of ecotoxicological data (ToxRat: https://www.toxrat.com/Home_en.html) and it gives the same p value as PMCMRplus::jonckheereTest().

So the discrepancies of results lie in the fact that "g" is treated as a factor all the time for DescTools::JonckheereTerpstraTest(), whereas it is treated as integer in PMCMRplus::jonckheereTest(), cor.test() and ToxRat??