kendall tau correlation test for ties: Potential error (PR#8076)
dkoschuetzki at gmx.de writes:
} else {
STATISTIC <- c(z = r / sqrt((4 * n + 10) / (9 * n*(n-1))))
p <- pnorm(STATISTIC)
if(exact && TIES)
warning("Cannot compute exact p-value with ties")
}
}
} else {
// OMITTED
}
}
if(is.null(PVAL)) # for "pearson" only, currently
PVAL <- switch(alternative,
"less" = p,
"greater" = 1 - p,
"two.sided" = 2 * min(p, 1 - p))
...
Please look at the computation of the p-value for Kendalls tau. There is an assignment to "p" right above the warning. In the bottom of the function there is a comment that for the pearson case we have to use the modification and set PVAL. The problem is: * Either the comment is wrong because the modification should be done with kendall too, or * The variable PVAL has to be assigned in the kendall block. I hope this is clear so far.
I think it is the comment that is wrong. The calculation of opposite-side one-sided and two-sided alternatives make OK sense when the normal approximation of the test statistic is being used. It's when you use a discrete distribution that you need to be careful. (As brought up recently, the normal approximation itself is not too hot in the tied case, but that's another matter.)
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