Thank you for responding, and so quickly at that.
Yes, I do understand that this is a floating point issue.
However, since wilcox.test() works on ranks this might be a bit
dangerous in my opinion. Maybe more so than for magnitude based tests.
Any small precision error will be ranked and it becomes a matter of
errors being systematically >0 or <0 in one group.
Here is one example that I do not like:
x <- seq(0.9, 0.2, -0.1)
y <- seq(0.8, 0.1, -0.1)
wilcox.test(x, y, paired=TRUE, mu=0.1)
Wilcoxon signed rank test with continuity correction
data: x and y
V = 0, p-value = 0.01471
alternative hypothesis: true location shift is not equal to 0.1
# ... Warning, due to some precision deviations being duplicated ...
x-y
[1] 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
sign(x-y - 0.1)
[1] -1 -1 -1 -1 -1 -1 -1 0
t.test() uses .Machine$double.eps with stderr and avoids this issue:
t.test(x, y, paired=TRUE, mu=0.1)
Error in t.test.default(x, y, paired = TRUE, mu = 0.1) :
data are essentially constant
On 2019-12-07 14:41, Ben Bolker wrote:
Your second issue seems like a more or less unavoidable floating-point
computation issue. The paired test operates by computing differences
between corresponding values of x and y.
It's not impossible to try to detect "almost-ties" (by testing for
differences less than, say, sqrt(.Machine$double.eps)), but it's
delicate and somewhat subjective/problem-dependent.
Example:
options(digits=20)
unique(c(4,3,2)-c(3,2,1))
[1] 1
unique(c(0.4,0.3,0.2)-c(0.3,0.2,0.1))
[1] 0.100000000000000033307 0.099999999999999977796 0.100000000000000005551
On 2019-12-07 1:55 p.m., Karolis Koncevičius wrote:
Hello,
Writing to share some things I've found about wilcox.test() that seem a
a bit inconsistent.
1. Inf values are not removed if paired=TRUE
# returns different results (Inf is removed):
wilcox.test(c(1,2,3,4), c(0,9,8,7))
wilcox.test(c(1,2,3,4), c(0,9,8,Inf))
# returns the same result (Inf is left as value with highest rank):
wilcox.test(c(1,2,3,4), c(0,9,8,7), paired=TRUE)
wilcox.test(c(1,2,3,4), c(0,9,8,Inf), paired=TRUE)
2. tolerance issues with paired=TRUE.
wilcox.test(c(4, 3, 2), c(3, 2, 1), paired=TRUE)
# ...
# Warning: cannot compute exact p-value with ties
wilcox.test(c(0.4,0.3,0.2), c(0.3,0.2,0.1), paired=TRUE)
# ...
# no warning
3. Always 'x observations are missing' when paired=TRUE
wilcox.test(c(1,2), c(NA_integer_,NA_integer_), paired=TRUE)
# ...
# Error: not enough (finite) 'x' observations
4. No indication if normal approximation was used:
# different numbers, but same "method" name
wilcox.test(rnorm(10), exact=FALSE, correct=FALSE)
wilcox.test(rnorm(10), exact=TRUE, correct=FALSE)
From all of these I am pretty sure the 1st one is likely unintended,
so attaching a small patch to adjust it. Can also try patching others if
consensus is reached that the behavioiur has to be modified.
Kind regards,
Karolis Koncevičius.
---
Index: wilcox.test.R
===================================================================
--- wilcox.test.R (revision 77540)
+++ wilcox.test.R (working copy)
@@ -42,7 +42,7 @@
if(paired) {
if(length(x) != length(y))
stop("'x' and 'y' must have the same length")
- OK <- complete.cases(x, y)
+ OK <- is.finite(x) & is.finite(y)
x <- x[OK] - y[OK]
y <- NULL
}
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