To be more specific, this replicates the computations that t.test is
doing (stripped of all the different cases that stats:::t.test.default
handles)
z <- err1-err2
se <- sqrt(var(z)/length(z))
mz <- mean(z)
tstat <- mz/se
2*pt(tstat, df= length(z)-1, lower.tail = FALSE)
On 2024-09-16 10:54 a.m., Michael Dewey wrote:
Dear Toby
I see no problem there. If you compute the mean and variance of err1 -
err2 which is what the paired test is working on then that might help to
see what is going on.
Michael
On 16/09/2024 15:47, Toby Hocking wrote:
Hi! I expected that t.test should report a very large p-value (close
to 1), even when using paired=TRUE, for the data below (which are very
similar). However, I observe p-value = 0.02503 which indicates a
significant difference, even though there is none. Can this be fixed
please? This is with R-4.4.1. For reference below I use paired=FALSE
with the same data, and I get p-value = 1 as expected.
err1 = c(-1.6076199373862132, -1.658521185520103,
-1.6549424312339873, -1.5887767975086149, -1.634129577540383,
-1.7442711937982249)
err2 = c(-1.6076199373862132, -1.6585211855201032,
-1.6549424312339875, -1.5887767975086149, -1.6341295775403832,
-1.7442711937982252)
t.test(err1,err2,paired=TRUE)
Paired t-test
data: err1 and err2
t = 3.1623, df = 5, p-value = 0.02503
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
2.769794e-17 2.683615e-16
sample estimates:
mean difference
1.480297e-16
t.test(err1,err2,paired=FALSE)
Welch Two Sample t-test
data: err1 and err2
t = 0, df = 10, p-value = 1
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.06988771 0.06988771
sample estimates:
mean of x mean of y
-1.648044 -1.648044
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Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
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