[R] t-test bootstrap versus permutation question

[Philippe Grosjean]

Hi,

I have a little problem that puzzles me about contradictory results returned
by a bootstraped t-test (as in MASS 3rd ed p. 146) versus a permutation
t-test (as in MASS 3rd ed, p 147).

Data are measurements done on 100 cells in 9 slides of fish blood. With one
method, cells are randomly sampled, and with the other method, the operator
selects cells arbitrarily (in a way it is done usually with this test). We
want to determine wheither the methods yield same results or not. Since we
are interested by the mean measurement for 100 cells, we take the average
for each slide and each method. We compare then the nine paired samples
(that is, for the nine slides) with a paired t-test. However, since we
cannot make the hypothesis that both distributions are normal, we prefer to
use a bootstraped test.

We do:
(1) 1000 simple bootstraps with:
boot(B-A, function(x,i), mean(x[i]), R=1000)
and then:
boot.ci(...)
and check wheter the CI includes 0 (no significant difference between
methods) or not.

(2) a permutation test with the perm.t.test() function of MASS p. 147
and calculate a bootstraped p-value corresponding to the fraction of values
larger or equal to the observed one. If this p-value is > 5%, we consider
there is no significant difference between both methods.

Is this correct?

The problem is that, in our particular case, both test give opposite
results: the bootstrap test indicates significant differences at 5%, while
the permutation test gives p-value = 0.35-0.45, thus no differences between
methods. I think I probably miss something here! Does somebody could help
me?

Best,

Philippe Grosjean

...........]<(({°<...............<°}))><...............................
( ( ( ( (
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( ( ( ( (      "I'm 100% confident that p is between 0 and 1"
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