[tgv]

You're right about the paired test (although I think there's an issue with the group variance). But your final calculation is for a sign test. For a t-test where every point shifts a very little bit (e.g. 0.01 stddev), p is larger, I think.

[hervature]

Yes, my edit was more meant to illustrate how 6 data points can yield a significant result. Paired t-test is all about the differences. So if all test subjects shift up by 0.01 (no variance in the differences) then the statistic will actually be infinite (i.e. very large) and so p is theoretically 0 (very small). I also agree that the paired testing needs more convincing from the researchers.