Student's t is a more advanced thing. Basically it widens the error
bars if the sample is small because the uncertainty is uncertain. It
takes the uncertainty of the uncertainty into account by assuming the
worst case.

Thanks for all the replies on error and student-t. As it is I stopped
by to bother a couple of professors on this and they explained it to
me. They even derived it. (It comes from a combination of the
chi-squared distribution of the population deviation and the
normalized Gaussian. Which I repeat to show off.) Some said the idea
that it takes into acount "the uncretainty of the uncertainty" isn't
kind of right, others said it is kind of right. But what was
interesting though, is that my attempt to play the trick, what about
the uncertainty of that uncertainty, didn't work. The reason, they
pointed out, is that Student-t is parameter free. The only parameter
that goes into it is N, the number of samples. Thus to continue my
crusade at the foolishness of the whole thing, I'd have to devote my
efforts to the uncertainty in N, a crusade I think I will most
certainly loose. Thus the "uncertainty of the uncertainty of the
uncertainty... etc." appears at the moment to me to end at student-t.
(At least for a Gaussian, which is still at least fine for me to think
about.) But I'm still not completely convinced, although I am more
so, and still am trying to find tricks to prove the foolishness of the
whole thing. (One thing is okay, student-t gives a precise, well
defined uncertainty [for a Gaussian], but what about the uncertainty
of the "measurements" of that Gaussian? I don't know.)


And yet you specify 90% of something, what happens if I change it to
90.0000001%?

It makes the interval a tiny bit wider.

Damn ! My attempts at slightly perturbing the beliefs of others, in
an attempt at rougishness, COMPLETELY fell on its face this time.
(And you were the rogue.) And I have been so successfull elsewhere at
this .

ps: I wrote an earlier message (a number of days ago) that looks like
it didn't go through. I am actually very glad of this and approve the
discretion of the moderators, as it was a load of cr*p.