Re: ATM mirror mirror on the wall part 2

["Albert Highe" <ahighe@ix.netcom.com>]

>
> Albert's statistical analysis of sample size is correct, of course.
> But, if we can 'forget' our measurements after making them, we can each
> test each mirror 30 times.

This is possible, with some risk, and not a lot of benefit.  The intent of
doing thirty random (different) samples is to capture all the possible
sources of variation and have them contribute in a random, rather than
systematic way. Making thirty measurements on the same mirror is unlikely to
capture all the sources of variation and, therefore, present a smaller
variation than reality. It is likely that a person will leave the tester and
mirror in the same position and then repeat thirty times. This does not
capture sources of variation such as setting up the tester, mirror
orientation, temperature of the room, or whatever other variables we can or
can't imagine but contribute to variation in the results. If one is going to
make multiple tests, there is a lot more value doing it on different
mirrors.

If thirty people test (one or) two mirrors you will be able to say, with 95%
confidence, what the expected variation is in Foucault testing for mirrors
of that size and f/#. This will say little about the variation an individual
can expect from his or her setup. It will say little about the variation one
could expect in other size mirrors or mirrors with different focal ratios.

Also, getting interferometric testing done on the two mirrors won't add
much, so I wouldn't recommend doing it. We don't know the confidence limit
for interferometric testing. If we could get that data, it would be great.
Comparing one's individual results to interferometric testing is
statistically meaningless. Comparing the interferometric results to the
distribution of all the results will only allow us to conclude, at best,
that its variation isn't inconsistent with the Foucault measurements. Not a
strong result.

>
> I think this mirror round robin is of statistical validity because we
> will have 30 people testing, as an aggregate sample of amateur mirror
> testers.

Yes, it is statistically significant for one result - the distribution of
the variation in those two mirrors for the group as a whole.

I was hoping for more. For example, what is the sensitivity experienced
ATMer's achieve with their Foucault setups with mirrors of X diameter and Y
f/#?  If the test result turns out to be a large number (e.g. a variation of
+_ 50%), I think people will be disappointed. A variation of +_50% means the
group as a whole can't distinguish between a 1/6 wave, 1/4 wave, or 1/12
wave. I would expect (and hope) some individuals and their equipment could
do a lot better. That would tell me the capability of the test when done
correctly. It would tell me whose example I should follow.

Conversely, if the variation of the group as a whole is small (e.g. a
variation of +_10%), the result is great. That says that just about everyone
is able to distinguish variations as small as approximately 1/10th wave.
However, a few individuals could have much worse results on their particular
equipment. We wouldn't know who.

Looking forward to the results,
Albert