Rich, I had a thought or two about this problem, or more precisely about
one that may be something like it. Don't know if Selim's problem is
anything like this, but ...
When I was in the U.S. Army many years ago, one of the bits of
military hardware we learned to play with in basic training was hand
grenades. Now the thing about a hand grenade was, once it had left your
hand it was not only armed, the fuse was burning, and it was going to
explode (with probability 1 (!)) in a rather short time. If the person
at whom one had thrown the thing had really good reflexes, (s)he (but it
was only "he" in those days...) might pick it up and throw it back.
>From the point of view of the originating thrower, this was not a nice
prospect. One was therefore taught to hold the grenade for a few seconds
AFTER the firing pin was released, so there wouldn't be time for the
competition to heave it back. BUT one thereby ran some risk of having
the grenade blow up in one's hand. This was not a nice prospect, either.
Military specifications for the manufacture of hand grenades
therefore specified not only the mean fuse time, but also limited the
variability of that mean time (essentially by requiring the standard
deviation, what Selim calls RMS, to be less than a specified value).
A manufacturer would therefore need to measure and control the RMS, which
would mean knowing (or assuming) something about the sampling
distribution of RMS (or of MS, or of SS) to generate proper control
charts and the like. (Of course, once one had mastered the control of
the variability of the fuse time, controlling the mean fuse time was a
piece of cake.) I forget where I first encountered the statistical
aspect of this problem -- I think it was an a text I was teaching from
some years ago -- but having had hand grenades "in hand", so to speak,
sort of gave the example an immediacy and color that I think was not much
shared among my colleagues -- or students!
-- Don.
On Thu, 27 Apr 2000, Rich Ulrich wrote:
> From your description, there is no reason to think that there has to
> be any "error" at all.
>
> You have a set of measures. The are somewhat spread, for real,
> physical reasons. The dispersion looks like gaussian, but it would
> not have to be that shape. (How were the points selected? Why were
> they selected?) If you want to describe the spread of that set of
> measures by the RMS, you may do so -- though it might be more useful,
> it seems to me, to describe the extremes and the conditions that
> produced them.
>
> Why do you think there may be error in the measurements, and how would
> you detect it if there were?
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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