Re: [Phys-L] pseudo-pundits +- systematic error

[Jeff Bigler <jcb@mit.edu>]

On 11/6/2012 6:23 PM, LaMontagne, Bob wrote:
> Thanks for the link to your page on probability. I have not had a chance to read it in detail, but I really like what I have seen in a casual read.
>
> I have always been frustrated and annoyed at cook book experiments that try to force you to estimate an uncertainty distribution when it doesn't exist. If you have an object (perhaps a brass cylinder) that is manufactured to 3 inches in length (to a 10 thousandth of an inch) and you have a class perform a set of measurements of its length using ordinary rulers - they are going to come up with 3 inches every single time. The fact that the smallest division of the ruler is 1/16 inch, your eye tells you that it is incredibly close to being 3 inches and everyone will report it as such. Just as picking red and blue marbles from a jar has no inherent uncertainty distribution (an individual marble is either red or blue), the length of the cylinder in this case is 3 inches for anyone who uses a simple ruler to measure it.
>
> Even something variable like the length of a set of wooden match does not produce a distribution when an individual match is measured. An individual match measured with a digital vernier caliper will have a length of, say, 57.6 mm. Everyone in the room who measures the length of that match with care should end up with 57.6 mm. The distribution is with the ensemble of matches - not the individual ones.

I stumbled upon an unexpected distribution when I had my students
measure the corridor outside of my room.  The surface is a
pebble-and-epoxy floor made of large tiles with regularly spaced
expansion joints.  I decided that my students should decide how
precisely they could measure the tiles with a meter stick, and see how
the uncertainty propagated when they used their average measurement for
one tile to estimate the length, width, and area of the hallway.

I measured one tile to get a sense of what kinds of numbers I should
expect them to get.  It was very close to exactly 75 cm, so I decided
that each tile was probably manufactured to be exactly 75 cm (or as
nearly exact as manufacturing tolerances allow), and used that number
for my calculations.

When my students obtained their data by measuring multiple tiles, it
turned out that the dimensions of the tiles varied by about +/- 2 cm.
Evidently, the expansion joints were measured and hand cut after the
floor was laid, and I happened to choose one that was exactly a
convenient round number.

Because it turned out that we had a distribution of tiles centered
around 75.5 cm, the length of the corridor outside my room as measured
with the tiles came out to approximately 36 m +/- 1 m.

-- 
Jeff Bigler
Lynn English HS; Lynn, MA, USA
"Magic" is what we call Science before we understand it.