Re: Accuracy / precision / resolution / etc.

[John Denker <jsd@MONMOUTH.COM>]

Hi --

I reallly like the story that Lois Breur Krause wrote at 08:29 AM 9/1/99 -0400:
> I teach precision vs. accuracy with a set of 4 targets; real targets (50
> yard type) with real .38 holes in them.  I tell a story that I had a new
> .38 cal. revolver, and needed to give it a try.....
...
> I see the need to make things concrete and memorable for most of my
> students, and since this is one of the first topics of the semester, I also
> use it to impress my students. ;-)

It sure impressed me!

-------

I was thinking this setup has other applications, such as shedding some
light on the "resolution" issue.

When somebody says "precision of measurement" it begs the question,
"precision of WHAT measurement".

You could use a caliper to measure the position of a particular bullet hole
within a tiny fraction of a millimeter.  That provides lots of resolution,
and lots of precision on the measurement of THAT bullet-hole.  But the
question of the precision of the gun is another question entirely.  So in
this case the resolution of the raw measurement exceeds the precision of
what we are trying to measure.

 -- There is no harm in excess resolution, beyond the cost of obtaining it.
 -- On the other side of the coin, if the resolution is too low, bad things
happen to the precision and the accuracy.   For any of Lois's four targets,
we know that 6.00000000 bullets hit the target *somewhere*.  The problem is
that "somewhere" does not have enough resolution to be useful.

I like to think of everything as a probability distribution.  The
resolution is, roughly speaking, the bin-size of the histogram that is
being used to describe the distribution.

You want to have enough resolution so that you are limited by the real
physics (ballistics in this case) and not artificially limited by the
instrumental resolution.

============

Tangentially related point:

At some point the terminology (and indeed the entire conceptual basis)
breaks down.  We are trying to describe a probability distribution.  For
simple distributions, a few words suffice to describe it.  But there are
lots of non-simple distributions in the world, and at some point we have to
face that fact head-on.

Lois's third target (two holes there, two holes here, and two holes
somewhere else) is a fine example of a distribution where we cannot
describe it in terms of a mean and standard deviation, and we shouldn't
even try.

============

An even more tangentially related point, which students often miss:

The precision of a number is not a property of the number itself.  Case in
point:
  a) the mass of the sun is known to about one percent.
  b) Newton's gravitational constant is known to a little better than a
tenth of a percent.
  c) The product of these two quantities is known to about one part in ten
to the eighth.  There's no way you could have known that from the numbers
themselves.  You have to understand the physics.

Reference:
  http://ssd.jpl.nasa.gov/astro_constants.html

Cheers --- jsd